DSP

Blockset
®
For Use with Simulink

Modeling

Simulation

Implementation

User’s Guide
Version 4
How to Contact The MathWorks:

www.mathworks.com Web
comp.soft-sys.matlab Newsgroup

support@mathworks.com Technical support

suggest@mathworks.com Product enhancement suggestions
bugs@mathworks.com Bug reports
doc@mathworks.com Documentation error reports
service@mathworks.com Order status, license renewals, passcodes
info@mathworks.com Sales, pricing, and general information

508-647-7000 Phone

508-647-7001 Fax

The MathWorks, Inc. Mail

3 Apple Hill Drive
Natick, MA 01760-2098

For contact information about worldwide offices, see the MathWorks Web site.

DSP Blockset User’s Guide

 COPYRIGHT 1995 - 2001 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by
or for the federal government of the United States. By accepting delivery of the Program, the government
hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR
Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part
252.227-7014. The terms and conditions of The MathWorks, Inc. Software License Agreement shall pertain
to the government’s use and disclosure of the Program and Documentation, and shall supersede any
conflicting contractual terms or conditions. If this license fails to meet the government’s minimum needs or
is inconsistent in any respect with federal procurement law, the government agrees to return the Program
and Documentation, unused, to MathWorks.
MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and
Target Language Compiler is a trademark of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: April 1995 First printing DSP Blockset 1.0
May 1997 Second printing DSP Blockset 2.0
January 1998 Third printing DSP Blockset 2.2 (Release 10)
January 1999 Fourth printing DSP Blockset 3.0 (Release 11)
November 2000 Fifth printing DSP Blockset 4.0 (Release 12)
June 2001 (Online only) DSP Blockset 4.1 (Release 12.1)
 Contents
Introduction
1
Welcome to the DSP Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

What Is the DSP Blockset? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

Key Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

What Is in the DSP Blockset? . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7

Getting Started with the DSP Blockset . . . . . . . . . . . . . . . . . 1-8

How to Get Help Online . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
How to Use This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9
Technical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12

R12 Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13

Simulink and the DSP Blockset

2
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

The Simulink Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

Starting Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Getting Started with Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Learning More About Simulink . . . . . . . . . . . . . . . . . . . . . . . . 2-10

Configuring Simulink for DSP Systems . . . . . . . . . . . . . . . . 2-11

Using dspstartup.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Customizing dspstartup.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Performance-Related Settings . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
Miscellaneous Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15

i
 Working with Signals
3
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2

Signal Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3

Discrete-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
Continuous-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Multichannel Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11
Benefits of Frame-Based Processing . . . . . . . . . . . . . . . . . . . . . 3-14

Sample Rates and Frame Rates . . . . . . . . . . . . . . . . . . . . . . . . 3-16

Sample Rate and Frame Rate Concepts . . . . . . . . . . . . . . . . . . 3-16
Inspecting Sample Rates and Frame Rates . . . . . . . . . . . . . . . 3-17
Converting Sample Rates and Frame Rates . . . . . . . . . . . . . . 3-20
Changing Frame Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31

Creating Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33

Creating Signals Using Constant Blocks . . . . . . . . . . . . . . . . . 3-33
Creating Signals Using Signal Generator Blocks . . . . . . . . . . 3-36
Creating Signals Using the Signal From Workspace Block . . 3-38

Constructing Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42

Constructing Multichannel Sample-Based Signals . . . . . . . . . 3-42
Constructing Multichannel Frame-Based Signals . . . . . . . . . . 3-45

Deconstructing Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-54

Deconstructing Multichannel Sample-Based Signals . . . . . . . 3-54
Deconstructing Multichannel Frame-Based Signals . . . . . . . . 3-57

Importing Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-62

Importing a Multichannel Sample-Based Signal . . . . . . . . . . . 3-62
Importing a Multichannel Frame-Based Signal . . . . . . . . . . . 3-68
Importing WAV Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-71

Exporting Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-72

Exporting Multichannel Signals . . . . . . . . . . . . . . . . . . . . . . . . 3-72
Exporting and Playing WAV Files . . . . . . . . . . . . . . . . . . . . . . 3-79

Viewing Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-80

ii Contents
 Displaying Signals in the Time-Domain . . . . . . . . . . . . . . . . . . 3-80
Displaying Signals in the Frequency-Domain . . . . . . . . . . . . . 3-82
Displaying Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-83

Delay and Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-85

Computational Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-85
Algorithmic Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-86

DSP Operations
4
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
Filter Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
Multirate Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10
Using the FFT and IFFT Blocks . . . . . . . . . . . . . . . . . . . . . . . . 4-10

Power Spectrum Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16

Solving Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16
Factoring Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17
Inverting Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19

Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21
Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21
Running Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23

DSP Blockset Demos Overview . . . . . . . . . . . . . . . . . . . . . . . . 4-24

Adaptive Processing Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Audio Processing Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Communications Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25
Filtering Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25

iii
 Queues Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
Sigma-Delta A/D Conversion Demo . . . . . . . . . . . . . . . . . . . . . 4-26
Sine Wave Generation Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
Spectral Analysis Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
Statistical Functions Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
Wavelets Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26

DSP Block Reference

5
Features of the Online DSP Block Reference . . . . . . . . . . . . 5-2
Main Sections of a Block Reference Page . . . . . . . . . . . . . . . . . . 5-2
Ways to Access Online DSP Block Reference Pages . . . . . . . . . 5-4
Running Example Code in the MATLAB Help browser . . . . . . 5-4
Running Example Models in the MATLAB Help browser . . . . . 5-4

Blocks Supporting Code Generation . . . . . . . . . . . . . . . . . . . 5-6

Block Library List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9

Block Library Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Block Library Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Analog Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
Analytic Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-22
Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-24
Autocorrelation LPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-26
Backward Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-30
Biquadratic Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-32
Buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-36
Burg AR Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-43
Burg Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-45
Check Signal Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-49
Chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-56
Cholesky Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-73
Cholesky Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-75
Cholesky Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-77
Complex Cepstrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-79
Complex Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-81

iv Contents
Constant Diagonal Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-82
Constant Ramp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-84
Contiguous Copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-86
Convert 1-D to 2-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-88
Convert 2-D to 1-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-90
Convert Complex DSP To Simulink . . . . . . . . . . . . . . . . . . . . . 5-91
Convert Complex Simulink To DSP . . . . . . . . . . . . . . . . . . . . . 5-93
Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-95
Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-97
Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-99
Covariance AR Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-106
Covariance Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-108
Create Diagonal Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Cumulative Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
dB Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-113
dB Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-115
DCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-117
Delay Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-119
Detrend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-123
Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-124
Digital Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-126
Direct-Form II Transpose Filter . . . . . . . . . . . . . . . . . . . . . . . 5-129
Discrete Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-133
Downsample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-136
DSP Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-143
Dyadic Analysis Filter Bank . . . . . . . . . . . . . . . . . . . . . . . . . . 5-146
Dyadic Synthesis Filter Bank . . . . . . . . . . . . . . . . . . . . . . . . . 5-154
Edge Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-161
Event-Count Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-163
Extract Diagonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-165
Extract Triangular Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-166
FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-168
Filter Realization Wizard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-178
FIR Decimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-188
FIR Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-195
FIR Rate Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-202
Flip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-206
Forward Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-208
Frame Status Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-210
From Wave Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-212

v
 From Wave File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-217
Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-219
IDCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-223
Identity Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-225
IFFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-227
Inherit Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-234
Integer Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-236
Kalman Adaptive Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-244
LDL Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-249
LDL Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-252
LDL Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-254
Least Squares Polynomial Fit . . . . . . . . . . . . . . . . . . . . . . . . . 5-256
Levinson-Durbin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-259
LMS Adaptive Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-263
LU Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-267
LU Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-269
LU Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-270
Magnitude FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-272
Matrix 1-Norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-275
Matrix Multiply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-277
Matrix Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-279
Matrix Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-281
Matrix Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-283
Matrix Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-285
Matrix Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-287
Maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-293
Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-298
Median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-302
Minimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-304
Modified Covariance AR Estimator . . . . . . . . . . . . . . . . . . . . 5-309
Modified Covariance Method . . . . . . . . . . . . . . . . . . . . . . . . . . 5-311
Multiphase Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-314
Multiport Selector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-317
N-Sample Enable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-320
N-Sample Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-322
Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-324
Overlap-Add FFT Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-326
Overlap-Save FFT Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-329
Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-332
Permute Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-334

vi Contents
Polynomial Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-338
Polynomial Stability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-340
Pseudoinverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-342
QR Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-344
QR Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-346
Queue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-348
Random Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-353
Real Cepstrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-360
Reciprocal Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-362
Repeat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-364
RLS Adaptive Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-370
RMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-374
Sample and Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-378
Short-Time FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-380
Signal From Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-383
Signal To Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-387
Sine Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-393
Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 5-400
Sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-402
Spectrum Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-404
Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-408
Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-413
Submatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-417
SVD Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-425
Time Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-427
Time-Varying Direct-Form II Transpose Filter . . . . . . . . . . . 5-428
Time-Varying Lattice Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 5-433
Toeplitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-437
To Wave Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-439
To Wave File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-444
Transpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-446
Triggered Delay Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-448
Triggered Signal From Workspace . . . . . . . . . . . . . . . . . . . . . 5-451
Triggered To Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-455
Unbuffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-458
Uniform Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-461
Uniform Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-465
Unwrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-469
Upsample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-479
Variable Fractional Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-486

vii
 Variable Integer Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-491
Variable Selector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-499
Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-502
Vector Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-506
Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-524
Wavelet Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-530
Window Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-536
Yule-Walker AR Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-541
Yule-Walker Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-544
Zero Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-547

DSP Function Reference

6
DSP Blockset Utility Functions . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
dsp_links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3
dsplib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4
dspstartup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5
liblinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7
rebuffer_delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8

viii Contents
 1

Introduction
Welcome to the DSP Blockset . . . . . . . . . . . . 1-2

What Is the DSP Blockset? . . . . . . . . . . . . . 1-3

Key Features . . . . . . . . . . . . . . . . . . . . 1-3

What Is in the DSP Blockset? . . . . . . . . . . . . 1-6

Installation . . . . . . . . . . . . . . . . . . . . . 1-7

Getting Started with the DSP Blockset . . . . . . . . 1-8

How to Get Help Online . . . . . . . . . . . . . . . . 1-8
How to Use This Guide . . . . . . . . . . . . . . . . 1-9
Technical Conventions . . . . . . . . . . . . . . . . 1-10
Typographical Conventions . . . . . . . . . . . . . . 1-12
R12 Related Products . . . . . . . . . . . . . . . . 1-13
1 Introduction

Welcome to the DSP Blockset

Welcome to the DSP Blockset, the premier tool for digital signal processing
(DSP) algorithm simulation and code generation. This section contains the
following topics, which help introduce you to the DSP Blockset:

• “What Is the DSP Blockset?”

• “What Is in the DSP Blockset?”
• “Getting Started with the DSP Blockset”
• “R12 Related Products”

The DSP Blockset brings the full power of Simulink® to DSP system design and
prototyping by providing key DSP algorithms and components in Simulink’s
adaptable block format. From buffers to linear algebra solvers, from dyadic
filter banks to parametric estimators, the blockset gives you all the core
components to rapidly and efficiently assemble complex DSP systems.
Use the DSP Blockset and Simulink to develop your DSP concepts, and to
efficiently revise and test until your design is production-ready. Use the DSP
Blockset together with the Real-Time Workshop® to automatically generate
code for real-time execution on DSP hardware.
We hope you enjoy using the DSP Blockset, and we look forward to hearing
your comments and suggestions.
support@mathworks.com Technical support
suggest@mathworks.com Product enhancement suggestions
bugs@mathworks.com Bug reports
doc@mathworks.com Documentation error reports

Visit the MathWorks Web site at www.mathworks.com for complete contact

information.

1-2
 What Is the DSP Blockset?

What Is the DSP Blockset?

The DSP Blockset is a collection of block libraries for use with the Simulink
dynamic system simulation environment.
The DSP Blockset libraries are designed specifically for digital signal
processing (DSP) applications, and include key operations such as classical,
multirate, and adaptive filtering, matrix manipulation and linear algebra,
statistics, time-frequency transforms, and more.

Key Features
The DSP Blockset extends the Simulink environment by providing core
components and algorithms for DSP systems. You can use blocks from the DSP
Blockset in the same way that you would use any other Simulink blocks,
combining them with blocks from other libraries to create sophisticated DSP
systems.
A few of the important features are described in the following sections:

• “Frame-Based Operations”
• “Matrix Support”
• “Adaptive and Multirate Filtering”
• “Statistical Operations”
• “Linear Algebra”
• “Parametric Estimation”
• “Real-Time Code Generation”

Frame-Based Operations
Most real-time DSP systems optimize throughput rates by processing data in
“batch” or “frame-based” mode, where each batch or frame is a collection of
consecutive signal samples that have been buffered into a single unit. By
propagating these multisample frames instead of the individual signal
samples, the DSP system can best take advantage of the speed of DSP
algorithm execution, while simultaneously reducing the demands placed on the
data acquisition (DAQ) hardware.
The DSP Blockset delivers this same high level of performance for both
simulation and code generation by incorporating frame-processing capability

1-3
1 Introduction

into all of its blocks. A completely frame-based model can run several times
faster than the same model processing sample-by-sample; faster still if data
sources are frame based.
See “Sample Rates and Frame Rates” on page 3-16 for more information.

Matrix Support
The DSP Blockset takes full advantage of Simulink’s matrix format. Some
typical uses of matrices in DSP simulations are:

• General two-dimensional array

A matrix can be used in its traditional mathematical capacity, as a simple
structured array of numbers. Most blocks for general matrix operations are
found in the Matrices and Linear Algebra library.
• Factored submatrices
A number of the matrix factorization blocks in the Matrix Factorizations
library store the submatrix factors (i.e., lower and upper submatrices) in a
single compound matrix. See the LDL Factorization and LU Factorization
blocks for examples.
• Multichannel frame-based signal
The standard format for multichannel frame-based data is a matrix
containing each channel’s data in a separate column. A matrix with three
columns, for example, contains three channels of data, one frame per
channel. The number of rows in such a matrix is the number of samples in
each frame.

See the following sections for more information about working with matrices:

• “Multichannel Signals” on page 3-11

• “Creating Signals” on page 3-33
• “Constructing Signals” on page 3-42
• “Importing Signals” on page 3-62

Adaptive and Multirate Filtering

The Adaptive Filters and Multirate Filters libraries provide key tools for the
construction of advanced DSP systems. Adaptive filter blocks are
parameterized to support the rapid tailoring of DSP algorithms to
application-specific environments, and effortless “what if” experimentation.

1-4
 What Is the DSP Blockset?

The multirate filtering algorithms employ polyphase implementations for

efficient simulation and real-time code execution.

Statistical Operations
Use the blocks in the Statistics library for basic statistical analysis. These
blocks calculate measures of central tendency and spread (e.g., mean, standard
deviation, and so on), as well as the frequency distribution of input values
(histograms).

Linear Algebra
The Matrices and Linear Algebra library provides a wide variety of matrix
factorization methods, and equation solvers based on these methods. The
popular Cholesky, LU, LDL, and QR factorizations are all available.

Parametric Estimation
The Parametric Estimation library provides a number of methods for modeling
a signal as the output of an AR system. The methods include the Burg AR
Estimator, Covariance AR Estimator, Modified Covariance AR Estimator, and
Yule-Walker AR Estimator, which allow you to compute the AR system
parameters based on forward error minimization, backward error
minimization, or both.

Real-Time Code Generation

You can also use the separate Real-Time Workshop product to generate
optimized, compact, C code for models containing blocks from the
DSP Blockset.

1-5
1 Introduction

What Is in the DSP Blockset?

The DSP Blockset contains a collection of blocks organized in a set of nested
libraries. The best way to explore the blockset is to expand the DSP Blockset
entry in the Simulink Library Browser. The fully expanded library list is
shown below.

See the Simulink documentation for complete information about the Library
Browser. To access the blockset through its own window (rather than through
the Library Browser), type
dsplib

in the command window. Double-click on any library in the window to display

its contents. The Demos block opens the MATLAB® Demos utility with the
DSP Blockset demos selected.

1-6
 What Is in the DSP Blockset?

Double-click on a demo in the list to open that model, and select Start from the
model window’s Simulation menu to run it.
For a complete list of all the blocks in the DSP Blockset by library, see “Block
Library Contents” on page 5-10.

Installation
The DSP Blockset follows the same installation procedure as the MATLAB
toolboxes. See the MATLAB Installation Guide for your platform.

1-7
1 Introduction

Getting Started with the DSP Blockset

To get started with the DSP Blockset, open the Simulink Library Browser by
pressing the button on the MATLAB toolbar, or by typing
simulink

at the command line. Expand the DSP Blockset library tree in the Simulink
Library Browser by clicking the symbol next to the DSP Blockset entry. You
can drag blocks directly from the Library Browser into a Simulink model.
Alternatively, you can open the DSP Blockset in its own window by typing
dsplib

at the MATLAB command line. Double-click on any library in the DSP Blockset
window to view its contents, and double-click on a block to access its parameter
dialog box.
The following sections provide additional information to help get you started
with the DSP Blockset:

• “How to Get Help Online”

• “How to Use This Guide”
• “Technical Conventions”
• “Typographical Conventions”

How to Get Help Online

There are a number of easy ways to get help on the DSP Blockset while you’re
working at the computer:

• Block Help – Press the Help button in any block dialog box to view the online
reference documentation for that block.

• Simulink Library Browser – Right-click on a block to access the help for that
block.

1-8
 Getting Started with the DSP Blockset

• Help browser – Select Full Product Family Help from the Help menu, or
type doc or helpdesk at the command line to display the Help browser. Select
DSP Blockset in the Contents pane.
• Command Line – Type doc('block name') at the command line to access the
help for a block with the name block name. Spaces and capitalization in the
block name are ignored.
• Help Desk (remote) – Use a Web browser or the Help browser to connect to
the MathWorks Web site at www.mathworks.com. Follow the Documentation
link on the Support Web page for remote access to the documentation.
• Release Information – Select Full Product Family Help from the Help
menu, or type whatsnew at the MATLAB command line and select the DSP
Blockset Release Notes from the Contents pane of the Help browser. The
Release notes contain information about new features and recent changes to
the version of the DSP Blockset that you are using. You can also type
info dspblks at the MATLAB command line to view detailed release
information related to bug fixes and enhancements.

How to Use This Guide

This guide contains tutorial sections that are designed to help you become
familiar with using Simulink and the DSP Blockset, as well as a reference
section for finding detailed information on particular blocks in the blockset:

• Read Chapter 2, “Simulink and the DSP Blockset,” to get an overview of

fundamental Simulink and DSP Blockset concepts. Also see the Simulink
documentation for more information on the Simulink environment.

• Read Chapter 3, “Working with Signals,” for details on key operations

common to many signal processing tasks.
• Read Chapter 4, “DSP Operations,” for a discussion of important block
applications.
• Read Chapter 5, “DSP Block Reference,” for a description of each block’s
operation, parameters, and characteristics.
• Read the “DSP Blockset” sections of R12.1 Release Notes and to learn about
enhancements made to the blockset in the current version.

Use this guide in conjunction with the software to learn about the powerful
features that the DSP Blockset provides.

1-9
1 Introduction

Technical Conventions
The following sections provides a brief overview of the technical conventions
used in this guide, and provides pointers to more detailed information:

• “Signal Dimension Nomenclature”

• “Frame-Based Signal Nomenclature”
• “Sampling Nomenclature”

Signal Dimension Nomenclature

The DSP Blockset fully supports Simulink’s matrix format, which is described
in “Working with Signals” in the Simulink documentation. The nomenclature
used for vectors and matrices in the DSP Blockset is described below.

Matrices. A Simulink matrix is the same as a MATLAB matrix, a

two-dimensional (2-D) array of values, organized as rows and columns. As in
MATLAB, a matrix can be indexed by one or two values. The size of a matrix is
described by the number of rows M and the number of columns N. In the DSP
Blockset, matrix size is usually denoted by the compact expression M-by-N or
M×N, and occasionally by the MATLAB notation [M N].
For instance, a 2-by-3 matrix, like matrix u below, has two rows and three
columns.

u = 1 2 3
4 5 6

This matrix can be represented in MATLAB notation as

u = [1 2 3;4 5 6] % A 2-by-3 matrix

In the online help, matrix elements are indexed using either subscript notation
or MATLAB notation. For example, u23 and u(2,3) both refer to the element
in the third column of the second row. The number of channels in a frame-based
matrix is the number of columns, N. More information about matrices can be
found in “Multichannel Signals” on page 3-11.

Vectors. Strictly speaking, a Simulink vector is a one-dimensional (1-D) array of

values, an ordered list that has no row or column orientation. For convenience,
the DSP Blockset help uses the plain term vector to refer to any of the following
three entities:

1-10
 Getting Started with the DSP Blockset

• One-dimensional array, also called a 1-D vector

• 1-by-N matrix, also called a row vector
• M-by-1 matrix, also called a column vector

The size or length of a vector, M for a column vector or N for a row vector, is the
number of elements that it contains. There is no MATLAB equivalent for a 1-D
Simulink vector (i.e., all MATLAB vectors have either a row or column
orientation), and most blocks in the DSP Blockset treat a 1-D vector as a
column vector.

Arrays. The number of pages, P, of a three-dimensional array in the MATLAB

workspace refers to the size of its third dimension
A(:,:,1) = [1 2 3;4 5 6] % The first page of a 3-page array
A(:,:,2) = [7 8 9;0 1 2] % The second page
A(:,:,3) = [3 4 5;6 7 8] % The last page

Array size is frequently denoted by the compact expression M-by-N-by-P or

M×N×P.

Frame-Based Signal Nomenclature

A frame of data is a collection of sequential samples from a single channel. In
Simulink, a length-M frame of data is represented by an M-by-1 matrix
(column vector). A multichannel signal with N channels and M samples per
frame is represented as an M-by-N matrix. See “Multichannel Signals” on
page 3-11 for more about multichannel signals.
Signals in Simulink can be either frame-based or sample-based. You can
typically specify the frame status (frame-based or sample-based) of any signal
that you generate using a source block (from the DSP Sources library). Most
other DSP blocks generally preserve the frame status of an input signal, but
some do not. See “Creating Signals” on page 3-33 for more information.

Sampling Nomenclature
Important sampling-related notational conventions are listed in “Sample Rates
and Frame Rates” on page 3-16.

1-11
1 Introduction

Typographical Conventions
This manual uses some or all of these conventions.

Item Convention to Use Example

Example code Monospace font To assign the value 5 to A,

enter
A = 5

Function names/syntax Monospace font The cos function finds the

cosine of each array element.

Syntax line example is

MLGetVar ML_var_name

Keys Boldface with an initial Press the Return key.

capital letter

Literal strings (in syntax Monospace bold for f = freqspace(n,'whole')

descriptions in Reference literals
chapters)

Mathematical Italics for variables This vector represents the

expressions polynomial
Standard text font for
functions, operators, and p = x2 + 2x + 3
constants

MATLAB output Monospace font MATLAB responds with

A =
5

Menu names, menu items, and Boldface with an initial Choose the File menu.
controls capital letter

New terms Italics An array is an ordered

collection of information.

String variables (from a finite Monospace italics sysc = d2c(sysd,’method’)

list)

1-12
 R12 Related Products

R12 Related Products

The MathWorks provides several products that are especially relevant to the
kinds of tasks you can perform with the DSP Blockset.
For more information about any of these products, see either:

• The online documentation for that product if it is installed or if you are

reading the documentation from the CD
• The MathWorks Web site, at http://www.mathworks.com; see the “products”
section

Note The toolboxes listed below all include functions that extend MATLAB’s
capabilities. The blocksets all include blocks that extend Simulink’s
capabilities. The DSP Blockset requires MATLAB, Simulink, and Signal
Processing Toolbox.

Product Description

Communications Simulink block libraries for modeling the

Blockset physical layer of communications systems

Developer’s Kit for Texas Developer’s kit that unites MATLAB,

Instruments™ DSP Simulink, and Real-Time Workshop code
generation with the Texas Instruments Code
Composer Studio™ to provide DSP software/
systems architects with suite of tools for DSP
development, from simulating signal
processing algorithms to optimizing and
running code on Texas Instruments DSPs

Filter Design Toolbox Advanced filter design and analysis methods

for real-world systems with stringent
specifications, including support for bit-true
simulation and analysis of quantized filters,
signals, and FFTs

1-13
1 Introduction

Product Description

Motorola DSP Developer's kit for co-simulating and verifying

Developer’s Kit Motorola 56300 and 56600 fixed-point DSP
code. Combines the algorithm development,
simulation, and verification capabilities of the
MathWorks system-level design tools with the
Motorola Suite 56® assembly language
development and debugging tools

Real-Time Workshop Tool that generates customizable C code from

Simulink models and automatically builds
programs that can run in real time in a variety
of environments

Signal Processing Tool for algorithm development, signal and

Toolbox linear system analysis, and time-series data
modeling

Simulink Interactive, graphical environment for

modeling, simulating, and prototyping
dynamic systems

1-14
 2
Simulink and the
DSP Blockset
Overview . . . . . . . . . . . . . . . . . . . . . 2-2

The Simulink Environment . . . . . . . . . . . . . 2-3

Starting Simulink . . . . . . . . . . . . . . . . . . 2-3
Getting Started with Simulink . . . . . . . . . . . . . 2-5
Learning More About Simulink . . . . . . . . . . . . . 2-10

Configuring Simulink for DSP Systems . . . . . . . . 2-11

Using dspstartup.m . . . . . . . . . . . . . . . . . 2-12
Customizing dspstartup.m . . . . . . . . . . . . . . . 2-12
Performance-Related Settings . . . . . . . . . . . . . 2-13

Miscellaneous Settings . . . . . . . . . . . . . . . . 2-15

2 Simulink and the DSP Blockset

Overview
This chapter will help you get started building DSP models with Simulink and
the DSP Blockset. It contains the following sections:

• “The Simulink Environment”

• “Configuring Simulink for DSP Systems”

The first section provides a brief overview of the Simulink environment. The
second section provides guidance in tailoring the environment for DSP system
simulation.

2-2
 The Simulink Environment

The Simulink Environment

Simulink is an environment for simulating dynamic systems. It provides a
modeling and simulation “foundation” on which you can build digital signal
processing applications. All of the blocks in the DSP Blockset are designed for
use together with the blocks in the Simulink libraries.
This section includes the following topics:

• “Starting Simulink”
• “Getting Started with Simulink”
• “Learning More About Simulink”

Starting Simulink
To start Simulink, click the icon in the MATLAB toolbar, or type
simulink

at the command line.

Simulink on PC Platforms
On PC platforms, the Simulink Library Browser opens when you start
Simulink. The left pane contains a list of all of the blocksets that you currently
have installed.

2-3
2 Simulink and the DSP Blockset

The first item in the list is the Simulink blockset itself, which is already
expanded to show the available Simulink libraries. Click the symbol to the
left of any blockset name to expand the hierarchical list and display that
blockset’s libraries within the browser.
See the Simulink documentation for a complete description of the Library
Browser.

Simulink on UNIX Platforms

On UNIX platforms, the Simulink window below opens when you start
Simulink. To view other installed blocksets, double-click the Blocksets &
Toolboxes button.

2-4
 The Simulink Environment

The following tutorial makes use of the Simulink Library Browser, available
only on PC platforms. If you are working on a UNIX platform, instead of
clicking the symbol in the Library Browser to open a library, simply
double-click the appropriate library in the main Simulink or DSP Blockset
windows. To open the DSP Blockset window from the MATLAB command line,
type dsplib.

The Simulink Libraries

The eight libraries in the Simulink window contain all of the basic elements
you need to construct a model. Look here for basic math operations, switches,
connectors, simulation control elements, and other items that do not have a
specific DSP orientation.
To create a new model, select New from the Simulink File menu or press
Ctrl+N. Then simply drag a block from one of the Simulink libraries into the
new model window to begin building a system.

Getting Started with Simulink

If you have never used Simulink before, take some time to get acquainted with
its features. You can begin by learning the two basic stages in model
construction, discussed in the following sections:

• “Model Definition”
• “Model Simulation”

Model Definition
Simulink is a model definition environment. You define a model by creating a
block diagram that represents the computations and data flow of your system
or application. Try building a simple model that adds two sine waves and
displays the result.

2-5
2 Simulink and the DSP Blockset

1 Type dspstartup at the MATLAB command line to configure Simulink for

DSP simulation (optional).

One of the things that dspstartup does is set the Stop time value in the
Simulation parameters dialog box to inf for all new models. The inf
setting instructs Simulink to run the model until you click the simulation
stop button. You can access this dialog box and enter a different Stop time
value by selecting Simulation parameters from the model window’s
Simulation menu.

2 Start Simulink by clicking the button in the MATLAB toolbar. The

Library Browser appears.

3 Select New > Model from the File menu in the Library Browser. A new
model window appears on your screen.

4 Add a Sine Wave block to the model.

a In the Library Browser, click the symbol next to DSP Blockset to

expand the hierarchical list of DSP libraries.
b In the expanded list, click DSP Sources to view the blocks in the DSP
Sources library.
c Drag the Sine Wave block into the new model window.

5 Add a Matrix Sum block to the model.

a Click the symbol next to Math Functions to expand the Math

Functions library.
b Click the symbol next to Matrices and Linear Algebra to expand the
Matrices and Linear Algebra sublibrary.
c In the expanded list, click Matrix Operations to view the blocks in the
Matrix Operations library.
d Drag the Matrix Sum block into the model window.

2-6
 The Simulink Environment

6 Add a Scope block to the model.

a Click Sinks (in the Simulink tree) to view the blocks in the Simulink
Sinks library.
b Drag the Scope block from the Sinks library into the model window. (The
Simulink Scope block is the same as the Time Scope block in the DSP
Sinks library.)

7 Connect the blocks.

a Position the pointer near the output port of the Sine Wave block. Hold
down the mouse button (the left button for a multibutton mouse) and
drag the line that appears until it touches the input port of the Matrix
Sum block. Release the mouse button.
b Using the same technique, connect the output of the Matrix Sum block to
the input port of the Scope block.

8 Set the block parameters.

a Double-click on the Sine Wave block. The dialog box that appears allows
you to set the block’s parameters. Parameters are defining values that tell
the block how to operate.
For this example, configure the block to generate a 10 Hz sine wave and
a 20 Hz sine wave by entering [10 20] for the Frequency parameter.
Both sinusoids will have the default amplitude of 1 and phase of 0
specified by the Amplitude and Phase offset parameters. They also both
share the default sample period of 0.001 seconds specified by the Sample
time parameter, which represents a sample rate of 1000 Hz.

2-7
2 Simulink and the DSP Blockset

Close the dialog box by clicking on the OK button or by pressing Enter on

the keyboard.
b Double-click on the Matrix Sum block. Select Rows from the Sum along
parameter, and close the dialog box.

You can now move on to the model simulation phase.

Model Simulation
Simulink is also a model simulation environment. You can run the simulation
block diagram that you have built to see how the system behaves. To do this:

1 Select Signal dimensions from the Format menu (optional). The symbol
“[1x2]” appears on the output line from Sine Wave indicating that the
output is a 1-by-2 matrix.

At each sample time, the output matrix contains one sample from each of the
two sinusoids. The Matrix Sum block adds the two matrix elements together

2-8
 The Simulink Environment

to produce a scalar output. Thus, the input to the Scope block is the
point-by-point sum of the two sinusoids.

2 Double-click on the Scope block if the Scope window is not already open on
your screen. The scope window appears.

3 Select Start from the Simulation menu in the block diagram window. The
signal containing the summed 10 Hz and 20 Hz component sinusoids is
plotted on the scope.

4 Adjust the Scope block’s display.

a While the simulation is running, right-click on the y-axis of the scope and
select Autoscale. The vertical range of the scope is adjusted to better fit
the signal.
b Click the Properties button on the scope, , and enter 0.1 for Time
range. This resizes the scope’s time axis to display only one cycle of the
signal.

5 Vary the Sine Wave block parameters.

a While the simulation is running, double-click on the Sine Wave block to

open it.
b Change the frequencies of the two sinusoids. Try entering [1 5] or
[100 400] in the Frequency field. Press Apply after entering each new
value, and observe the changes on the scope.

Note that the sample rate of both sinusoids is 1000 Hz, so aliasing will
occur for sinusoid frequencies above 500 Hz. You can increase the sample
rate by entering a smaller value in the Sine Wave block’s Sample time
parameter. This parameter is not tunable (see below), so you will need to
stop the simulation before making any adjustment.

6 Select Stop from the Simulation menu to stop the simulation.

Many parameters cannot be changed while a simulation is running. This is

usually the case for parameters that directly or indirectly alter a signal’s
dimensions or sample rate. There are some parameters, however, like the Sine
Wave Frequency parameter, that you can tune without terminating the
simulation. In the online “DSP Block Reference” these parameters are marked
“Tunable,” indicating that they are tunable while the simulation runs.

2-9
2 Simulink and the DSP Blockset

Running a Simulation from an M-File. You can also modify and run a Simulink
simulation from within a MATLAB M-file. By doing this, you can automate the
variation of model parameters to explore a large number of simulation
conditions rapidly and efficiently. For information on how to do this, see “Delay
and Latency” on page 3-85 and “Running a Simulation from the Command
Line” in the Simulink documentation.

Learning More About Simulink

Here are a few more suggestions to help you get started with Simulink:

• Browse through the Simulink documentation to get complete exposure to all

of Simulink’s capabilities.
• Open the Simulink library as described in “Starting Simulink” on page 2-3.
Build a few simple models using blocks from the Simulink and DSP Blockset
libraries.
• Open some of the models in the DSP Blockset Demos library. Most of the
advanced demos have blocks that you can double-click to get information
about the algorithm or implementation. The Demos library also contains
easy-to-understand models that demonstrate some of the blockset’s
elementary math and statistics blocks. In each case, just select Start from
the Simulation menu to run the simulation.

2-10
 Configuring Simulink for DSP Systems

Configuring Simulink for DSP Systems

When you create a new DSP model, you may want to adjust certain Simulink
settings to suit your own needs. A typical change, for example, is to adjust the
Stop time parameter (in the Simulation Parameters dialog box) to a different
value. Another common change is to specify the Fixed-step option in the
Solver options panel to reflect the discrete-time nature of the DSP model.
The DSP Blockset provides an M-file, dspstartup, that lets you automate this
configuration process so that every new model you create is preconfigured for
DSP simulation. The M-file executes the following commands.
set_param(0, ...
'SingleTaskRateTransMsg','error', ...
'Solver', 'fixedstepdiscrete', ...
'SolverMode', 'SingleTasking', ...
'StartTime', '0.0', ...
'StopTime', 'inf', ...
'FixedStep', 'auto', ...
'SaveTime', 'off', ...
'SaveOutput', 'off', ...
'AlgebraicLoopMsg', 'error', ...
'InvariantConstants', 'on', ...
'ShowInportBlksSampModeDlgField','on', ...
'RTWOptions', [get_param(0,'RTWOptions')
' -aRollThreshold=2']);

The following sections provide information about dspstartup:

• “Using dspstartup.m”
• “Customizing dspstartup.m”
• “Performance-Related Settings”
• “Miscellaneous Settings”

For complete information on any of the settings, see the Simulink

documentation.

2-11
2 Simulink and the DSP Blockset

Using dspstartup.m
There are two ways to use the dspstartup M-file to preconfigure Simulink for
DSP simulations:

• Run it from the MATLAB command line, by typing dspstartup, to

preconfigure all of the models that you subsequently create. Existing models
are not affected.
• Place a call to dspstartup within the startup.m file. This is an efficient way
to use dspstartup if you would like these settings to be in effect every time
you start Simulink.

If you do not have a startup.m file on your path, you can create one from the
startupsav.m template in the toolbox/local directory.

To edit startupsav.m, simply replace the load matlab.mat command with a

call to dspstartup, and save the file as startup.m. The result should look like
something like this.
%STARTUP Startup file
% This file is executed when MATLAB starts up,
% if it exists anywhere on the path.

dspstartup;

The default settings in dspstartup will now be in effect every time you launch
Simulink.
For more information about performing automated tasks at startup, see the
documentation for the startup command in the “MATLAB Function
Reference.”

Customizing dspstartup.m
You can edit the dspstartup M-file to change any of the settings above or to
add your own custom settings. For example, you can change the 'StopTime'
option to a value that is better suited to your particular simulations, or set the
'SaveTime' option to 'on' if you prefer to record the simulation sample times.

2-12
 Configuring Simulink for DSP Systems

Performance-Related Settings
A number of the settings in the dspstartup M-file are chosen to improve the
performance of the simulation:

• 'SaveTime' is set to 'off'

When 'SaveTime' is set to 'off', Simulink does not save the tout time-step
vector to the workspace. The time-step record is not usually needed for
analyzing discrete-time simulations, and disabling it saves a considerable
amount of memory, especially when the simulation runs for an extended
period of time. To enable time recording for a particular model, select the
Time check box in the Workspace I/O panel of the Simulation Parameters
dialog box (shown below).

• 'SaveOutput' is set to 'off'

When 'SaveOutput' is set to 'off', Simulink Outport blocks in the top level
of a model do not generate an output (yout) in the workspace. To reenable
output recording for a particular model, select the Output check box in the
Workspace I/O panel of the Simulation Parameters dialog box (above).
• 'InvariantConstants' is set to 'on'
When 'InvariantConstants' is set to 'on', Simulink precomputes the
values of all constant blocks (e.g., DSP Constant, Constant Diagonal Matrix)
at the start of the simulation, and does not update them again for the

2-13
2 Simulink and the DSP Blockset

duration of the simulation. Simulink additionally precomputes the outputs

of all downstream blocks driven exclusively by constant blocks.
In the example below, the input to the top port (U) of the Matrix Multiply
block is computed only once, at the start of the simulation.

precomputed

This eliminates the computational overhead of continuously reevaluating

these constant branches, which in turn results in faster simulation, and
smaller and more efficient generated code.
Note, however, that when 'InvariantConstants' is set to 'on', changes
that you make to parameters in a constant block while the simulation is
running are not registered by Simulink, and do not affect the simulation. If
you would like to adjust the model constants while the simulation is running,
you can turn off 'InvariantConstants' by deselecting the Inline
Parameters check box in the Advanced panel of the Simulation
Parameters dialog box.

• 'RTWOptions' sets loop-rolling threshold to 2

By default, the Real-Time Workshop “unrolls” a given loop into inline code
when the number of loop iterations is less than five. This avoids the overhead

2-14
 Configuring Simulink for DSP Systems

of servicing the loop in cases when inline code can be used with only a modest
increase in the file size.
However, because typical DSP processors offer zero-overhead looping, code
size is the primary optimization constraint in most designs. It is therefore
more efficient to minimize code size by generating a loop for every instance
of iteration, regardless of the number of repetitions. This is what the
'RTWOptions' loop-rolling setting in dspstartup accomplishes.

Miscellaneous Settings
The dspstartup M-file adjusts several other parameters to make it easier to
run DSP simulations. Two of the important settings are:

• 'StopTime' is set to 'inf', which allows the simulation to run until you
manually stop it by selecting Stop from the Simulation menu, or by pressing
the Stop Simulation button on the toolbar. To set a finite stop time, enter a
value for the Stop time parameter in the Simulation Parameters dialog
box.

• 'Solver' is set to 'fixedstepdiscrete', which selects the fixed-step solver

option instead of Simulink’s default variable-step solver (this mode enables
code generation from the model using the Real-Time Workshop). See
“Discrete-Time Signals” on page 3-3 for more information about the various
solver settings.

2-15
2 Simulink and the DSP Blockset

2-16
 3

Working with Signals

Overview . . . . . . . . . . . . . . . . . . . . . 3-2

Signal Concepts . . . . . . . . . . . . . . . . . . 3-3

Sample Rates and Frame Rates . . . . . . . . . . . 3-16

Creating Signals . . . . . . . . . . . . . . . . . . 3-33

Constructing Signals . . . . . . . . . . . . . . . . 3-42

Deconstructing Signals . . . . . . . . . . . . . . . 3-54

Importing Signals . . . . . . . . . . . . . . . . . 3-62

Exporting Signals . . . . . . . . . . . . . . . . . 3-72

Viewing Signals . . . . . . . . . . . . . . . . . . 3-80

Delay and Latency . . . . . . . . . . . . . . . . . 3-85

3 Working with Signals

Overview
The first part of this chapter will help you understand how signals are
represented in Simulink. It covers a number of topics that are especially
important in DSP simulations, such as sample rates and frame-based
processing:

• “Signal Concepts”
• “Sample Rates and Frame Rates”

The second part of the chapter explains the practical aspects of how to create,
construct, import, export, and view signals:

• “Creating Signals”
• “Constructing Signals”
• “Deconstructing Signals”
• “Importing Signals”
• “Exporting Signals”
• “Viewing Signals”

The last part of the chapter deals with the advanced topic of delay and latency:
• “Delay and Latency”

3-2
 Signal Concepts

Signal Concepts
Simulink models can process both discrete-time and continuous-time signals,
although models that are built with the DSP Blockset are often intended to
process only discrete-time signals. The next few sections cover the following
topics:

• “Discrete-Time Signals” – A brief introduction to some of the common

terminology used for discrete-time signals, and a discussion of how
discrete-time signals are represented within Simulink
• “Continuous-Time Signals” – An explanation of how continuous-time signals
are treated by various blocks in the DSP Blockset
• “Multichannel Signals” – A description of how multichannel signals are
represented in Simulink
• “Benefits of Frame-Based Processing” – An explanation of how frame-based
processing achieves higher throughput rates

Discrete-Time Signals
A discrete-time signal is a sequence of values that correspond to particular
instants in time. The time instants at which the signal is defined are the
signal’s sample times, and the associated signal values are the signal’s samples.
Traditionally, a discrete-time signal is considered to be undefined at points in
time between the sample times. For a periodically sampled signal, the equal
interval between any pair of consecutive sample times is the signal’s sample
period, Ts. The sample rate, Fs, is the reciprocal of the sample period, or 1/Ts.
The sample rate is the number of samples in the signal per second.
For example, the 7.5-second triangle wave segment below has a sample period
of 0.5 seconds, and sample times of 0.0, 0.5, 1.0, 1.5, ...,7.5. The sample rate of
the sequence is therefore 1/0.5, or 2 Hz.

Ts

0 1 2 3 4 5 6 7 time (s)

3-3
3 Working with Signals

The following sections provide definitions for a number of terms commonly

used to describe the time and frequency characteristics of discrete-time signals,
and explain how these characteristics relate to Simulink models:

• “Time and Frequency Terminology”

• “Discrete-Time Signals in Simulink”

Time and Frequency Terminology

A number of different terms are used to describe the characteristics of
discrete-time signals found in Simulink models. These terms, which are listed
in the table below, are frequently used in Chapter 5, “DSP Block Reference,” to
describe the way that various blocks operate on sample-based and frame-based
signals.

Term Symbol Units Notes

Sample period Ts Seconds The time interval between consecutive

Tsi samples in a sequence, as the input to a block
Tso, (Tsi) or the output from a block (Tso).

Frame period Tf Seconds The time interval between consecutive frames

Tfi in a sequence, as the input to a block (Tfi) or
Tfo the output from a block (Tfo).

Signal period T Seconds The time elapsed during a single repetition of

a periodic signal.

Sample rate, or Fs Hz (samples The number of samples per unit time,

Sample frequency per second) Fs = 1/Ts.

Frequency f Hz (cycles The number of repetitions per unit time of a

per second) periodic signal or signal component, f = 1/T.

Nyquist rate Hz (cycles The minimum sample rate that avoids

per second) aliasing, usually twice the highest frequency
in the signal being sampled.

Nyquist frequency fnyq Hz (cycles Half the Nyquist rate.

per second)

3-4
 Signal Concepts

Term Symbol Units Notes

Normalized fn Two cycles Frequency (linear) of a periodic signal

frequency per sample normalized to half the sample rate,
fn = ω/π = 2f/Fs.

Angular frequency Ω Radians per Frequency of a periodic signal in angular

second units, Ω = 2πf.

Digital (normalized ω Radians per Frequency (angular) of a periodic signal

angular) frequency sample normalized to the sample rate, ω = Ω/Fs = πfn.

Note In the block dialog boxes, the term sample time is used to refer to the
sample period, Ts. An example is the Sample time parameter in the Signal
From Workspace block, which specifies the imported signal’s sample period.

Discrete-Time Signals in Simulink

Simulink allows you to select from among several different simulation solver
algorithms through the Solver options controls of the Solver panel in the
Simulation Parameters dialog box. The selections that you make here
determine how discrete-time signals are processed in Simulink.

3-5
3 Working with Signals

The following sections explain the parameters available in this dialog box:

• “Recommended Settings for Discrete-Time Simulations”

• “Sample Time Offsets”
• “Cross-Rate Operations in Variable-Step and Fixed-Step SingleTasking
Modes”
• “Sample Time Offsets”

Recommended Settings for Discrete-Time Simulations. The recommended Solver

options settings for DSP simulations are:

• Type = Fixed-step discrete

• Fixed step size = auto
• Mode = SingleTasking

You can automatically set the above solver options for all new models by
running the dspstartup M-file. See “Configuring Simulink for DSP Systems”
on page 2-11 for more information.
In Fixed-step SingleTasking mode, discrete-time signals differ from the
prototype described in “Discrete-Time Signals” on page 3-3 by remaining
defined between sample times. For example, the representation of the
discrete-time triangle wave looks like this.

Ts

0 1 2 3 4 5 6 7 time (s)

The above signal’s value at t=3.112 seconds is the same as the signal’s value at
t=3 seconds. In Fixed-step SingleTasking mode, a signal’s sample times are
the instants where the signal is allowed to change values, rather than where
the signal is defined. Between the sample times, the signal takes on the value
at the previous sample time.
As a result, in Fixed-step SingleTasking mode, Simulink permits cross-rate
operations such as the addition of two signals of different rates. This is
explained further in “Cross-Rate Operations in Variable-Step and Fixed-Step
SingleTasking Modes” on page 3-7.

3-6
 Signal Concepts

Additional Settings for Discrete-Time Simulations. It is worthwhile to know how the

other solver options available in Simulink affect discrete-time signals. In
particular, you should be aware of the properties of discrete-time signals under
the following settings:

• Type = Fixed-step, Mode = MultiTasking

• Type = Variable-step (Simulink’s default solver)
• Type = Fixed-step, Mode = Auto

When the Fixed-step MultiTasking solver is selected, discrete signals in

Simulink most accurately model the prototypical discrete signal described in
“Discrete-Time Signals” on page 3-3. In particular, when these settings are in
effect, discrete signals are undefined between sample times. Simulink
generates an error when operations attempt to reference the undefined region
of a signal, as, for example, when signals with different sample rates are added.
To perform cross-rate operations like the addition of two signals with different
sample rates, you must explicitly convert the two signals to a common sample
rate. There are several blocks provided for precisely this purpose in the Signal
Operations and Multirate Filters libraries. See “Converting Sample Rates and
Frame Rates” on page 3-20 for more information. By requiring explicit rate
conversions for cross-rate operations in discrete mode, Simulink helps you to
identify sample rate conversion issues early in the design process.
When the Variable-step solver is selected, discrete time signals remain
defined between sample times, just as in the Fixed-step SingleTasking
setting previously described in “Recommended Settings for Discrete-Time
Simulations”. In this mode, cross-rate operations are allowed by Simulink.
In the Fixed-step Auto setting, Simulink automatically selects a tasking mode
(single-tasking or multitasking) that is best suited to the model. See “Simulink
Tasking Mode” on page 3-91 for a description of the criteria that Simulink uses
to make this decision. For the typical model containing multiple rates,
Simulink selects the multitasking mode.

Cross-Rate Operations in Variable-Step and Fixed-Step SingleTasking Modes. In

Simulink’s Variable step and Fixed-step SingleTasking modes, a
discrete-time signal is defined between sample times. Therefore, if you sample
the signal with a rate or phase that is different from the signal’s own rate and
phase, you will still measure meaningful values.

3-7
3 Working with Signals

Note In the recommended dspstartup settings, SingleTask rate transition

is set to Error in the Diagnostics pane in the Simulation Parameters dialog
box. Thus, in the dspstartup configurations, cross-rate operations will
generate errors even though the solver is in fixed-step single-tasking mode.

Example: Cross-Rate Operations. Consider the model below, which sums two
signals having different sample periods. The fast signal (Ts=1) has sample
times 1, 2, 3, ..., and the slow signal (Ts=2) has sample times 1, 3, 5, ....
This example will generate an error under the dspstartup settings, as
explained in the previous Note.

Ts = 1

Ts = 2

The output, yout, is a matrix containing the fast signal (Ts=1) in the first
column, the slow signal (Ts=2) in the second column, and the sum of the two in
the third column.
yout =

1 1 2
2 1 3
3 2 5
4 2 6
5 3 8
6 3 9
7 4 11
8 4 12
9 5 14
10 5 15

As expected, the slow signal (second column) changes once every two seconds,
half as often as the fast signal. Nevertheless, it has a defined value at every

3-8
 Signal Concepts

moment inbetween because Simulink implicitly auto-promotes the rate of the

slower signal to match the rate of the faster signal before the addition
operation is performed.
In general, for Variable-step and Fixed-step SingleTasking modes, when you
measure the value of a discrete signal between sample times, you are observing
the value of the signal at the previous sample time.

Sample Time Offsets. Simulink offers the ability to shift a signal’s sample times
by an arbitrary value, which is equivalent to shifting the signal’s phase by a
fractional sample period. However, sample-time offsets are rarely used in DSP
systems, and blocks from the DSP Blockset do not support them.

Continuous-Time Signals
Most signals in a DSP model are discrete-time signals, and all of the blocks in
the DSP Blockset accept discrete-time inputs. However, many blocks can also
operate on continuous-time signals, whose values vary continuously with time.
Similarly, most blocks generate discrete-time signals, but some also generate
continuous-time signals.
The sampling behavior of a particular block (continuous or discrete)
determines which other blocks you can connect as an input or output. The
following sections describe the behavior for two types of blocks:

• “Source Blocks”
• “Nonsource Blocks”

See Chapter 5, “DSP Block Reference,” for information about the particular
sample characteristics of each block in the blockset.

Source Blocks
Source blocks are those blocks that generate or import signals in a model. Most
source blocks appear in the DSP Sources library. See section “Importing
Signals” on page 3-62 to fully explore the features of these blocks.

Continuous-Time Source Blocks. The sample period for continuous-time source

blocks is set internally to zero, which indicates a continuous-time signal.
Simulink’s Signal Generator block is an example of a continuous-time source
block. Continuous-time signals are rendered in black when Sample time
colors is selected from the Format menu. When connecting such blocks to

3-9
3 Working with Signals

discrete-time blocks, you may need to interpose a Zero-Order Hold block to

discretize the signal (see the following diagram). Specify the desired sample
period for the signal in the Sample time parameter of the Zero-Order Hold
block.

Wrong: Error: Continuous sample

times not allowed for
upsample blocks.

Correct:

The Triggered Signal From Workspace block is also a continuous-time block.

Discrete-Time Source Blocks. Discrete-time source blocks such as Signal From

Workspace require a discrete (nonzero) sample period to be specified in the
block’s Sample time parameter. Simulink generates an error if a zero value is
specified for the Sample time parameter of a discrete-time source block.

Nonsource Blocks
All nonsource blocks in the DSP Blockset accept discrete signals, and inherit
the sample period of the input. Others additionally accept continuous-time
discrete signals.

Discrete-Time Nonsource Blocks. Discrete-time nonsource blocks can accept only

discrete-time inputs, and generate only discrete-time outputs. Examples are
all of the resampling and delay blocks, including Upsample and Integer Delay.
A discrete-time nonsource block inherits the sample period and sample rate of
its driving block (the block supplying its input). For example, if the driving
block’s sample period is 0.5 seconds, the inheriting block also executes at 0.5
second intervals. Simulink generates an error if a continuous input is
connected to a discrete-only block.

Continuous/Discrete Nonsource Blocks. In the continuous/discrete blocks,

continuous-time inputs generate continuous-time outputs, and discrete-time
inputs generate discrete-time outputs. Examples are Complex Exponential and
dB Gain. The nonsource triggered blocks such as Triggered Delay Line are also
in this category.

3-10
 Signal Concepts

Multichannel Signals
The following figure shows the prototypical discrete-time signal discussed in
“Discrete-Time Signals” on page 3-3. If this signal were propagated through a
model sample-by-sample, rather than in batches of samples, it would be called
sample-based. It would also be called single-channel, because there is only one
independent sequence of numbers.

Ts

0 1 2 3 4 5 6 7 time (s)

In practice, signal samples are frequently transmitted in batches, or frames,

and several channels of data are often transmitted simultaneously. Hence, the
general signal is frame-based and multichannel.
The following sections explain how sample-based and frame-based
multichannel signals are represented in Simulink:

• “Sample-Based Multichannel Signals”

• “Frame-Based Multichannel Signals”

The representation of single-channel signals follows naturally as a special case

(one channel) of the general multichannel signal.

Sample-Based Multichannel Signals

Sample-based multichannel signals are represented as matrices. An M-by-N
sample-based matrix represents M∗N independent channels, each containing a
single value. In other words, each matrix element represents one sample from
a distinct channel.
As an example, consider the 24-channel (6-by-4) sample-based signal in the
figure below, where ut=0 is the first matrix in the series, ut=1 is the second, ut=2
is the third, and so on.

3-11
3 Working with Signals

4 4 4 4 sample 4 (u t=3) A sequence of sample-based

4 4 4 4 matrices. Each of the 24
4 4 2 2 elements in a given matrix
3 3 3 3 sample 3 (u t=2)
4 4 2 2 represents a single channel.
3 3 3 3
4 4 22
3 2 3 2
4 4 2 22 2 2 2 sample 2 (u t=1)
3 3 2 2
2 2 2 2
3 3 2 2
2 2 2 2
3 3 2 21 1 1 1 sample 1 (u t=0)
2 2 2 2
1 1 1 1
2 2 2 2
1 1 1 1
2 2 2 2
1 1 1 1
1 1 1 1
1 1 1 1

Then the signal in channel 1 is composed of the following sequence.

t=0 t=1 t=2
u 11 , u 11 , u 11 , …

Similarly, channel 9 (counting down the columns) contains the following

sequence.
t=0 t=1 t=2
u 32 , u 32 , u 32 , …

See the following sections for information about working with sample-based
multichannel signals:

• “Creating Signals” on page 3-33

• “Constructing Signals” on page 3-42
• “Deconstructing Signals” on page 3-54
• “Importing Signals” on page 3-62
• “Exporting Signals” on page 3-72
• “Viewing Signals” on page 3-80

Frame-Based Multichannel Signals

Frame-based multichannel signals are also represented as matrices. An
M-by-N frame-based matrix represents M consecutive samples from each of N
independent channels. In other words, each matrix row represents one sample

3-12
 Signal Concepts

(or time slice) from N distinct signal channels, and each matrix column
represents M consecutive samples from a single channel.
This is a simple structure, as illustrated below for a sample 6-by-4 frame
matrix.

1 1 1 1
2 2 2 2 Frame matrix:
3 3 3 3 4 channels,
4 4 4 4 1 frame per channel,
5 5 5 5 6 samples per frame
6 6 6 6

ch1 ch2 ch3 ch4

Consider a sequence of frame matrices, where ut=0 is the first matrix in a

series, ut=1 is the second, ut=2 is the third, and so on.

sample 5 5 5 5 5 A sequence of frame-based

frame 3 (u t=2)
sample 6 6 6 6 6 matrices. Each column in a given
matrix represents a single channel.
sample 3 3 3 3 3
frame 2 (u t=1)
sample 4 4 4 4 4

sample 1 1 1 1 1
frame 1 (u t=0)
sample 2 2 2 2 2

ch1 ch2 ch3 ch4

Then the signal in channel 1 is the following sequence.

t=0 t=0 t=0 t=0 t=1 t=1 t=1 t=1 t=2 t=2
u 11 , u 21 , u 31 , …, u M1 , u 11 , u 21 , u 31 , …, u M1 , u 11 , u 21 , …

Similarly, the signal in channel 3 is the following sequence.

t=0 t=0 t=0 t=0 t=1 t=1 t=1 t=1 t=2 t=2
u 13 , u 23 , u 33 , …, u M3 , u 13 , u 23 , u 33 , …, u M3 , u 13 , u 23 , …

See the following sections for information about working with frame-based
multichannel signals:

• “Creating Signals” on page 3-33

• “Constructing Signals” on page 3-42
• “Deconstructing Signals” on page 3-54

3-13
3 Working with Signals

• “Importing Signals” on page 3-62

• “Exporting Signals” on page 3-72
• “Viewing Signals” on page 3-80

Benefits of Frame-Based Processing

Frame-based processing is an established method of accelerating both
real-time systems and simulations.

Accelerating Real-Time Systems

Framed-based data is a common format in real-time systems. Data acquisition
hardware often operates by accumulating a large number of signal samples at
a high rate, and propagating these samples to the real-time system as a block
of data. This maximizes the efficiency of the system by distributing the fixed
process overhead across many samples; the “fast” data acquisition is suspended
by “slow” interrupt processes after each frame is acquired, rather than after
each individual sample.
The figure below illustrates how throughput is increased by frame-based data
acquisition. The thin blocks each represent the time elapsed during acquisition
of a sample. The thicker blocks each represent the time elapsed during the
interrupt service routine (ISR) that reads the data from the hardware.
In this example, the frame-based operation acquires a frame of 16 samples
between each ISR. The frame-based throughput rate is therefore many times
higher than the sample-based alternative.

3-14
 Signal Concepts

Sample-based operation

ISR

time
acquire sample

Frame-based operation

acquire 16 samples ISR

time
latency

It’s important to note that frame-based processing will introduce a certain

amount of latency into a process due to the inherent lag in buffering the initial
frame. In many instances, however, it is possible to select frame sizes that
improve throughput without creating unacceptable latencies.

Accelerating Simulations
Simulation also benefits from frame-based processing. In this case, it is the
overhead of block-to-block communications that is reduced by propagating
frames rather than individual samples.

3-15
3 Working with Signals

Sample Rates and Frame Rates

Sample rates are an important issue in most DSP models, especially in systems
incorporating rate conversions. Fortunately, in most cases, when you build a
Simulink model you only need to worry about setting sample rates in the source
blocks, such as Signal From Workspace; Simulink automatically computes the
appropriate sample rates for all downstream blocks.
Nevertheless, it is important to become familiar with the concepts of “sample
rate” and “frame rate” as they apply in the Simulink world. The next sections
cover the following important topics:

• “Sample Rate and Frame Rate Concepts”

• “Inspecting Sample Rates and Frame Rates”
• “Converting Sample Rates and Frame Rates”
• “Changing Frame Status”

Sample Rate and Frame Rate Concepts

The input frame period (Tfi) of a frame-based signal is the time interval
between consecutive vector or matrix inputs to a block. This interval is what
the Probe block displays when you connect it to a frame-based input line.
Similarly, the output frame period (Tfo) is the time interval at which the block
updates the frame-based vector or matrix value at the output port. This
interval is what the Probe block displays when you connect it to a frame-based
output line. (See “Inspecting Sample Rates and Frame Rates” on page 3-17 for
more about using the Probe block.)
In contrast, the sample period, Ts, is the time interval between individual
samples in a frame, which is necessarily shorter than the frame period when
the frame size is greater than 1. The sample period of a frame-based signal is
the quotient of the frame period and the frame size, M.

Ts = Tf ⁄ M

More specifically, the sample periods of inputs (Tsi) and outputs (Tso) are
related to their respective frame periods by

T si = T fi ⁄ M i

T so = T fo ⁄ M o

3-16
 Sample Rates and Frame Rates

where Mi and Mo are the input and output frame sizes, respectively.
The illustration below shows a one-channel frame-based signal with a frame
size (Mi) of 4 and a frame period (Tfi) of 1. The sample period, Tsi, is therefore 1/
4, or 0.25 seconds. A Probe block connected to this signal would display the
frame period Tfi = 1.
Tfi = 1
first input frame

13 9 5 1
Tsi = 0.25
14 10 6 2
15 11 7 3
16 12 8 4

t=3 t=2 t=1 t=0

In most cases, the sequence sample period Tsi is of primary interest, while the
frame rate is simply a consequence of the frame size that you choose for the
signal. For a sequence with a given sample period, a larger frame size
corresponds to a slower frame rate, and vice versa.
For information on converting a signal from one sample rate or frame rate to
another, see “Converting Sample Rates and Frame Rates” on page 3-20.

Inspecting Sample Rates and Frame Rates

When constructing a frame-based or multirate model, it is often helpful to
check the rates that Simulink computes for different signals. There are two
basic ways to inspect the sample rates and frame rates in a model. These are
described in the following sections:

• “Using the Probe Block to Inspect Rates”

• “Using Sample Time Color Coding to Inspect Sample Rates”

Using the Probe Block to Inspect Rates

Connect Simulink’s Probe block to any line to display the period of the signal
on that line. The period is displayed in the block icon itself (together with the
line width and data type, if desired), making it easy to verify that the sample
rates in the model are what you expect them to be. When the line width and
data type displays are suppressed (by deselecting the appropriate check boxes
in the block dialog box), the Probe block looks like this.

3-17
3 Working with Signals

The block displays the label Ts or Tf, followed by a two-element vector. The
first (left) element is the period of the signal being measured. The second
(right) is the signal’s sample time offset, which is usually 0, as explained in
“Sample Time Offsets” on page 3-9.
For sample-based signals, the value shown in the Probe block icon is the
sample period of the sequence, Ts. For frame-based signals, the value shown in
the Probe block icon is the frame period, Tf. The difference between sample
rates and frame rates is explained in “Sample Rate and Frame Rate Concepts”
on page 3-16.

Probe Block Example: Sample-Based. The three Probe blocks in the sample-based
model below verify that the signal’s sample period is halved with each
upsample operation: The output from the Signal From Workspace block has a
sample period of 1 second, the output from the first Upsample block has a
sample period of 0.5 seconds, and the output from the second Upsample block
has a sample period of 0.25 seconds.

Probe Block Example: Frame-Based. The three Probe blocks in the frame-based
model below again verify that the signal’s sample period is halved with each
upsample operation: The output from the Signal From Workspace block has a
frame period of 16 seconds, the output from the first Upsample block has a
frame period of 8 seconds, and the output from the second Upsample block has
a sample period of 4 seconds.

3-18
 Sample Rates and Frame Rates

Note that the sample rate conversion is implemented through a change in the
frame period rather than the frame size. This is because the Frame-based
mode parameter in the Upsample blocks is set to Maintain input frame size
rather than Maintain input frame rate. See “Converting Sample Rates and
Frame Rates” on page 3-20 for more information.

Using Sample Time Color Coding to Inspect Sample Rates

Turn on Simulink’s sample time color coding option by selecting Sample time
colors from the Format menu. For sample-based signals, this assigns each
sample rate a different color. For frame-based signals, this assigns each frame
rate a different color.

Sample Time Color Coding Example: Sample-Based. Here is the sample-based model
from “Probe Block Example: Sample-Based” on page 3-18 with the Probe blocks
removed and sample time color coding turned on.

Green = second fastest sample rate

Blue = third fastest sample rate Red = fastest sample rate

Since every sample-based signal in this model has a different sample rate, each
signal is assigned a different color.

Sample Time Color Coding Example: Frame-Based. Here’s the frame-based model
from “Probe Block Example: Frame-Based” on page 3-18 with the Probe blocks
removed and sample time color coding turned on.

3-19
3 Working with Signals

Because the Frame-based mode parameter in the Upsample blocks is set to

Maintain input frame size rather than Maintain input frame rate, each
Upsample block changes the frame rate. Therefore, each frame-based signal in
the model is assigned a different color.
If the Upsample blocks are instead set to Maintain input frame rate, then
every signal in the model shares the same frame rate, and as a result, every
signal is coded with the same color.

For more information about sample time color coding, see “Sample Time
Colors” in the Simulink documentation.

Converting Sample Rates and Frame Rates

In a DSP Blockset model, there are two types of periods that you will commonly
be concerned with: sample periods and frame periods. The input and output
sample periods of a block (Tsi and Tso, respectively) are related to the input and
output frame periods (Tfi and Tfo, respectively) by

T si = T fi ⁄ M i

T so = T fo ⁄ M o

where Mi and Mo are the input and output frame sizes, respectively.
The buffering and rate-conversion capabilities of the DSP Blockset generally
allow you to independently vary any two of the three parameters (Tso, Tfo, Mo).
In most cases, the sample period and the frame size are the two parameters of
primary interest; the frame period is simply a consequence of your choices for
the other two.
There are two common types of operations that impact the frame and sample
rates of a signal:

3-20
 Sample Rates and Frame Rates

• Direct rate conversions

Direct rate conversions, such as upsampling and downsampling, are a
feature of most DSP systems, and can be implemented by altering either the
frame rate or the frame size of a signal.
• Frame rebuffering
The principal purpose of frame rebuffering is to alter the frame size of a
signal, usually to improve simulation throughput. By redistributing the
signal samples to frames of a new size, rebuffering usually changes either
the sample rate or frame rate of the signal.

Both operations are discussed in the following sections, along with ways to
avoid unintentional rate conversions:

• “Direct Rate Conversion”

• “Frame Rebuffering”
• “Avoiding Unintended Rate Conversions”

You may also want to look at the Sample Rate Conversion demo,
dspsrcnv.mdl.

Note Technically, when a Simulink model contains signals with various

frame rates, the model is called multirate. You can find a discussion of
multirate models in “Delay and Latency” on page 3-85 and in the “Discrete
Time Systems” section of the Simulink documentation.

Direct Rate Conversion

Rate conversion blocks accept an input signal at one sample rate, and
propagate the same signal at a new sample rate. Several of these blocks contain
a Frame-based mode parameter offering two options for adjusting the sample
rate of the signal:

• Maintain input frame rate: Change the sample rate by changing the frame
size (i.e., Mo ≠ Mi), but keep the frame rate constant (i.e., Tfo = Tfi)
• Maintain input frame size: Change the sample rate by changing the output
frame rate (i.e., Tfo ≠ Tfi), but keep the frame size constant (i.e., Mo = Mi)

The setting of this parameter does not affect sample-based inputs.

3-21
3 Working with Signals

Rate Conversion Blocks. The following table lists the principal rate conversion
blocks in the DSP Blockset. Blocks marked with an asterisk (*) offer the option
of changing the rate by either adjusting the frame size or frame rate.

Block Library

Downsample * Signal Operations

Dyadic Analysis Filter Bank Filtering / Multirate Filters

Dyadic Synthesis Filter Bank Filtering / Multirate Filters

FIR Decimation * Filtering / Multirate Filters,

FIR Interpolation * Filtering / Multirate Filters

FIR Rate Conversion Filtering / Multirate Filters

Repeat * Signal Operations

Upsample * Signal Operations

Wavelet Analysis Filtering / Multirate Filters

Wavelet Synthesis Filtering / Multirate Filters

The following examples illustrate the two sample rate conversion modes:

• “Example: Rate Conversion by Frame-Rate Adjustment”

• “Example: Rate Conversion by Frame-Size Adjustment”

Example: Rate Conversion by Frame-Rate Adjustment. A common example of direct

rate conversion is shown in the model below, where the signal is directly
downsampled to half its original rate by a Downsample block. The values next
to input and output ports are the signal dimensions, displayed by selecting
Signal dimensions from the model window’s Format menu.

3-22
 Sample Rates and Frame Rates

The sample period and frame size of the original signal are set to 0.125 seconds
and 8 samples per frame, respectively, by the Sample time and Samples per
frame parameters in the Signal From Workspace block. This results in a frame
rate of 1 second (0.125∗8), as shown by the first Probe block.
The Downsample block is configured to downsample the signal by changing the
frame rate rather than the frame size. The dialog box with this setting is shown
below.

Maintain input frame size :

Downsample the signal by
changing the frame rate.

The second Probe block in the model verifies that the output from the
Downsample block has a frame period of 2, twice that of the input (i.e., half the
rate). As a result, the sequence sample period is doubled to 0.25 seconds
without any change to the frame size.

Example: Rate Conversion by Frame-Size Adjustment. The model from “Example: Rate
Conversion by Frame-Rate Adjustment” on page 3-22 is shown again below,
but this time with the rate conversion implemented by adjusting the frame
size, rather than the frame rate.

3-23
3 Working with Signals

As before, the frame rate of the original signal is 1 second (0.125∗8), shown by
the first Probe block. Now the Downsample block is configured to downsample
the signal by changing the frame size rather than the frame rate. The dialog
box with this setting is shown below.

Maintain input frame rate:

Downsample the signal by
changing the frame size.

The line width display on the Downsample output port verifies that the
downsampled output has a frame size of 4, half that of the input. As a result,
the sequence sample period is doubled to 0.25 seconds without any change to
the frame rate.

Frame Rebuffering
Buffering operations provide another mechanism for rate changes in DSP
models. The purpose of many buffering operations is to adjust the frame size of
the signal, M, without altering the sequence sample rate Ts. This usually
results in a change to the signal’s frame rate, Tf, according to the relation

T f = MT s

3-24
 Sample Rates and Frame Rates

However, this is only true when the original signal is preserved in the buffering
operation, with no samples added or deleted. Buffering operations that
generate overlapping frames, or that only partially unbuffer frames, alter the
data sequence by adding or deleting samples. In such cases, the above relation
is not valid.

Buffering Blocks. The following table lists the principal buffering blocks in the
DSP Blockset.

Block Library

Buffer Signal Management / Buffers

Delay Line Signal Management / Buffers

Unbuffer Signal Management / Buffers

Variable Selector Signal Management / Indexing

Zero Pad Signal Operations

The following sections discuss two general classes of buffering operations:

• “Buffering with Preservation of the Signal”

• “Buffering with Alteration of the Signal”

Buffering with Preservation of the Signal. There are various reasons that you may
need to rebuffer a signal to a new frame size at some point in a model. For
example, your data acquisition hardware may internally buffer the sampled
signal to a frame size that is not optimal for the DSP algorithm in the model.
In this case, you would want to rebuffer the signal to a frame size more
appropriate for the intended operations, but without introducing any change to
the data or sample rate.
There are two blocks in the Buffers library that can be used to change a signal’s
frame size without altering the signal itself:
• Buffer – redistributes signal samples to a larger or smaller frame size
• Unbuffer – unbuffers a frame-based signal to a sample-based signal (frame
size = 1)

3-25
3 Working with Signals

The Buffer block preserves the signal’s data and sample period only when its
Buffer overlap parameter is set to 0. The output frame period, Tfo, is

M o T fi
T fo = ----------------
Mi

where Tfi is the input frame period, Mi is the input frame size, and Mo is the
output frame size specified by the Buffer size parameter.
The Unbuffer block is specialized for completely unbuffering a frame-based
signal to its sample-based equivalent, and always preserves the signal’s data
and sample period:

T so = T fi ⁄ M i

where Tfi and Mi are the period and size, respectively, of the frame-based input.
Both the Buffer and Unbuffer blocks preserve the sample period of the
sequence in the conversion (Tso = Tsi).

Example: Buffering with Preservation of the Signal. In the model below, a signal with
a sample period of 0.125 seconds is rebuffered from a frame size of 8 to a frame
size of 16. This doubles the frame period from 1 to 2 seconds, but does not
change the sample period of the signal (Tso = Tsi = 0.125).

Buffering with Alteration of the Signal. Some forms of buffering alter the signal’s
data or sample period, in addition to adjusting the frame size. There are many
instances when this type of buffering is desirable, for example when creating
sliding windows by overlapping consecutive frames of a signal, or selecting a
subset of samples from each input frame for processing.
The blocks that alter a signal while adjusting its frame size are listed below. In
this list, Tsi is the input sequence sample period, and Tfi and Tfo are the input
and output frame periods, respectively.

3-26
 Sample Rates and Frame Rates

• Buffer adds duplicate samples to a sequence when the Buffer overlap

parameter, L, is set to a nonzero value. The output frame period is related to
the input sample period by
T fo = ( M o – L )T si

where Mo is the output frame size specified by the Buffer size parameter. As
a result, the new output sample period is
( M o – L )T si
T so = -------------------------------
Mo

• Delay Line adds duplicate samples to the sequence when the Delay line size
parameter, Mo, is greater than 1. The output and input frame periods are the
same, Tfo = Tfi = Tsi, and the new output sample period is
T si
T so = --------
Mo

• Variable Selector can remove, add, and/or rearrange samples in the input
frame when Select is set to Rows. The output and input frame periods are
the same, Tfo = Tfi, and the new output sample period is
M i T si
T so = ----------------
Mo

where Mo is the length of the block’s output, determined by the Elements

vector.
• Zero Pad adds samples to the sequence by appending zeros to each frame
when Zero pad along is set to Columns. The output and input frame periods
are the same, Tfo = Tfi, and the new output sample period is
M i T si
T so = ----------------
Mo

where Mo is the length of the block’s output, determined by the Number of

output rows parameter.
In all of these cases, the sample period of the output sequence is not equal to
the sample period of the input sequence.

3-27
3 Working with Signals

Example: Buffering with Alteration of the Signal. In the model below, a signal with a
sample period of 0.125 seconds is rebuffered from a frame size of 8 to a frame
size of 16 with an overlap of 4.

The relation for the output frame period for the Buffer block is

T fo = ( M o – L )T si

which indicates that Tfo should be (16-4)∗0.125, or 1.5 seconds, as confirmed by

the second Probe block. The sample period of the signal at the output of the
Buffer block is no longer 0.125 seconds, but rather 0.0938 seconds (i.e., 1.5/16).
Thus, both the signal’s data and the signal’s sample period have been altered
by the buffering operation.

Avoiding Unintended Rate Conversions

The previous sections discussed a number of the blocks that are responsible for
rate conversions. It is important to be aware of where in a model these rate
conversions are taking place; in a few cases, unintentional rate conversions can
produce misleading results. The following pair of examples illustrate how
unintended rate conversion can occur:

• “Example 1: No Rate Conversion”

• “Example 2: Unintended Rate Conversion”

Example 1: No Rate Conversion. The model below plots the magnitude FFT of a
signal composed of two sine waves, with frequencies of 1 Hz and 2 Hz.

3-28
 Sample Rates and Frame Rates

To build the model, configure one Sine Wave block with Frequency = 1, and
the other with Frequency = 2. In addition, both Sine Wave blocks should have
the following settings:

• Sample time = 0.1

• Samples per frame = 128

The frame period of the resulting summed sinusoid is 12.8 seconds (i.e.,
128∗0.1), which is confirmed by the Probe block when the model is updated.
Select Inherit FFT length from input dimensions in the Magnitude FFT
block. This setting instructs the block to use the input frame size (128) as the
FFT length (which is also the output size).
Configure the Vector Scope block as follows:

• Select Frequency from the Input domain parameter.

• Select the Axis properties check box to expose the Axis properties panel.
• Set Minimum Y-limit to -10.
• Set Maximum Y-limit to 40.

The plot generated by the Vector Scope block is shown below.

3-29
3 Working with Signals

The Vector Scope block uses the input frame size (128) and period (12.8) to
deduce the original signal’s sample period (0.1), which allows it to correctly
display the peaks at 1 Hz and 2 Hz.

Example 2: Unintended Rate Conversion. Now alter the previous example by setting
the Magnitude FFT block parameters as follows:

• Deselect the Inherit FFT length from input dimensions check box.
• Set the FFT length parameter to 256.

This setting instructs the block to zero-pad the length-128 input frame to a
length of 256 before performing the FFT. The signal dimension display on the
new version of the model shows that the output of the Magnitude FFT block is
now a length-256 frame.

The plot generated by the Vector Scope block is shown below.

3-30
 Sample Rates and Frame Rates

In this case, based on the input frame size (256) and period (12.8), the Vector
Scope block calculates the original signal’s sample period to be 0.05 seconds
(12.8/256), which is wrong. As a result, the spectral peaks appear at the
incorrect frequencies, 2 Hz and 4 Hz rather than 1 Hz and 2 Hz.
The problem is that the zero-pad operation performed by the Magnitude FFT
block halves the sample period of the sequence by appending 128 zeros to each
frame. The Vector Scope block, however, needs to know the sample period of
the original signal. The problem is easily solved by changing the Sample time
of original time series setting in the Axis properties panel of the Vector
Scope block to the actual sample period of 0.1. The plot generated with this
setting is identical to the first Vector Scope plot above.
In general, be aware that when you do zero-padding or overlapping buffering
you are changing the sample period of the signal. As long as you keep this in
mind, you should be able to anticipate and correct problems like the one above.

Changing Frame Status

The frame status of a signal refers to whether the signal is sample-based or
frame-based. In a Simulink model, the frame status is symbolized by a single
line, →, for a sample-based signal and a double line, ⇒, for a frame-based
signal.
In most cases, the appropriate way to convert a sample-based signal to a
frame-based signal is by using the Buffer block, and the appropriate way to

3-31
3 Working with Signals

convert a frame-based signal to a sample-based signal is by using the Unbuffer

block. See the following sections for more information about these methods:

• “Buffering Sample-Based and Frame-Based Signals” on page 3-47

• “Unbuffering a Frame-Based Signal into a Sample-Based Signal” on
page 3-60

On occasion it may be desirable to change the frame status of a signal without

performing a buffering operation. You can do this by using the Frame Status
Conversion block in the Signal Attributes library.

The Output signal parameter (or the signal at the optional Ref input port)
determines the frame status of the output If the frame status of the input
differs from the Output signal setting, then the frame status is altered as
specified. If the frame status of the input is the same as that specified by the
Output signal parameter, then no change is made to the signal.
The block’s input and output port rates are the same, and because the block
does not make any sample rate accommodation, the sample rate of the signal
is generally not preserved under a change of frame status. (The exception to
this rule occurs when a sample-based signal is converted to a frame-based
signal with frame size 1, or vice versa.)
See the Frame Status Conversion block’s reference page for complete
information.

3-32
 Creating Signals

Creating Signals
There are a variety of different ways to create signals using Simulink and DSP
blocks. The following sections explore the most common techniques:

• “Creating Signals Using Constant Blocks” on page 3-33

• “Creating Signals Using Signal Generator Blocks” on page 3-36
• “Creating Signals Using the Signal From Workspace Block” on page 3-38

The above sections discuss creating signals (single-channel and multichannel)

using source blocks. For information about constructing multichannel signals
from existing single-channel signals, see the following sections:

• “Constructing Multichannel Sample-Based Signals” on page 3-42

• “Constructing Multichannel Frame-Based Signals” on page 3-45

Creating Signals Using Constant Blocks

A constant signal is a sample-based signal in which successive samples are
identical, or a frame-based signal in which successive frames are identical. The
DSP Sources library provides the following blocks for creating sample-based
and frame-based constant signals:

• Constant Diagonal Matrix

• Constant Ramp
• DSP Constant
• Identity Matrix
• Window Function

Although some of these blocks generate continuous-time outputs and some

generate discrete-time outputs, in each case the output of the block remains
constant throughout the simulation.
The most versatile of these blocks is the DSP Constant, which is discussed
further in the following example. See Chapter 5, “DSP Block Reference,” for
complete explanation of all the constant blocks.
For information about creating signals with other types of blocks, see the
following sections:

• “Creating Signals Using Signal Generator Blocks” on page 3-36

3-33
3 Working with Signals

• “Creating Signals Using the Signal From Workspace Block” on page 3-38

For information about importing signals, see the following sections:

• “Importing a Multichannel Sample-Based Signal” on page 3-62

• “Importing a Multichannel Frame-Based Signal” on page 3-68

Example: Creating Signals with the DSP Constant Block

The DSP Constant block has the following parameters:
• Constant value
• Interpret vector parameters as 1-D
• Sample mode
• Sample time
• Frame-based output
To generate a constant matrix signal, simply enter the desired matrix in the
Constant value parameter using standard MATLAB notation. Some common
examples of MATLAB’s matrix notation are shown below.
[1 2 3;4 5 6] % A 2-by-3 matrix

[1 2 3;4 5 6]' % The transpose, a 3-by-2 matrix

randn(2,3) % A 2-by-3 matrix with random elements

[1 2 3] % A 1-by-3 row vector

[1 2 3]' % The transpose, a 3-by-1 column vector

As with all numerical parameters, you can also enter any valid MATLAB
variable or expression that evaluates to a matrix. See the MATLAB
documentation for a thorough introduction to constructing and indexing
matrices.
The Interpret vector parameters as 1-D and Frame-based output
parameters are discussed following the example below. See the DSP Constant
block’s reference page for information about the Sample mode and Sample
time parameters.
The model below shows five DSP Constant blocks, each generating one of the
constant signals listed above. Two of the blocks have non-default settings for
the other parameters: The third block (DSP Constant2) has the Frame-based

3-34
 Creating Signals

output check box selected, and the fourth block (DSP Constant3) has the
Interpret vector parameters as 1-D check box selected.

Sample-based matrix
(6 channels)

Sample-based matrix
(6 channels)

Frame-based matrix
(3 channels)

1-D vector

Frame-based matrix
(1 channel)

In addition to the various output dimensions in the model, you can observe
three different kinds of signals:

• Sample-based matrix signal – The DSP Constant and DSP Constant1 blocks
generate sample-based matrices (2-by-3 and 3-by-2, respectively) because
the Frame-based output check box in those blocks is not selected. The
sample-based matrices can each be considered to each have six independent
channels.
• Frame-based matrix signal – The DSP Constant2 and DSP Constant4 blocks
generate frame-based matrices (2-by-3 and 3-by-1, respectively, and
represented by double lines) because the Frame-based output check box in
those blocks is selected. The 2-by-3 frame-based matrix is considered to have
three independent channels, each containing two consecutive samples. The
3-by-1 frame-based matrix (column vector) is considered to have one
independent channel, containing three consecutive samples.
• 1-D vector signal – The DSP Constant3 block generates a length-3 1-D vector
signal because the Interpret vector parameters as 1-D check box in that

3-35
3 Working with Signals

block is selected. This means that the output is not a matrix. However, most
nonsource DSP blocks interpret a length-M 1-D vector as an M-by-1 matrix
(column vector).

Note A 1-D vector signal must always be sample-based. The Interpret

vector parameters as 1-D parameter is ignored when Frame-based output
is selected, or when a matrix is specified for the Constant value parameter.

See “Multichannel Signals” on page 3-11 for more information about the
representation of sample-based and frame-based data.

Creating Signals Using Signal Generator Blocks

The DSP Sources library provides the following blocks for automatically
generating common sample-based and frame-based signals:

• Chirp
• Counter
• Discrete Impulse
• Multiphase Clock
• N-Sample Enable
• Sine Wave

One of the most commonly used of these is the Sine Wave block, which is
discussed further in the example below. See Chapter 5, “DSP Block Reference,”
for a complete explanation of the other signal generation blocks. The Simulink
Sources library offers a collection of continuous-time signal generation blocks
that you may also find useful. Consult the Simulink documentation for more
information.
For more information about creating signals, see the following sections:

• “Creating Signals Using Constant Blocks” on page 3-33

• “Creating Signals Using the Signal From Workspace Block” on page 3-38

Example: Creating Signals with the Sine Wave Block

The Sine Wave block dialog box contains the following key parameters.

3-36
 Creating Signals

• Amplitude
• Frequency
• Phase offset
• Sample time
• Samples per frame
In the model below, a Sine Wave block generates a frame-based (multichannel)
matrix containing three independent signals:

• Sine wave of amplitude 1 and frequency 100 Hz

• Sine wave of amplitude 3 and frequency 250 Hz
• Sine wave of amplitude 2 and frequency 500 Hz

Each channel has a frame size of 64 samples. The three signals are summed
point-by-point by a Matrix Sum block, and exported to the workspace.

To build the model, set the Sum along parameter of the Matrix Sum block to
Rows, and make the following parameter settings in the Sine Wave block:

• Set Amplitude to [1 3 2]. This specifies the amplitudes for three

independent sinusoids (and therefore dictates a three-column output).
• Set Frequency to [100 250 500]. This specifies the frequency for each of
the output sinusoids.
• Set Sample time to 1/5000. (This is ten times the highest sinusoid
frequency, and so satisfies the Nyquist criterion.)
• Set Samples per frame to 64. This specifies a frame size of 64 for all
sinusoids (and therefore dictates a 64-row output).

After running the model, you can look at a portion of the resulting summed
sinusoid by typing
plot(yout(1:100))

at the command line.

3-37
3 Working with Signals

−2

−4

−6
0 20 40 60 80 100

See “Multichannel Signals” on page 3-11 for more information about the
representation of sample-based and frame-based data.

Creating Signals Using the Signal From Workspace

Block
You can easily create custom signals using the Signal From Workspace block.

This block allows you to generate arbitrary sample-based and frame-based

signals, as illustrated in the following examples:

• “Example 1: Generating Sample-Based Output” on page 3-39

• “Example 2: Generating Frame-Based Output” on page 3-39

As the name implies, the Signal From Workspace block is more commonly used
to import custom signals from the workspace. See the following sections for
more information:

• “Importing a Multichannel Sample-Based Signal” on page 3-62

• “Importing a Multichannel Frame-Based Signal” on page 3-68

3-38
 Creating Signals

For more information about creating signals, see the following sections:

• “Creating Signals Using Constant Blocks” on page 3-33

• “Creating Signals Using Signal Generator Blocks” on page 3-36

Example 1: Generating Sample-Based Output

In the model below, the Signal From Workspace creates a four-channel
sample-based signal with the following data:

• Channel 1: 1, 2, 3, 0, 0,...
• Channel 2: -1, -2, -3, 0, 0,...
• Channel 3: 0, 0, 0, 0, 0,...
• Channel 4: 5, 5, 5, 0, 0,...

00 3 –3 2 –2 1 –1
00 0 5 0 5 0 5

t=3 t=2 t=1 t=0

first matrix output

To create the model, specify the following parameter values in the Signal From
Workspace block:

• Signal = cat(3,[1 -1;0 5],[2 -2;0 5],[3 -3;0 5])

• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero

The Sample time setting of 1 yields a sample-based output with sample period
of 1 second. Each of the four elements in the matrix signal represents an
independent channel (the channel numbering is arbitrary). The Form output
after final data value parameter setting specifies that all outputs after the
third are zero.

Example 2: Generating Frame-Based Output

In the model below, the Signal From Workspace creates a two-channel
frame-based signal with the following data:

3-39
3 Working with Signals

• Channel 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0,...

• Channel 2: 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,...

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2
0 0 9 1 5 1 1 1
0 0 10 1 6 1 2 1
0 0 0 0 7 0 3 0
0 0 0 0 8 0 4 0
t=12 t=8 t=4 t=0

first matrix output

To create the model, specify the following parameter values in the Signal From
Workspace block:

• Signal = [1 2 3 4 5 6 7 8 9 10;1 1 0 0 1 1 0 0 1 1]'

• Sample time = 1
• Samples per frame = 4
• Form output after final data value = Setting to zero

The Sample time setting of 1 and the Samples per frame setting of 4 yield a
frame-based output with a frame size of 4 samples and a frame period of
4 seconds. The Form output after final data value parameter setting
specifies that all outputs after the third frame are zero.
Note that the output of the To Workspace block, yout, is the original signal
with appended zeros in each channel.

3-40
 Creating Signals

yout =

1 1
2 1
3 0
4 0
5 1
6 1
7 0
8 0
9 1
10 1
0 0
0 0

3-41
3 Working with Signals

Constructing Signals
When you want to perform a given sequence of operations on several
independent signals, it is frequently very convenient to group those signals
together as a multichannel signal. Most DSP blocks accept multichannel
signals, and process each channel independently. By taking advantage of this
capability, you can do the same job with fewer blocks and have a cleaner, leaner
model.
For example, if you need to filter each of four independent signals using a
direct-form II transpose filter with the same coefficients, combine the signals
into a multichannel signal, and run that multichannel signal into a
Direct-Form II Transpose Filter block. The block will apply the filter to each
channel independently.
The following sections explain how to construct multichannel signals from
existing independent signals:

• “Constructing Multichannel Sample-Based Signals” on page 3-42

• “Constructing Multichannel Frame-Based Signals” on page 3-45

For information about creating multichannel signals using source blocks, see
the following sections:

• “Creating Signals Using Constant Blocks” on page 3-33

• “Creating Signals Using Signal Generator Blocks” on page 3-36
• “Creating Signals Using the Signal From Workspace Block” on page 3-38

Constructing Multichannel Sample-Based Signals

A sample-based signal with M∗N channels is represented by a sequence of
M-by-N matrices. (The special case of M = N = 1 represents a single-channel
signal.) Multiple individual signals can be combined into a multichannel
matrix signal using the Matrix Concatenation block. Individual signals can be
added to an existing multichannel signal in the same way. The following
sections explain how to do this:

• “Constructing Sample-Based Multichannel Signals from Independent

Sample-Based Signals” on page 3-43
• “Constructing Sample-Based Multichannel Signals from Existing
Sample-Based Multichannel Signals” on page 3-44

3-42
 Constructing Signals

Constructing Sample-Based Multichannel Signals

from Independent Sample-Based Signals
You can combine individual sample-based signals into a multichannel signal by
using the Matrix Concatenation block in Simulink’s Sources library.

Example: Concatenating Single-Channel Signals. In the model below, four

independent sample-based signals are combined into a 2-by-2 multichannel
matrix signal.

Four single-channel signals Multichannel signals

To build the model, make the following parameter settings:

• In Signal From Workspace, set Signal = 1:10

• In Signal From Workspace1, set Signal = -1:-1:-10
• In Signal From Workspace2, set Signal = zeros(10,1)
• In Signal From Workspace3, set Signal = 5*ones(10,1)
• In Matrix Concatenation, set:
- Number of inputs = 4
- Concatenation method = Vertical
• In Reshape, set:
- Output dimensionality = Customize
- Output dimensions = [2,2]

3-43
3 Working with Signals

Each 4-by-1 output from the Matrix Concatenation block contains one sample
from each of the four input signals. All four samples in the output correspond
to the same instant in time. The Reshape block simply rearranges the samples
into a 2-by-2 matrix. Note that the Reshape block works columnwise, so that a
column vector input is reshaped as shown below.

1
2 1 3
3 2 4
4

The 4-by-1 matrix and the 2-by-2 matrix in the above model represent the same
sample-based four-channel signal. In some cases one representation may be
more useful than the other. See “Sample-Based Multichannel Signals” on
page 3-11 for more about sample-based signals.

Constructing Sample-Based Multichannel Signals

from Existing Sample-Based Multichannel Signals
You can combine existing multichannel sample-based signals into a larger
multichannel signal by using the Matrix Concatenation block in Simulink’s
Sources library.

Example: Concatenating Multichannel Signals. The model below shows two

two-channel sample-based signals (four channels total) being combined into a
2-by-2 multichannel matrix signal.

Two 2-channel signals,

4-channel signal
Four distinct channels

To build the model, make the following parameter settings:

• In Signal From Workspace, set Signal = [1:10;-1:-1:-10]'

3-44
 Constructing Signals

• In Signal From Workspace1, set Signal = [zeros(10,1) 5*ones(10,1)]

• In Matrix Concatenation, set:
- Number of inputs = 2
- Concatenation method = Vertical
Each 2-by-2 output from the Matrix Concatenation block contains both
samples from each of the two input signals, so that all four samples in the
output correspond to the same instant in time. See “Sample-Based
Multichannel Signals” on page 3-11 for more about sample-based signals.

Constructing Multichannel Frame-Based Signals

A frame-based signal with N channels and frame size M is represented by a
sequence of M-by-N matrices. (The special case of N = 1 represents a
single-channel signal.) There are two basic ways to construct a multichannel
frame-based signal from existing signals:

• By horizontally concatenating existing frame-based signals – Multiple

individual frame-based signals (with the same frame rate and size) can be
combined into a multichannel frame-based signal using the Simulink Matrix
Concatenation block. Individual signals can be added to an existing
multichannel signal in the same way.

1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6

sig1 sig2 sig3 sig4 ch1 ch2 ch3 ch4

Four frame-based signals : Multichannel frame-based signal :

1 channel each, 4 channels,
6 samples per frame 6 samples per frame

• By buffering existing sample-based or frame-based signals – Multichannel

sample-based and frame-based signals can be buffered into multichannel

3-45
3 Working with Signals

frame-based signals using the Buffer block in the Buffers library (in Signal
Management).

sample 1 1 1 1 1

sample 2 2 2 2 2

sample 3 3 3 3 3 1 1 1 1
2 2 2 2
sample 4 4 4 4 4
3 3 3 3

sample 5 5 5 5 5 4 4 4 4
5 5 5 5
sample 6 6 6 6 6 6 6 6 6

ch1 ch2 ch3 ch4 ch1 ch2 ch3 ch4

Multichannel sample-based signal : Multichannel frame-based signal :

4 channels 4 channels, 6 samples per frame

The following sections explain the two methods of constructing multichannel

frame-based signals:

• “Concatenating Independent Frame-Based Signals into Multichannel

Signals” on page 3-46
• “Buffering Sample-Based and Frame-Based Signals” on page 3-47

Concatenating Independent Frame-Based Signals

into Multichannel Signals
You can combine existing frame-based signals into a larger multichannel
signal by using the Matrix Concatenation block in Simulink’s Sources library.
All signals must have the same frame rate and frame size.

Example: Concatenating Frame-Based Signals. In the model below, a single-channel

frame-based signal is combined with a two-channel frame-based signal to
produce a three-channel frame-based signal.

3-46
 Constructing Signals

1 –1
2 –2
3 –3
4 –4 1 –1 5
2 –2 5
3 –3 5
5 4 –4 5
5
5
5

2-channel frame-based signal (top) and 3-channel frame-based signal

1-channel frame-based signal (bottom)

To build the model, make the following parameter settings:

• In Signal From Workspace, set Signal = [1:10;-1:-1:-10]'

• In Signal From Workspace1, set Signal = 5*ones(10,1)
• In Matrix Concatenation, set:
- Number of inputs = 2
- Concatenation method = Horizontal
The 4-by-3 matrix output from the Matrix Concatenation block contains all
three input channels, and preserves their common frame rate and frame size.
See “Frame-Based Multichannel Signals” on page 3-12 for more about
frame-based signals.
Note that you could also create or import the three-channel signal using just
one Signal From Workspace block. See the following sections for more
information:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38
• “Importing a Multichannel Frame-Based Signal” on page 3-68

Buffering Sample-Based and Frame-Based Signals

You can buffer a multichannel sample-based or frame-based signal into a
multichannel frame-based signal by using the Buffer block in the Buffers
library (in Signal Management). The Buffer block has the following key
parameters:

3-47
3 Working with Signals

• Output buffer size (per channel), Mo

• Buffer overlap, L
• Initial conditions
Buffering an N-channel (1-by-N or N-by-1) sample-based signal produces a
Mo-by-N frame-based signal. Buffering an Mi-by-N frame-based signal (N
channels and Mi samples per frame) results in an Mo-by-N output frame-based
signal.
For each output buffer, the block acquires the number of new input samples
specified by the difference between the Buffer size (Mo) and Buffer
overlap (L) parameters. Each new input sample enters at the bottom of the
buffer, and is pushed upwards as later samples enter. The first row in the
output therefore corresponds to the earliest input sample. Because the block
can buffer a signal to a larger or smaller frame size, the number of samples
acquired from the input can be greater or less than the number of samples in
an individual input frame.
In general, the output frame period, Tfo, is related to the input sample
period, Tsi, by

T fo = ( M o – L )T si

where Mo is the Output buffer size (per channel), and L is the Buffer
overlap.
As a result, the new output sample period, Tso, is

( M o – L )T si
T so = -------------------------------
Mo

Clearly, this is equal to the input sample period only when the Buffer overlap
is zero. See “Converting Sample Rates and Frame Rates” on page 3-20 for more
information about rate conversions.
The following sections provide examples of buffering, and explore related
buffering issues:

• “Example: Buffering Sample-Based Signals without Overlap” on page 3-49

• “Overlapping Buffers” on page 3-50
• “Example: Buffering Sample-Based Signals with Overlap” on page 3-50

3-48
 Constructing Signals

• “Example: Buffering Frame-Based Signals with Overlap” on page 3-52

• “Buffering Delay and Initial Conditions” on page 3-53

Example: Buffering Sample-Based Signals without Overlap. In the model below, a

two-channel sample-based signal is buffered into a two-channel frame-based
signal.

1 –1
[4 -4] [3 -3] [2 -2] [1 -1] 2 –2
3 –3
t=3 t=2 t=1 t=0 4 –4

Four consecutive samples from a 2-channel frame-based signal

2-channel sample-based signal

To build the model, make the following parameter settings:

• In Signal From Workspace:

- Signal = [1:10;-1:-1:-10]'
- Sample time = 1
- Samples per frame = 1
• In Buffer
- Output buffer size = 4
- Buffer overlap = 0
- Initial conditions = 0
The Signal From Workspace block generates one two-channel sample at each
sample time due to the Samples per frame parameter setting of 1. The Buffer
size setting of 4 in the Buffer block results in a frame-based output with frame
size 4.
A much better way to create the frame-based signal shown above is to set the
Samples per frame parameter of the Signal From Workspace block to 4. The
Signal From Workspace block then performs the buffering internally, and
directly generates the two-channel frame-based signal; the separate Buffer
block is not needed. See the following sections for more information:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38

3-49
3 Working with Signals

• “Importing a Multichannel Frame-Based Signal” on page 3-68

Overlapping Buffers. In some cases it is useful to work with data that represents
overlapping sections of an original sample-based or frame-based signal. In
estimating the power spectrum of a signal, for example, it is often desirable to
compute the FFT of overlapping sections of data. Overlapping buffers are also
needed in computing statistics on a sliding window, or for adaptive filtering.
The Buffer overlap parameter of the Buffer block specifies the number of
overlap points, L.
In the overlap case (L > 0), the frame period for the output is (Mo-L)∗Tsi, where
Tsi is the input sample period and Mo is the Buffer size.

Note Set the Buffer overlap parameter to a negative value to achieve output
frame rates slower than in the nonoverlapping case. The output frame period
is still Tsi∗(Mo-L), but now with L < 0. Only the Mo newest inputs are included
in the output buffer; the previous L inputs are discarded.

Example: Buffering Sample-Based Signals with Overlap. In the following model, a

four-channel sample-based signal with sample period 1 is buffered to a
frame-based signal with frame size 3 and frame period 2. Because of the
overlap, the input sample period is not conserved, and the output sample
period is 2/3.

3-50
 Constructing Signals

ch2 ch3
ch1 ch4
Sample-based input,
t=5 6 1 5 –6 sample period = Tsi
Tsi = 1
t=4 5 1 5 –5
Frame-based output ,
t=3 4 0 5 –4 frame period = (Mo-L)∗Tsi
first
t=2 3 0 5 –3
first sample-based frame-based
t=1 2 1 5 –2 input output

ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4
t=0 1 1 5 –1
4 0 5 –4 2 1 5 –2 0 0 0 0 0000
5 1 5 –5 3 0 5 –3 1 1 5 –1 0000
6 1 5 –6 4 0 5 –4 2 1 5 –2 0000

t=6 t=4 t=2 t=0

(Mo=3, L=1)

To build the model, define the following variable in the MATLAB workspace.
A = [1 1 5 -1;2 1 5 -2;3 0 5 -3;4 0 5 -4;5 1 5 -5;6 1 5 -6];

Connect the Buffer block to a Signal From Workspace source and a To

Workspace sink with the following parameter settings:

• In the Signal From Workspace block, set:

- Signal = A
- Sample time = 1
- Samples per frame = 1
• In the Buffer block, set:
- Output buffer size (per channel) = 3
- Buffer overlap = 1
- Initial conditions = 0
Note that the inputs do not begin appearing at the output until the second row
of the second matrix. This is due to the block’s latency. See “Delay and Latency”
on page 3-85 for general information about algorithmic delay, and see
“Buffering Delay and Initial Conditions” on page 3-53 for instructions on how
to calculate buffering delay.

3-51
3 Working with Signals

Example: Buffering Frame-Based Signals with Overlap. In the model below, a

two-channel frame-based signal with frame period 4 is rebuffered to a
frame-based signal with frame size 3 and frame period 2. Because of the
overlap, the input sample period is not conserved, and the output sample
period is 2/3.
ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2
5 1 1 1
6 1 2 1 51 30 11 00 00 00
7 0 3 0 61 40 21 00 00 00
8 0 4 0 70 51 30 11 00 00

t=4 t=0 (Mo=3, L=1) t=10 t=8 t=6 t=4 t=2 t=0

first input first output

Input frame period = 4∗Tsi Output frame period = (M o-L)∗Tsi

To build the model, define the following variable in the MATLAB workspace.
A = [1 1;2 1;3 0;4 0;5 1;6 1;7 0;8 0];

Connect the Buffer block to a Signal From Workspace source and a To

Workspace sink with the following parameter settings:

• In the Signal From Workspace block, set:

- Signal = A
- Sample time = 1
- Samples per frame = 4
• In the Buffer block, set:
- Output buffer size (per channel) = 3
- Buffer overlap = 1
- Initial conditions = 0
Note that the inputs do not begin appearing at the output until the last row of
the third matrix. This is due to the block’s latency. See “Delay and Latency” on
page 3-85 for general information about algorithmic delay, and see “Buffering
Delay and Initial Conditions” on page 3-53 for instructions on how to calculate
buffering delay.

3-52
 Constructing Signals

Buffering Delay and Initial Conditions. In both of the previous buffering examples
the input signal is delayed by a certain number of samples. In “Example:
Buffering Sample-Based Signals with Overlap” the delay is four samples. In
“Example: Buffering Frame-Based Signals with Overlap” the delay is eight
samples. The initial output samples adopt the value specified for the Initial
condition parameter, which is zero in both examples above.
In fact, under most conditions the Buffer and Unbuffer blocks have some
amount of latency. This latency depends on both the block parameter settings
and Simulink’s tasking mode. You can use the rebuffer_delay function to
determine the length of the block’s latency for any combination of frame size
and overlap.
The syntax rebuffer_delay(f,n,m) returns the delay (in samples) introduced
by the buffering and unbuffering blocks in multitasking operations, where f is
the input frame size, n is the Buffer size parameter setting, and m is the Buffer
overlap parameter setting.
For example, if you had run the frame-based example model in multitasking
mode, you could compute the latency by entering the following command at the
MATLAB command line.
d = rebuffer_delay(4,3,1)

d =
8

This agrees with the block’s output in that example. See “Delay and Latency”
on page 3-85 and the “Latency” section on each block reference page for more
information.

3-53
3 Working with Signals

Deconstructing Signals
Multichannel signals, represented by matrices in Simulink, are frequently
used in DSP models for efficiency and compactness. An M-by-N sample-based
multichannel signal represents M*N independent signals (one sample from
each), whereas an M-by-N frame-based multichannel signal represents N
independent channels (M consecutive samples from each). See “Multichannel
Signals” on page 3-11 for more information about the matrix format.
Even though most of the DSP blocks can process multichannel signals, you may
sometimes need to access just one channel or a particular range of samples in
a multichannel signal. There are a variety of ways to deconstruct multichannel
signals, the most common of which are explained in the following sections:

• “Deconstructing Multichannel Sample-Based Signals” on page 3-54

• “Deconstructing Multichannel Frame-Based Signals” on page 3-57

For information about constructing multichannel signals from individual

sample-based or frame-based signals, see the following sections:

• “Constructing Multichannel Sample-Based Signals” on page 3-42

• “Constructing Multichannel Frame-Based Signals” on page 3-45

Deconstructing Multichannel Sample-Based Signals

A sample-based signal with M∗N channels is represented by a sequence of
M-by-N matrices. (The special case of M = N = 1 represents a single-channel
signal.) You can access individual channels of the multichannel signal by using
the blocks in the Indexing library (in Signal Management). The following
sections explain how to do this:

• “Deconstructing a Sample-Based Multichannel Signal into Multiple

Independent Signals” on page 3-54
• “Deconstructing a Sample-Based Multichannel Signal into a Related
Multichannel Signal” on page 3-55

Deconstructing a Sample-Based Multichannel Signal

into Multiple Independent Signals
You can split a multichannel sample-based signal into individual sample-based
signals (single-channel or multichannel) by using the Multiport Selector block

3-54
 Deconstructing Signals

in the Indexing library (in Signal Management). Any subset of rows or columns
can be selected for propagation to a given output port.

Example: Deconstructing to Independent Signals. In the model below, a six-channel

sample-based signal (3-by-2 matrix) is deconstructed to yield three
independent sample-based signals. Two of the output signals have four
channels, and the third signal has two channels.

To build the model, make the following parameter settings:

• In Signal From Workspace, set Signal = randn(3,2,10)

• In Multiport Selector, set:
- Select = Rows
- Indices to output = {[1 2],[1 3],3}
The Indices to output setting specifies that rows 1 and 2 of the input should
be reproduced at output 1, that rows 1 and 3 of the input should be reproduced
at output 2, and that row 3 of the input should be reproduced alone at output 3.
See “Sample-Based Multichannel Signals” on page 3-11 for more about
sample-based signals.

Deconstructing a Sample-Based Multichannel Signal

into a Related Multichannel Signal
You can select a subset of channels from a multichannel sample-based signal
by using one of the following blocks in the Indexing library (in Signal
Management):

• Selector (Simulink)
• Submatrix

3-55
3 Working with Signals

• Variable Selector

The next section provides an example of using the Submatrix block to extract
a portion of a multichannel sample-based signal. The Submatrix block is the
most versatile of the above blocks in that it allows you to make completely
arbitrary channel selections.

Example: Deconstructing to a Multichannel Signal. In the model below, a 35-channel

sample-based signal (5-by-7 matrix) is deconstructed to yield a sample-based
signal containing only six of the original channels.

To build the model, make the following parameter settings:

• In DSP Constant, set Constant value = rand(5,7)

• In Submatrix, set:
- Row span = Range of rows
- Starting row = Index
- Starting row index = 3
- Ending row = Last
- Column span = Range of columns
- Starting column = Offset from last
- Starting column index = 1
- Ending column = Last
See “Sample-Based Multichannel Signals” on page 3-11 for more about
sample-based signals.

3-56
 Deconstructing Signals

Deconstructing Multichannel Frame-Based Signals

A frame-based signal with N channels and frame size M is represented by a
sequence of M-by-N matrices. (The special case of N = 1 represents a
single-channel signal.) There are two basic ways to deconstruct a multichannel
frame-based signal:

• Split the channels into independent signals – The constituent channels of a

multichannel frame-based signal can be extracted to form individual frame
based signals (with the same frame rate and size) by using the Multiport
Selector block in the Indexing library (in Signal Management).

1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6

ch1 ch2 ch3 ch4 sig1 sig2 sig3 sig4

Multichannel frame-based signal : Four frame-based signals :

4 channels, 1 channel each,
6 samples per frame 6 samples per frame

• Unbuffer the samples – Multichannel frame-based signals can be unbuffered

into multichannel sample-based signals using the Unbuffer block in the
Buffers library (in Signal Management).

3-57
3 Working with Signals

sample 6 6 6 6 6

sample 5 5 5 5 5

1 1 1 1 sample 4 4 4 4 4

2 2 2 2
sample 3 3 3 3 3
3 3 3 3
4 4 4 4 sample 2 2 2 2 2
5 5 5 5
6 6 6 6 sample 1 1 1 1 1

ch1 ch2 ch3 ch4 ch1 ch2 ch3 ch4

Multichannel frame-based signal : Multichannel sample-based signal :

4 channels, 6 samples per frame 4 channels

The following sections explain the two methods of deconstructing multichannel

frame-based signals:

• “Splitting a Multichannel Signal into Individual Signals” on page 3-58

• “Unbuffering a Frame-Based Signal into a Sample-Based Signal” on
page 3-60

The final section explains how to reorder the channels in a frame-based signal
without splitting the channels apart:
• “Reordering Channels in a Frame-Based Multichannel Signal” on page 3-61

Splitting a Multichannel Signal into Individual Signals

You can split a frame-based multichannel signal into its constituent
frame-based signals by using the Multiport Selector block in the Indexing
library (in Signal Management).

Example: Splitting a Multichannel Frame-Based Signal. In the model below, a

three-channel frame-based signal is split into a single-channel frame-based
signal and a two-channel frame-based signal.

3-58
 Deconstructing Signals

1 5
2 5
3 5
1 –1 5 4 5
2 –2 5
3 –3 5
–1
4 –4 5
–2
–3
–4

2-channel frame-based signal (top) and

3-channel frame-based signal
1-channel frame-based signal (bottom)

To build the model, make the following parameter settings:

• In Signal From Workspace, set:

- Signal = [1:10;-1:-1:-10;5*ones(1,10)]'
- Samples per frame = 4
• In Multiport Selector, set:
- Select = Columns
- Indices to output = {[1 3],2}
The top (4-by-2) output from the Multiport Selector block contains the first and
third input channels, and the bottom output contains the second input channel.
The Multiport Selector block preserves the frame rate and frame size of the
input as long as Select is set to Columns. See “Frame-Based Multichannel
Signals” on page 3-12 for more about frame-based signals.
Note that you could also create or import the two signals by using two distinct
Signal From Workspace blocks. See the following sections for more
information:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38
• “Importing a Multichannel Frame-Based Signal” on page 3-68

3-59
3 Working with Signals

Unbuffering a Frame-Based Signal into a Sample-Based Signal

You can unbuffer a multichannel frame-based signal into a multichannel
sample-based signal by using the Unbuffer block in the Buffers library (in
Signal Management).
The Unbuffer block performs the inverse operation of the Buffer block’s
“sample-based to frame-based” buffering process, and generates an N-channel
sample-based output from an N-channel frame-based input. The first row in
each input matrix is always the first sample-based output. In other words, the
Unbuffer block unbuffers each input frame from the top down.
The sample period of the sample-based output, Tso, is related to the input
frame period, Tfi, by the input frame size, Mi.

T so = T fi ⁄ M i

The Unbuffer block always preserves the signal’s sample period (Tso = Tsi). See
“Converting Sample Rates and Frame Rates” on page 3-20 for more
information about rate conversions.

Example: Unbuffering a Frame-Based Signal. In the model below, a two-channel

frame-based signal is unbuffered into a two-channel sample-based signal.

1 –1
2 –2 [4 -4] [3 -3] [2 -2] [1 -1]
3 –3
4 –4 t=7 t=6 t=5 t=4

Four consecutive samples from a

2-channel frame-based signal
2-channel sample-based signal

To build the model, make the following parameter settings:

• In Signal From Workspace:

- Signal = [1:10;-1:-1:-10]'
- Sample time = 1
- Samples per frame = 4

3-60
 Deconstructing Signals

The Signal From Workspace block generates a two-channel frame based-signal

with frame size 4 (because the Samples per frame parameter is set to 4). The
Unbuffer block unbuffers this signal to a two-channel sample-based signal.

Note The Unbuffer block generates initial conditions (not shown in the figure
above) with the value specified by the Initial conditions parameter. See the
Unbuffer reference page for information about the number of initial conditions
that appear in the output.

Reordering Channels in a Frame-Based Multichannel Signal

Use the Permute Matrix block to swap channels in a frame-based signal.

3-61
3 Working with Signals

Importing Signals
Although a number of signal generation blocks are available in Simulink and
the DSP Blockset, it is very common to import custom signals from the
MATLAB workspace as well. The following sections explain how to do this:

• “Importing a Multichannel Sample-Based Signal” on page 3-62

• “Importing a Multichannel Frame-Based Signal” on page 3-68
• “Importing WAV Files” on page 3-71

For information about creating signals, see the following sections:

• “Creating Signals Using Constant Blocks” on page 3-33

• “Creating Signals Using Signal Generator Blocks” on page 3-36
• “Creating Signals Using the Signal From Workspace Block” on page 3-38

Importing a Multichannel Sample-Based Signal

The Signal From Workspace block in the DSP Sources library is the key block
for importing sample-based signals of all dimensions from the MATLAB
workspace.

The dialog box has the following parameters:

• Signal
• Sample time
• Samples per frame
• Form output after final data value by
Use the Signal parameter to specify the name of a variable (vector, matrix, or
3-D array) in the MATLAB workspace. You can also enter any valid MATLAB
expressions involving workspace variables, as long as the expressions evaluate
to a vector, matrix, or 3-D array.
The Samples per frame parameter must be set to 1 for sample-based output;
any value larger that 1 produces a frame-based output. See “Importing a
Multichannel Frame-Based Signal” on page 3-68 for more information. The

3-62
 Importing Signals

Sample-time parameter specifies the sample period of the sample-based

output. See “Sample-Based Multichannel Signals” on page 3-11 for general
information about sample-based signals.
The following sections explain how the Signal From Workspace generates its
output:

• “Importing a Sample-Based Vector Signal” on page 3-63

• “Importing a Sample-Based Matrix Signal” on page 3-65

Importing a Sample-Based Vector Signal

The Signal From Workspace block generates a sample-based vector signal
when the variable (or expression) in the Signal parameter is a matrix and
Samples per frame = 1. Beginning with the first row of the matrix, the block
releases a single row of the matrix to the output at each sample time.
Therefore, if the Signal parameter specifies an M-by-N matrix, the output of
the Signal From Workspace block is a 1-by-N matrix (row vector), representing
N channels.
The figure below illustrates this for a 6-by-4 workspace matrix, A.

sample 6 6 6 6 6

sample 5 5 5 5 5

1 1 1 1 sample 4 4 4 4 4

2 2 2 2
sample 3 3 3 3 3
3 3 3 3
4 4 4 4 sample 2 2 2 2 2
5 5 5 5
6 6 6 6 sample 1 1 1 1 1

ch1 ch2 ch3 ch4 ch1 ch2 ch3 ch4

MATLAB workspace matrix, A : Sample-based vector signal :

4 channels, 6 samples each 4 channels

As the figure above suggests, the output of the Signal From Workspace block
can only be a valid sample-based signal (having N independent channels) if the
M-by-N workspace matrix A in fact represents N independent channels, each

3-63
3 Working with Signals

containing M consecutive samples. In other words, the workspace matrix must

be oriented so as to have the independent channels as its columns.
When the block has output all of the rows available in the specified variable, it
can start again at the beginning of the signal, or simply repeat the final value
(or generate zeros) until the end of the simulation. This behavior is controlled
by the Form output after final data value by parameter. See the Signal From
Workspace reference page for more information.
The following example illustrates how the Signal From Workspace block can be
used to import a sample-based vector signal into a model.

Example: Importing a Sample-Based Vector Signal. In the model below, the Signal
From Workspace creates a three-channel sample-based signal with the
following data:

• Channel 1: 1, 2, 3, 4, 5,..., 100, 0, 0, 0,...

• Channel 2: -1, -2, -3, -4, -5,..., -100, 0, 0, 0,...
• Channel 3: 5, 5, 5, 5, 5,..., 0, 0, 0,...

[4 -4 5] [3 -3 5] [2 -2 5] [1 -1 5]

t=3 t=2 t=1 t=0

Four consecutive samples from a

3-channel sample-based signal

To create the model, define the following variables at the MATLAB command
line
A = [1:100;-1:-1:-100]'; % 100-by-2 matrix
B = 5*ones(100,1); % 100-by-1 column vector

Matrix A represents a two-channel signal with 100 samples, and matrix B

represents a one-channel signal with 100 samples.
Specify the following parameter values in the Signal From Workspace block:

• Signal = [A B]
• Sample time = 1
• Samples per frame = 1

3-64
 Importing Signals

• Form output after final data value = Setting to zero

The Signal expression [A B] uses the standard MATLAB syntax for

horizontally concatenating matrices and appends column vector B to the right
of matrix A. Equivalently, you could set Signal = C, and define C at the
command line by
C = [A B]

The Sample time setting of 1 yields a sample-based output with sample period
of 1 second. The Form output after final data value parameter setting
specifies that all outputs after the third are zero.

Importing a Sample-Based Matrix Signal

The Signal From Workspace block generates a sample-based matrix signal
when the variable (or expression) in the Signal parameter is a
three-dimensional array and Samples per frame = 1. Beginning with the first
page of the array, the block releases a single page (i.e., matrix) of the array to
the output at each sample time. Therefore, if the Signal parameter specifies an
M-by-N-by-P array, the output of the Signal From Workspace block is an
M-by-N matrix, representing M∗N channels.
The figure below illustrates this for a 6-by-4-by-5 workspace array A.

3-65
3 Working with Signals

4 4 4 4
4 4 4 4
4 4 2 2
3 3 3 3
4 4 2 2
3 3 3 3
5 5 5 5 4 4 2
2
3 23 2
5 4 2 4 2 4 2 4 4 4 2 22 2 2 2
3 3 3 2 2
5 4 2 2 23 2 23 2 3 2 2 2 2
2 2 2 2 sample 4 3 3 2 2
4 3 2 22 2 22 2 2 2 2 2 2
5 2
3 2 1 2 1 2 1 2 1 3 3 2 21 1 1 1
5 4 2 2 22 2 22 2 2 2 2 2 2
3 2 1 2 1 2 1 2 1 sample 3 1 1 1 1
5 4 2 2 22 2 22 2 2 2 2 2 2
2 1 2 1 2 1 2 1 1 1 1 1
4 3 2 2 2 2 2 2 2 2 2 2
3 2 21 2 21 2 1
2 2 1 1 1 1 1
sample 2
2 1 2 1 2 1 2 1 1 1 1 1
1 1 1 1 1 1 1 1

sample 1

MATLAB workspace array, A: Sample-based matrix signal :

24 channels, 1 sample each 24 channels

As the figure above suggests, the output of the Signal From Workspace block
can only be a valid sample-based signal (having M∗N independent channels) if
the M-by-N-by-P workspace array A in fact represents M∗N independent
channels, each having P samples. In other words, the workspace array must be
oriented to have time running along its third (P) dimension.
When the block has output all of the pages available in the specified array, it
can start again at the beginning of the array, or simply repeat the final page
(or generate zero-matrices) until the end of the simulation. This behavior is
controlled by the Form output after final data value by parameter. See the
Signal From Workspace reference page for more information.
The following example illustrates how the Signal From Workspace block can be
used to import a sample-based matrix signal into a model.

Example: Importing a Sample-Based Matrix Signal. In the model below, the Signal
From Workspace imports a four-channel sample-based signal with the
following data:

• Channel 1: 1, 2, 3, 4, 5,..., 100, 0, 0, 0,...

• Channel 2: -1, -2, -3, -4, -5,..., -100, 0, 0, 0,...

3-66
 Importing Signals

• Channel 3: 0, 0, 0, 0, 0,...
• Channel 4: 5, 5, 5,..., 0, 0, 0,...

4 –4 3 –3 2 –2 1 –1
0 5 0 5 0 5 0 5

t=3 t=2 t=1 t=0

first matrix output

Four consecutive samples from a

4-channel sample-based signal

To create the model, define the following variables at the MATLAB command
line.
sig1 = reshape(1:100,[1 1 100]) % 1-by-1-by-100 array
sig2 = reshape(-1:-1:-100,[1 1 100]) % 1-by-1-by-100 array
sig3 = zeros(1,1,100) % 1-by-1-by-100 array
sig4 = 5*ones(1,1,100) % 1-by-1-by-100 array
sig12 = cat(2,sig1,sig2) % 1-by-2-by-100 array
sig34 = cat(2,sig3,sig4) % 1-by-2-by-100 array

A = cat(1,sig12,sig34) % 2-by-2-by-100 array

Array A represents a 4-channel signal with 100 samples.

Specify the following parameter values in the Signal From Workspace block:

• Signal = A
• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero

The Sample time and Samples per frame settings of 1 yield a sample-based
output with sample period of 1 second. Each of the four elements in the matrix
represents an independent channel. The Form output after final data value
parameter setting specifies that all outputs after the one-hundredth are zero.
The following two sections may also be of interest:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38

3-67
3 Working with Signals

• “Constructing Multichannel Sample-Based Signals” on page 3-42

Importing a Multichannel Frame-Based Signal

The Signal From Workspace in the DSP Sources library is the key block for
importing frame-based signals from the MATLAB workspace.

The dialog box has the following parameters:

• Signal
• Sample time
• Samples per frame
• Form output after final data value by
Use the Signal parameter to specify the name of a variable (vector or matrix)
in the MATLAB workspace. You can also enter any valid MATLAB expressions
involving workspace variables, as long as the expressions evaluate to a vector
or matrix.
The Samples per frame parameter must be set to a value greater than 1 for
frame-based output; a value of 1 produces sample-based output. See
“Importing a Multichannel Sample-Based Signal” on page 3-62 for more
information.
The Sample-time parameter specifies the sample period, Ts, of the
frame-based output. The frame period of the signal is M∗Ts, where M is the
value of the Samples per frame parameter. See “Frame-Based Multichannel
Signals” on page 3-12 for general information about frame-based signals.
The following section explains how the Signal From Workspace generates its
frame-based output.

Importing a Frame-Based Signal with

the Signal From Workspace Block
The Signal From Workspace block generates a frame-based multichannel
signal when the variable (or expression) in the Signal parameter is a matrix,
and the Samples per frame parameter specifies a value M greater than 1.

3-68
 Importing Signals

Beginning with the first M rows of the matrix, the block releases M rows of the
matrix (i.e., one frame from each channel) to the output every M∗Ts seconds.
Therefore, if the Signal parameter specifies a W-by-N workspace matrix, the
output of the Signal From Workspace block is an M-by-N matrix representing
N channels.
The figure below illustrates this for a 6-by-4 workspace matrix, A, and a frame
size of 2.

sample 5 5 5 5 5
1 1 1 1
sample 6 6 6 6 6
2 2 2 2
3 3 3 3 sample 3 3 3 3 3
4 4 4 4 sample 4 4 4 4 4
5 5 5 5
sample 1 1 1 1 1
6 6 6 6
sample 2 2 2 2 2
ch1 ch2 ch3 ch4
ch1 ch2 ch3 ch4

MATLAB workspace matrix, A : Frame-based signal :

4 channels, 6 samples each 4 channels, 2 samples per frame

As the figure above suggests, the output of the Signal From Workspace block
can only be a valid frame-based signal (having N independent channels) if the
W-by-N workspace matrix A in fact represents N independent channels. In
other words, the workspace matrix must be oriented so as to have the
independent channels as its columns.

Note Although independent channels are generally represented as columns,

a single-channel signal can be represented in the workspace as either a
column vector or row vector. The output from the Signal From Workspace
block is a column vector in both cases.

When the block has output all of the rows available in the specified variable, it
can start again at the beginning of the signal, or simply repeat the final value
(or generate zeros) until the end of the simulation. This behavior is controlled

3-69
3 Working with Signals

by the Form output after final data value by parameter. See the Signal From
Workspace reference page for more information.
The following example illustrates how the Signal From Workspace block is
used to import a frame-based multichannel signal into a model.

Example: Importing a Frame-Based Signal. In the model below, the Signal From
Workspace creates a three-channel frame-based signal with the following data:

• Channel 1: 1, 2, 3, 4, 5,..., 100, 0, 0, 0,...

• Channel 2: -1, -2, -3, -4, -5,..., -100, 0, 0, 0,...
• Channel 3: 5, 5, 5, 5, 5,..., 0, 0, 0,...

The frame size is four samples.

t=8 t=4 t=0
9 –9 5 5 –5 5 1 –1 5
10 – 10 5 6 –6 5 2 –2 5
11 – 11 5 7 –7 5 3 –3 5
12 – 12 5 8 –8 5 4 –4 5

Three consecutive frames from a

3-channel frame-based signal

To create the model, define the following variables at the MATLAB command
line.
A = [1:100;-1:-1:-100]'; % 100-by-2 matrix
B = 5*ones(100,1); % 100-by-1 column vector

Matrix A represents a two-channel signal with 100 samples, and matrix B

represents a one-channel signal with 100 samples.
Specify the following parameter values in the Signal From Workspace block:

• Signal = [A B]
• Sample time = 1
• Samples per frame = 4
• Form output after final data value = Setting to zero

3-70
 Importing Signals

The Signal expression [A B] uses the standard MATLAB syntax for

horizontally concatenating matrices and appends column vector B to the right
of matrix A. Equivalently, you could set Signal = C, and define C at the
command line by
C = [A B]

The Sample time setting of 1 and Samples per frame setting of 4 yield a
frame-based output with sample period of 1 second and frame period of
4 seconds. The Form output after final data value parameter setting
specifies that all samples after the hundredth are zero.

Importing WAV Files

The key blocks for importing WAV audio files are:

• From Wave Device

• From Wave File

See the reference pages for complete information.

3-71
3 Working with Signals

Exporting Signals
The To Workspace and Triggered To Workspace blocks are the primary
conduits for exporting signals from a Simulink model to the MATLAB
workspace. The following sections explain how to use these important blocks:

• “Exporting Multichannel Signals” on page 3-72

• “Exporting and Playing WAV Files” on page 3-79

Exporting Multichannel Signals

The To Workspace block in the Simulink Sources library is the key block for
exporting signals of all dimensions to the MATLAB workspace.

The dialog box has the following parameters:

• Variable name
• Limit data points to last
• Decimation
• Sample time
• Save format
Use the Variable name parameter to specify the workspace variable in which
the output should be saved. (An existing output with the same name is
overwritten.)
The Limit data points to last parameter specifies how many of the most recent
output samples should be retained in the specified workspace variable. For
example, if you specify Limit data points to last = 100, then even if the
simulation propagates thousands of samples to the To Workspace block, only
the most recent 100 samples will actually be saved in the workspace. By setting
a limit on the number of saved samples, you can prevent out-of-memory errors
for long-running simulations. Note, however, that the default setting for Limit
data points to last is inf, which allows the workspace variable to grow
indefinitely large.
The default values of 1 and -1 for the Decimation and Sample time
parameters (respectively) are generally adequate for DSP models. If you want

3-72
 Exporting Signals

to downsample a signal before exporting to the workspace, consider using the

Downsample or FIR Decimation blocks. See “Converting Sample Rates and
Frame Rates” on page 3-20 for more information about rate conversion.
The Save format parameter allows you to save the output in a variety of
formats. The default is Array, which is also generally the most accessible
output format. Although this format does not save a record of the sample times
corresponding to the output samples, you can create such a record for a given
model by selecting the Time option in the Workspace I/O panel of the
Simulation Parameters dialog box. See “Performance-Related Settings” on
page 2-13 for more information.
The following sections explain how the To Workspace block generates its
output:

• “Exporting a Sample-Based Signal Using the To Workspace Block” on

page 3-73
• “Exporting a Frame-Based Signal Using the To Workspace Block” on
page 3-76

The following two sections may also be of interest:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38
• “Constructing Multichannel Sample-Based Signals” on page 3-42

Exporting a Sample-Based Signal Using the To Workspace Block

Recall that a sample-based signal with M∗N channels is represented by a
sequence of M-by-N matrices. (The special case of M = N = 1 represents a
single-channel signal.) When the input to the To Workspace block is a
sample-based signal (and the Save format parameter is set to Array), the
block creates an M-by-N-by-P array in the MATLAB workspace containing the
P most recent samples from each channel. The number of pages, P, is specified
by the Limit data points to last parameter. The newest samples are added at
the back of the array.
The figure below illustrates this for a 6-by-4 sample-based signal exported to
workspace array A.

3-73
3 Working with Signals

1 1 1 1
1 1 1 1
1 1 1 1
2 2 2 2
11 1 1
2 2 2 2
1 1 1 1 5 5 5 5
2 2 2 2
3 3 3 31 1 1 1 sample 1 5 4 2 4 2 4 2 4
2 2 2 2 3
3 3 2 2 5 4 2 2 23 2 23 2 3
2 2 2 2 3 2 2 2 2
3 3 2 2 5 4 2 2 22 2 22 2 2
4 4 4 42 2 2 2 2 1 2 1 1 2 1
3 3 2 2 sample 2 4 3 2 22 2 22
2
2 2
4 4 2 2 5 2
3 2 1 2 1 2 1 2 1
3 3 3 3 5 4 2 2 22 2 22 2 2
4 4 2 2 2 1 2 1 2 1 2 1
3 3 3 3 sample 3 4 3 2 2 2 2 2 2
4 4 2 2
3 2 21 2 21 2 1
2 2 1
4 4 4 4 2 1 2 1 2 1 2 1
4 4 4 4 sample 4 1 1 1 1

Sample-based matrix signal : MATLAB workspace array, A :

6-by-4 (24 channels) 6-by-4-by-P (24 channels)

The workspace array always has time running along its third (P) dimension.
Samples are saved along the P dimension whether the input is a matrix, vector,
or scalar (single channel).
The following example illustrates how the To Workspace block can be used to
export a sample-based matrix signal to the MATLAB workspace.

Example: Exporting a Sample-Based Matrix Signal. In the model below, the

To Workspace block exports a four-channel sample-based signal with the
following data:

• Channel 1: 1, 2, 3, 4, 5,..., 100, 0, 0, 0,...

• Channel 2: -1, -2, -3, -4, -5,..., -100, 0, 0, 0,...
• Channel 3: 0, 0, 0, 0, 0,...
• Channel 4: 5, 5, 5,..., 0, 0, 0,...

The first four consecutive samples are shown in the figure.

3-74
 Exporting Signals

4 –4 3 –3 2 –2 1 –1
0 5 0 5 0 5 0 5

t=3 t=2 t=1 t=0

first matrix output

Four consecutive samples from a

4-channel sample-based signal

To create the model, define the following variables at the MATLAB command
line.
sig1 = reshape(1:100,[1 1 100]) % 1-by-1-by-100 array
sig2 = reshape(-1:-1:-100,[1 1 100]) % 1-by-1-by-100 array
sig3 = zeros(1,1,100) % 1-by-1-by-100 array
sig4 = 5*ones(1,1,100) % 1-by-1-by-100 array
sig12 = cat(2,sig1,sig2) % 1-by-2-by-100 array
sig34 = cat(2,sig3,sig4) % 1-by-2-by-100 array

A = cat(1,sig12,sig34) % 2-by-2-by-100 array

Array A represents a four-channel signal with 100 samples.

Specify the following parameter values in the Signal From Workspace block:

• Signal = A
• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero

Specify the following parameter values in the To Workspace block:

• Variable name = yout

• Limit data points to last = inf
• Decimation = 1
• Sample time = -1
• Save format = Array

Run the model, and look at output yout. The first four samples (pages) are
shown below.

3-75
3 Working with Signals

yout(:,:,1:4)

ans(:,:,1) =

1 -1
0 5

ans(:,:,2) =

2 -2
0 5

ans(:,:,3) =

3 -3
0 5

ans(:,:,4) =

4 -4
0 5

Exporting a Frame-Based Signal

Using the To Workspace Block
Recall that a frame-based signal with N channels and frame size M is
represented by a sequence of M-by-N matrices. (The special case of N = 1
represents a single-channel signal.) When the input to the To Workspace block
is a frame-based signal (and the Save format parameter is set to Array), the
block creates an P-by-N array in the MATLAB workspace containing the P
most recent samples from each channel. The number of rows, P, is specified by
the Limit data points to last parameter. The newest samples are added at the
bottom of the matrix.
The figure below illustrates this for three consecutive frames of a frame-based
signal (two samples per frame) exported to matrix A.

3-76
 Exporting Signals

1 1 1 1 sample 1 1 1 1 1
2 2 2 2 sample 2 2 2 2 2
3 3 3 3
3 3 3 3 sample 3
4 4 4 4 sample 4 4 4 4 4
5 5 5 5
5 5 5 5 sample 5 6 6 6 6
6 6 6 6 sample 6
ch1 ch2 ch3 ch4
ch1 ch2 ch3 ch4

Frame-based signal : MATLAB workspace matrix, A :

4 channels, 2 samples per frame 4 channels

The workspace matrix always has time running along its first (P) dimension.
Samples are saved along the P dimension whether the input is a matrix, vector,
or scalar (single channel).
The following example illustrates how the To Workspace block can be used to
export a frame-based multichannel signal to the MATLAB workspace.

Example: Exporting a Frame-Based Signal. In the model below, the To Workspace

block exports a three-channel frame-based signal with the following data:

• Channel 1: 1, 2, 3, 4, 5,..., 100, 0, 0, 0,...

• Channel 2: -1, -2, -3, -4, -5,..., -100, 0, 0, 0,...
• Channel 3: 5, 5, 5, 5, 5,..., 0, 0, 0,...

t=8 t=4 t=0

9 –9 5 5 –5 5 1 –1 5
10 – 10 5 6 –6 5 2 –2 5
11 – 11 5 7 –7 5 3 –3 5
12 – 12 5 8 –8 5 4 –4 5

Three consecutive frames from a

3-channel frame-based signal

3-77
3 Working with Signals

To create the model, define the following variables at the MATLAB command
line.
A = [1:100;-1:-1:-100]'; % 100-by-2 matrix
B = 5*ones(100,1); % 100-by-1 column vector

Matrix A represents a two-channel signal with 100 samples, and matrix B

represents a one-channel signal with 100 samples.
Specify the following parameter values in the Signal From Workspace block:

• Signal = [A B]
• Sample time = 1
• Samples per frame = 4
• Form output after final data value = Setting to zero

The Sample time setting of 1 and Samples per frame setting of 4 yield a
frame-based output with sample period of 1 second and frame period of
4 seconds.
Specify the following parameter values in the To Workspace block:

• Variable name = yout

• Limit data points to last = inf
• Decimation = 1
• Sample time = -1
• Save format = Array

Run the model, and look at output yout. The first 10 samples (rows) are shown.
yout =

1 -1 5
2 -2 5
3 -3 5
4 -4 5
5 -5 5
6 -6 5
7 -7 5
8 -8 5
9 -9 5
10 -10 5

3-78
 Exporting Signals

The following two sections may also be of interest:

• “Creating Signals Using the Signal From Workspace Block” on page 3-38
• “Constructing Multichannel Sample-Based Signals” on page 3-42

Exporting and Playing WAV Files

The key blocks for exporting and playing WAV audio files are:

• To Wave Device
• To Wave File

The To Wave Device and To Wave File blocks are limited to one-channel (mono)
or two-channel (stereo) inputs, selectable in the Stereo check box. See the
reference pages for complete information.
The following demos may also be of interest:

• Audio Flanger – PC/Windows

• Demonstration of Audio Reverberation
• Basic LPC Speech Coding - PC/Windows

3-79
3 Working with Signals

Viewing Signals
The following blocks in the DSP Sinks library are the key blocks for displaying
signals:

• Matrix Viewer
• Spectrum Scope
• Time Scope (Simulink Scope)
• Vector Scope

The following sections provide an introduction to how these blocks are

commonly used:

• “Displaying Signals in the Time-Domain” on page 3-80

• “Displaying Signals in the Frequency-Domain” on page 3-82
• “Displaying Matrices” on page 3-83

Displaying Signals in the Time-Domain

The Vector Scope block can display both time-domain and frequency-domain
data. It differs from the Spectrum Scope in that it does not compute the FFT of
inputs.

Example: Displaying Time-Domain Data

In the model below, two frame-based signals are simultaneously displayed on
the scope.

To create the model, first load the mtlb signal.

load mtlb % Contains variables 'mtlb' and 'Fs'

3-80
 Viewing Signals

Specify the following parameter values in the Signal From Workspace block:

• Signal = mtlb
• Sample time = 1
• Samples per frame = 16
• Form output after final data value = Cyclic Repetition

Specify the following parameter values in the Digital Filter Design block:

• Filter Type = Lowpass

• Design Method = FIR (Window)
• Filter Order (Specify order) = 22
• Window Specifications (Window) = Hamming
• Frequency Specifications (wc) = 0.25
• Frequency Specifications (Units) = Normalized (0 to 1)
• Magnitude Specifications (Units) = dB

Specify the following parameter values in the Scope properties pane of the
Vector Scope block:

• Input domain = Time

• Time display span (number of frames) = 2

When you run the model, the Vector Scope block plots two consecutive frames
of each channel at each update. You may want to set the Stop time in the
Simulation Parameters dialog box to inf to allow the simulation to run
longer. The following section provides a few tips for improving the display.

Improving the Appearance of the Display. You may want to alter the appearance of
the scope display by making some of the following adjustments from the
right-click popup menu. To access the right-click menu, click with the right
mouse button anywhere in the plot region. These options are also available
from the Axes and Channels menus that are visible at the top of the window
when Compact display is not selected. You can make all of these changes
while the simulation is running:

• Select Autoscale at any time from the right-click menu to rescale the vertical
axis to best fit the most recently displayed data.

3-81
3 Working with Signals

• Select Compact display from the right-click menu to allow the scope to use
all the available space in the window.
• Select CH 1 from the right-click menu, and then select Marker and “o” from
the submenus, to mark the data points on the channel 1 signal with circles.
• Select CH 1 from the right-click menu, and then select Color and Blue from
the submenus, to code the channel 1 signal with the color blue.
• Select CH 2 from the right-click menu, and then select Marker and
Diamond from the submenus, to mark the data points on the channel 2
signal with diamonds.

Displaying Signals in the Frequency-Domain

The Spectrum Scope block can display the frequency spectra of time-domain
input data. It differs from the Vector Scope by computing the FFT of inputs to
transform them to the frequency domain.

Example: Displaying Frequency-Domain Data

In the model below, the frequency content of two frame-based signals is
simultaneously displayed on the scope.

To create the model, first load the mtlb signal.

load mtlb % Contains variables 'mtlb' and 'Fs'

Specify the following parameter values in the Signal From Workspace block:

• Signal = mtlb
• Sample time = 1
• Samples per frame = 16
• Form output after final data value = Cyclic Repetition

Specify the following parameter values in the Digital Filter Design block:

3-82
 Viewing Signals

• Filter Type = Lowpass

• Design Method = FIR (Window)
• Filter Order (Specify order) = 22
• Window Specifications (Window) = Hamming
• Frequency Specifications (wc) = 0.25
• Frequency Specifications (Units) = Normalized (0 to 1)
• Magnitude Specifications (Units) = dB

Specify the following parameter values in the Scope properties pane of the
Spectrum Scope block:

• Buffer input =
• Buffer size = 128
• Buffer overlap = 64
• Specify FFT length =
• Number of spectral averages = 2

With these settings, the Spectrum Scope block buffers each input channel to a
new frame size of 128 (from the original frame size of 16) with an overlap of 64
samples between consecutive frames. Because Specify FFT length is not
selected, the frame size of 128 is used as the number of frequency points in the
FFT. This is the number of points plotted for each channel every time the scope
display is updated.
You may want to set the Stop time in the Simulation Parameters dialog box
to inf to allow the simulation to run longer. See “Improving the Appearance of
the Display” on page 3-81 for some tips on improving the scope display.

Displaying Matrices
The Matrix Viewer block provides general matrix display capabilities that can
be used with all matrix signals (frame-based and sample-based).

Example: Displaying Matrices

In the model below, a matrix of shifted sinusoids is displayed with the Matrix
Viewer block.

3-83
3 Working with Signals

To build the model, specify the following parameter values in the Sine Wave
block:

• Amplitude = 1
• Frequency = 100
• Phase offset = 0:pi/64:pi

Specify the following parameter values in the Submatrix block:

• Row span = All rows

• Column span = Range of columns
• Starting column = First
• Ending column = Offset from last
• Ending column offset = 1

Specify the following parameter values in the Reshape block:

• Output dimensionality = Customize

• Output dimensions = [8,8]

Specify Colormap matrix = bone(256) in the Image properties pane of the

Matrix Viewer block.
When you run the model, the Matrix Viewer displays each 8-by-8 matrix as it
is received. The 256 shades in the specified bone colormap are mapped to the
range of values specified by the Minimum input value and Maximum input
value parameters; see colormap for more information. In this example, these
values are -1.0 and 1.0 respectively, which are appropriate for the sinusoids
of amplitude 1 that compose the input signal.

3-84
 Delay and Latency

Delay and Latency

There are two distinct types of delay that affect Simulink models:
• Computational delay
• Algorithmic delay

The following sections explain how you can configure Simulink to minimize
both varieties of delay and increase simulation performance.

Computational Delay
The computational delay of a block or subsystem is related to the number of
operations involved in executing that component. For example, an FFT block
operating on a 256-sample input requires Simulink to perform a certain
number of multiplications for each input frame. The actual amount of time that
these operations consume (as measured in a benchmark test, for example)
depends heavily on the performance of both the computer hardware and
underlying software layers, such as MATLAB and the operating system.
Computational delay for a particular model therefore typically varies from one
computer platform to another.
The simulation time represented on a model’s status bar (which can be
accessed via Simulink’s Digital Clock block) does not provide any information
about computational delay. For example, according to the Simulink timer, the
FFT mentioned above executes instantaneously, with no delay whatsoever. An
input to the FFT block at simulation time t=25.0 is processed and output at
time t=25.0, regardless of the number of operations performed by the FFT
algorithm. The Simulink timer reflects only algorithmic delay (described
below), not computational delay.
The next section discussed methods of reducing computational delay.

Reducing Computational Delay

There are a number of ways to reduce computational delay without actually
running the simulation on faster hardware. To begin with, you should
familiarize yourself with “Improving Simulation Performance and Accuracy” in
the Simulink documentation, which describes some basic strategies. The
section below supplements that information with several additional options for
improving performance.

3-85
3 Working with Signals

A first step in improving performance is to analyze your model, and eliminate

or simplify elements that are adding excessively to the computational load.
Such elements might include scope displays and data logging blocks that you
had put in place for debugging purposes and no longer require. In addition to
these model-specific adjustments, there are a number of more general steps
you can take to improve the performance of any model:

• Use frame-based processing wherever possible. It is advantageous for the

entire model to be frame-based. See “Benefits of Frame-Based Processing” on
page 3-14 for more information.
• Use the dspstartup file to tailor Simulink for DSP models, or manually
make the adjustments described in “Performance-Related Settings” on
page 2-13.
• Turn off the Simulink status bar by deselecting the Status bar option in the
View menu. Simulation speed will improve, but the time indicator will not
be visible.
• Run your simulation from the MATLAB command line by typing
sim(gcs)
This method of launching a simulation can greatly increase the simulation
speed, but also has several limitations:
- You cannot interact with the simulation (to tune parameters, for instance).
- You must press Ctrl+C to stop the simulation, or specify start and stop
times.
- There are no graphics updates in M-file S-functions, which include blocks
such as the frame scopes (Vector Scope, etc.).
• Use the Real-Time Workshop to generate generic real-time (GRT) code
targeted to your host platform, and simulate the model using the generated
executable file. See the Real-Time Workshop documentation for more
information.

Algorithmic Delay
Algorithmic delay is delay that is intrinsic to the algorithm of a block or
subsystem, and is independent of CPU speed. In Chapter 5, “DSP Block
Reference,” and elsewhere in this guide, the algorithmic delay of a block is
referred to simply as the block’s delay. It is generally expressed in terms of the
number of samples by which a block’s output lags behind the corresponding

3-86
 Delay and Latency

input. This delay is directly related to the time elapsed on the Simulink timer
during that block’s execution.
The algorithmic delay of a particular block may depend on both the block’s
parameter settings and the general Simulink settings. To simplify matters, it
is helpful to categorize a block’s delay using the following levels:

• Zero algorithmic delay

• Basic algorithmic delay
• Excess algorithmic delay (tasking latency)

The following sections explain the different levels of delay, and how the
simulation and parameter settings can affect the level of delay that a
particular block experiences.

Zero Algorithmic Delay

The FFT block is an example of a component that has no algorithmic delay; the
Simulink timer does not record any passage of time while the block computes
the FFT of the input, and the transformed data is available at the output in the
same time step that the input is received. There are many other blocks that
have zero algorithmic delay, such as the blocks in the Matrices and Linear
Algebra libraries. Each of those blocks processes its input and generates its
output in a single time step.
In Chapter 5, “DSP Block Reference,” blocks are assumed to have zero delay
unless otherwise indicated. In cases where a block has zero delay for one
combination of parameter settings but nonzero delay for another, this is noted
on the block’s reference page.

Example: Zero Algorithmic Delay. Create the model below to observe the operation
of the zero-delay Normalization block.

3-87
3 Working with Signals

Use the default settings for the Normalization, Digital Clock, Mux, and To
Workspace blocks, and adjust the Signal From Workspace block parameters as
follows:

• Signal = 1:100
• Sample time = 1/4
• Samples per frame = 4

Select Sample-based from the Output signal menu in the Frame Status
Conversion block.
Note that the current value of the Simulink timer (from the Digital Clock block)
is prepended to each output frame. The frame-based signal is converted to a
sample-based signal by the Frame Status Conversion so that the output in the
command window will be more easily readable.
In the example, the Signal From Workspace block generates a new frame
containing four samples once every second (Tfo = ¼∗4). The first few output
frames are shown below.
(t=0) [ 1 2 3 4]'
(t=1) [ 5 6 7 8]'
(t=2) [ 9 10 11 12]'
(t=3) [13 14 15 16]'
(t=4) [17 18 19 20]'

When you run the simulation, the normalized output, yout, is saved in a
workspace array. To convert the array to an easier-to-read matrix format, type
squeeze(yout)'

The first few samples of the result, ans, are shown below.
ans =

0 0.0333 0.0667 0.1000 0.1333

1.0000 0.0287 0.0345 0.0402 0.0460
2.0000 0.0202 0.0224 0.0247 0.0269
3.0000 0.0154 0.0165 0.0177 0.0189
4.0000 0.0124 0.0131 0.0138 0.0146
time

3-88
 Delay and Latency

The first column of ans is the Simulink time provided by the Digital Clock
block. You can see that the squared 2-norm of the first input,
[1 2 3 4]' ./ sum([1 2 3 4]'.^2)

appears in the first row of the output (at time t=0), the same time step that the
input was received by the block. This indicates that the Normalization block
has zero algorithmic delay.

Zero Algorithmic Delay and Algebraic Loops. When several blocks with zero
algorithmic delay are connected in a feedback loop, Simulink may report an
algebraic loop error and performance may generally suffer. You can prevent
algebraic loops by injecting at least one sample of delay into a feedback loop (for
example, by including an Integer Delay block with Delay > 0). See the
Simulink documentation for more information about algebraic loops.

Basic Algorithmic Delay

A typical example of a block that does have algorithmic delay is the Variable
Integer Delay block.

The input to the Delay port of the block specifies the number of sample periods
that should elapse before an input to the In port is released to the output. This
value represents the block’s algorithmic delay. For example, if the input to the
Delay port is a constant 3, and the sample period at both ports is 1, then a
sample that arrives at the block’s In port at time t=0 is released to the output
at time t=3.

Example: Basic Algorithmic Delay. Create the model shown below to observe the
operation of a block with basic delay.

3-89
3 Working with Signals

Use the default settings for the Digital Clock, Mux, and To Workspace blocks,
and adjust the Signal From Workspace block’s parameters to the values below:

• Signal = 1:100
• Sample time = 1
• Samples per frame = 1

Set the DSP Constant block’s Constant value parameter to 3, and set the
Variable Integer Delay block’s Initial conditions parameter to -1.
Now run the simulation and look at the output, yout. The first few samples are
shown below.
yout =

0 -1
1 -1
2 -1
3 1
4 2
5 3
time

The first column of yout is the Simulink time provided by the Digital Clock
block, and the second column is the delayed input. As expected, the input to the
block at t=0 is delayed three samples, and appears as the fourth output sample,
at t=3. You can also see that the first three outputs from the Variable Integer
Delay block inherit the value of the block’s Initial conditions parameter, -1.
This period of time, from the start of the simulation until the first input is
propagated to the output, is sometimes called the initial delay of the block.
Many blocks in the DSP Blockset have some degree of fixed or adjustable
algorithmic delay. These include any blocks whose algorithms rely on delay or
storage elements, such as filters or buffers. Often (but not always), such blocks
provide an Initial conditions parameter that allows you to specify the output
values generated by the block during the initial delay. In other cases, the initial
conditions are internally fixed at 0.
Consult “DSP Block Reference” on page 5-1 for the delay characteristics of
particular DSP blocks.

3-90
 Delay and Latency

Excess Algorithmic Delay (Tasking Latency)

Under certain conditions, Simulink may force a block to delay inputs longer
than is strictly required by the block’s algorithm. This excess algorithmic delay
is called tasking latency, because it arises from synchronization requirements
of Simulink’s tasking mode. A block’s overall algorithmic delay is the sum of its
basic delay and tasking latency.
Algorithmic delay = Basic algorithmic delay + Tasking latency
The tasking latency for a particular block may be dependent on the following
block and model characteristics:

• Simulink tasking mode

• Block rate type
• Model rate type
• Block sample mode

Simulink Tasking Mode. Simulink has two tasking modes:

• Single-tasking
• Multitasking

Select a mode by choosing SingleTasking or MultiTasking from the Mode

pop-up menu in the Solver panel of the Simulation Parameters dialog box.
The Mode pop-up menu is only available when the Fixed-step option is
selected from the Type pop-up menu. (When the Variable-step option is
selected from the Type pop-up menu, Simulink always operates in
single-tasking mode.) The Auto option in the Mode pop-up menu automatically
selects single-tasking operation if the model is single-rate (see below), or
multitasking operation if the model is multirate.
Many multirate blocks have reduced latency in Simulink’s single-tasking mode;
check the “Latency” section of a multirate block’s reference page for details.
Also see “The Simulation Parameters Dialog Box” in the Simulink
documentation for more information about the tasking modes and other
simulation options.

Block Rate Type. A block is called single-rate when all of its input and output
ports operate at the same frame rate (as indicated by identical Probe block
measurements or sample time color coding on the input and output lines). A

3-91
3 Working with Signals

block is called multirate when at least one input or output port has a different
frame rate than the others.
Many blocks are permanently single-rate, which means that all input and
output ports always have the same frame rate. For other blocks, the block
parameter settings determine whether the block is single-rate or multirate.
Only multirate blocks are subject to tasking latency.

Note Simulink may report an algebraic loop error if it detects a feedback loop
composed entirely of multirate blocks. To break such an algebraic loop, insert
a single-rate block with nonzero delay, such as a Unit Delay block. For more
information about algebraic loops, see “Algebraic Loops” in the Simulink
documentation.

Model Rate Type. When all ports of all blocks in a model operate at a single frame
rate, the model is called single-rate. When the model contains blocks with
differing frame rates, or at least one multirate block, the model is called
multirate. Note that Simulink prevents a single-rate model from running in
multitasking mode by generating an error.

Block Sample Mode. Many blocks can operate in either sample-based or

frame-based modes. In source blocks, the mode is usually determined by the
Samples per frame parameter; a value of 1 for this parameter indicates
sample-based mode, while a value greater than 1 indicates frame-based mode.
In nonsource blocks, the sample mode is determined by the input signal. See
Chapter 5, “DSP Block Reference,” for additional information on particular
blocks.

Predicting Tasking Latency

The specific amount of tasking latency created by a particular combination of
block parameter and simulation settings is described in the “Latency” section
of the reference page for the block in question. The following examples show
how to use Chapter 5, “DSP Block Reference,” to predict tasking latency:

• “Example: Nonzero Tasking Latency” on page 3-93

• “Example: Zero Tasking Latency” on page 3-95

3-92
 Delay and Latency

Example: Nonzero Tasking Latency. Most multirate blocks experience tasking

latency only in Simulink’s multitasking mode. As an example, consider the
following model.

To engage Simulink’s multitasking mode, adjust the following settings in the

Solver panel of the Simulation Parameters dialog box:

• Type = Fixed-step
• Mode = MultiTasking

Use the default settings for the Mux and To Workspace blocks. Adjust the other
blocks’ parameter settings as follows:

• Set the Signal From Workspace block’s parameters to the values below.
- Signal = 1:100
- Sample time = 1/4
- Samples per frame = 4
• Set the Upsample block’s parameters to the values below. The Maintain
input frame size setting of the Frame-based mode parameter makes the
block (and model) multirate since the input and output frame rates will not
be equal.
- Upsample factor = 4
- Sample offset = 0
- Initial condition = -1
- Frame-based mode = Maintain input frame size
• Set the Sample time parameter of the Digital Clock block to 0.25 to match
the sample period of the Upsample block’s output.

3-93
3 Working with Signals

• Set the Output signal parameter of the Frame Status Conversion block to
Sample-based.

Notice that the current value of the Simulink timer (from the Digital Clock
block) is prepended to each output frame. The frame-based signal is converted
to a sample-based signal by the Frame Status Conversion block so that the
output in the command window will be easily readable.
In the example, the Signal From Workspace block generates a new frame
containing four samples once every second (Tfo = ¼∗4). The first few output
frames are shown below.
(t=0) [ 1 2 3 4]
(t=1) [ 5 6 7 8]
(t=2) [ 9 10 11 12]
(t=3) [13 14 15 16]
(t=4) [17 18 19 20]

The Upsample block upsamples the input by a factor of 4, inserting three zeros
between each input sample. The change in rates is confirmed by the Probe
blocks in the model, which show a decrease in the frame period from Tfi = 1 to
Tfo = 0.25.
Question: When does the first input sample appear in the output?
The “Latency and Initial Conditions” section of the reference page for the
Upsample block indicates that when Simulink is in multitasking mode, the
first sample of the block’s frame-based input appears in the output as
sample MiL+D+1, where Mi is the input frame size, L is the Upsample factor,
and D is the Sample offset. This formula therefore predicts that the first input
in this example should appear as output sample 17 (i.e., 4∗4+0+1).
To verify this, look at the output from the simulation, saved in the workspace
array yout. To convert the array to a easier-to-read matrix format, type
squeeze(yout)'

The first few samples of the result, ans, are shown below.

3-94
 Delay and Latency

ans =

0 -1.0000 0 0 0 1st output frame

0.2500 -1.0000 0 0 0
0.5000 -1.0000 0 0 0
0.7500 -1.0000 0 0 0
1.0000 1.0000 0 0 0 5th output frame
1.2500 2.0000 0 0 0
1.5000 3.0000 0 0 0
1.7500 4.0000 0 0 0
2.0000 5.0000 0 0 0
time

The first column of yout is the Simulink time provided by the Digital Clock
block. The four values to the right of each time are the values in the output
frame at that time. You can see that the first sample in each of the first four
output frames inherits the value of the block’s Initial conditions parameter.
As a result of the tasking latency, the first input value appears only as the first
sample of the 5th output frame (at t=1), which is sample 17.

Example: Zero Tasking Latency. Now try the previous example in Simulink’s
single-tasking mode. The model and all of the block parameter settings are the
same.

To engage Simulink’s single-tasking mode, adjust the following settings in the

Solver panel of the Simulation Parameters dialog box:

• Type = Fixed-step
• Mode = SingleTasking

When does the first input sample appear in the output?

3-95
3 Working with Signals

The “Latency and Initial Conditions” section of the reference page for
Upsample indicates that the block has zero latency for all multirate operations
in Simulink’s single-tasking mode. To verify this, look at the output from the
simulation, squeeze(yout)'. The first few samples are shown below.
ans =

0 1.0000 0 0 0 1st output frame

0.2500 2.0000 0 0 0
0.5000 3.0000 0 0 0
0.7500 4.0000 0 0 0
1.0000 5.0000 0 0 0 5th output frame
1.2500 6.0000 0 0 0
1.5000 7.0000 0 0 0
1.7500 8.0000 0 0 0
2.0000 9.0000 0 0 0
time

The first column of yout is the Simulink time provided by the Digital Clock
block. The four values to the right of each time are the values in the output
frame at that time.
You can see that the first input value appears as the first sample of the first
output frame (at t=0), as expected for zero-latency operation. Running this
model under Simulink’s single-tasking mode therefore eliminates the
17-sample delay that the model experiences under Simulink’s multitasking
mode (for the particular parameter settings in the example).

3-96
 4

DSP Operations
Overview . . . . . . . . . . . . . . . . . . . . . 4-2

Filters . . . . . . . . . . . . . . . . . . . . . . . 4-3

Transforms . . . . . . . . . . . . . . . . . . . . 4-10

Power Spectrum Estimation . . . . . . . . . . . . . 4-15

Linear Algebra . . . . . . . . . . . . . . . . . . . 4-16

Statistics . . . . . . . . . . . . . . . . . . . . . 4-21
DSP Blockset Demos Overview . . . . . . . . . . . 4-24
4 DSP Operations

Overview
This chapter discusses some basic DSP operations, and how they can be
implemented using the DSP Blockset. The following topics are covered:
• “Filters”
• “Transforms”
• “Power Spectrum Estimation”
• “Linear Algebra”
• “Statistics”

The discussion and examples included in these sections should help you
become familiar with the standard operations involved in simulating DSP
models. See Chapter 3, “Working with Signals” for more basic information on
sample rates, matrices, and frame-based processing.
A final section, “DSP Blockset Demos Overview” on page 4-24, provides a look
at the demonstration models that accompany the DSP Blockset.

4-2
 Filters

Filters
Filtering is one of the most important operations in signal processing, and is
supported in the DSP Blockset with three libraries of filtering blocks. The
following sections present a brief overview of these libraries:

• “Adaptive Filters” on page 4-3

• “Filter Designs” on page 4-4
• “Multirate Filters” on page 4-9

All libraries are located within the top-level Filtering library.

Adaptive Filters
Adaptive filters are filters whose transfer function coefficients or taps change
over time in response to an external error signal. The Adaptive Filters library
contains the following blocks:

• Kalman Adaptive Filter

• LMS Adaptive Filter
• RLS Adaptive Filter

The DSP Blockset provides a collection of adaptive filtering demos to illustrate

typical applications of these blocks:

• LMS Adaptive Equalization (lmsadeq)

• LMS Adaptive Linear Prediction (lmsadlp)
• LMS Adaptive Noise Cancellation (lmsdemo)
• LMS Adaptive Time-Delay Estimation (lmsadtde)
• Nonstationary Channel Estimation (kalmnsce)
• RLS Adaptive Noise Cancellation (rlsdemo)

Open the demos by clicking on the demo names above in the MATLAB Help
browser. Alternatively, open the demos by typing the demo name (provided in
parentheses above) at the MATLAB command line.

4-3
4 DSP Operations

Filter Designs
Filter Designs library blocks apply specified filters to an input signal and
output the result. Depending on the block, you specify a filter with its filter
coefficients, or by setting filter specification parameters. The following table
categorizes Filter Designs library blocks by the types of filters they implement.

Filter Designs Library Blocks: Categorization and Description

Analog Filter Blocks

Analog Filter Design Implements a variety of non-time-varying time-domain analog

filters.
Digital Non-Time-Varying Time-Domain Filter Blocks

Digital Filter Design Implements a variety of digital FIR and IIR filters. You specify the
filter using the Filter Design and Analysis Tool (FDATool)
graphical user interface.

Filter Realization Wizard Implements custom digital non-time-varying time-domain filters.

Biquadratic Filter and These blocks are included in the library for backward compatibility
Direct-Form II Transpose of models using blocks from pervious DSP Blockset versions. To
Filter implement biquadratic and direct-form II transpose filters in new
models, use the Digital Filter Design block.
Digital Time-Varying Time-Domain Filter Blocks

Time-Varying Implements a direct-form II transpose whose filter coefficients can

Direct-Form II Transpose be updated during the simulation.
Filter

Time-Varying Lattice Implements a moving average or autoregressive lattice filter whose

Filter filter reflection coefficients can be updated during the simulation.
Digital Frequency-Domain Filter Blocks

Overlap-Add FFT Filter Implements frequency-domain filters with the overlap-add method.

Overlap-Save FFT Filter Implements frequency-domain filters with the overlap-save

method.

4-4
 Filters

For details about a particular block, consult its reference page. Also see the rest
of this section, which discuss the following topics in detail:

• “Designing Digital Filters with Direct-Form II Transposed Structures” on

page 4-5
• “Designing Filters with Various Filter Structures” on page 4-6
• “Designing Continuous-Time Classical IIR Filters” on page 4-7

Designing Digital Filters with Direct-Form II Transposed Structures

The Digital Filter Design block in the Filter Designs library integrates the
Filter Design and Analysis Tool (FDATool) graphical user interface with the
DSP Blockset. Double-licking this block opens the FDATool GUI, which you
can use to quickly design, import, or directly specify the coefficients of a digital
FIR or IIR filter. Using these coefficients, the block filters the input signal and
outputs the result within Simulink.
To design a filter in FDATool, you enter the desired filter response
characteristics, such as cutoff frequency and bandwidth. You can also enter the
filter coefficients directly. As soon as you apply your filter changes in FDATool,
the Digital Filter Design block automatically updates to implement the filter.
To learn more about the Digital Filter Design block, see the Digital Filter
Design block reference page. To learn how to use FDATool, see the FDATool
section of the Signal Processing Toolbox documentation.

4-5
4 DSP Operations

The FDATool GUI Opened from the Digital Filter Design Block

Designing Filters with Various Filter Structures

Any realizable filter can be represented in the time domain by a difference
equation of the form

y(k) = b 1 u(k) + b 2 u(k – 1) + L + b m u(k – m – 1)

– a 2 y(k – 1) – … – a n y ( k – n – 1 )

4-6
 Filters

where y(k) and u(k) are, respectively, the output and input at the current time
step, y(k-1) and u(k-1) are the output and input at the previous time step, and
so on. The values b1, b2, ..., bm, and a2, ..., an are the filter coefficients, or taps.
Every realizable filter is therefore fundamentally a collection of
multiplications, additions, and delays. The order in which these assorted
operations are implemented in practice determines the filter structure (also
known as the filter realization, architecture, or implementation).
Implementations may differ from each other in terms of speed, memory
requirements, delay, and quantization error. See “Linear System Models” in
the Signal Processing Toolbox documentation for more information about
common filter structures.
The Filter Designs library provides a number of blocks for designing filters
with various filter structures:
• Digital Filter Design
• Filter Realization Wizard
• Overlap-Add FFT Filter
• Overlap-Save FFT Filter
• Time-Varying Direct-Form II Transpose Filter
• Time-Varying Lattice Filter

See the following demos, which make use of many of the filter structure blocks:

• Frequency Domain Filtering (olapfilt)

• LPC Analysis and Synthesis of Speech (dsplpc)
• Sample Rate Conversion (dspsrcnv)

Open the demos by clicking on the demo names above in the MATLAB Help
browser. Alternatively, open the demos by typing the demo name (provided in
parentheses above) at the MATLAB command line.

Designing Continuous-Time Classical IIR Filters

The Analog Filter Design block designs and implements continuous-time IIR
filters with standard band configurations. All of the analog filter designs let

4-7
4 DSP Operations

you specify a filter order. The other available parameters depend on the filter
type and band configuration, as shown in the table below.

Configuration Butterworth Chebyshev I Chebyshev II Elliptic

Lowpass Ωp Ωp, Rp Ωs, Rs Ωp, Rp, Rs

Highpass Ωp Ωp, Rp Ωs, Rs Ωp, Rp, Rs
Bandpass Ωp1, Ωp2 Ωp1, Ωp2, Rp Ωs1, Ωs2, Rs Ωp1, Ωp2, Rp, Rs
Bandstop Ωp1, Ωp2 Ωp1, Ωp2, Rp Ωs1, Ωs2, Rs Ωp1, Ωp2, Rp, Rs

where:
Ωp = passband edge frequency
Ωp1 = lower passband edge frequency
Ωp2 = upper cutoff frequency
Ωs = stopband edge frequency
Ωs1 = lower stopband edge frequency
Ωs2 = upper stopband edge frequency
Rp = passband ripple in decibels
Rs = stopband attenuation in decibels

For all of the analog filter designs, frequency parameters are in units of radians
per second.
The block uses a state-space filter representation, and applies the filter using
the State-Space block in the Simulink Continuous library. All of the design
methods use Signal Processing Toolbox functions to design the filter:

• The Butterworth design uses the toolbox function butter.

• The Chebyshev type I design uses the toolbox function cheby1.
• The Chebyshev type II design uses the toolbox function cheby2.
• The elliptic design uses the toolbox function ellip.

The Analog Filter Design block is built on the filter design capabilities of the
Signal Processing Toolbox. For more information on the filter design
algorithms, see the Filter Designs section of the Signal Processing Toolbox
documentation.

4-8
 Filters

Note The Analog Filter Design block does not work with Simulink’s discrete
solver, which is enabled when the discrete option is selected in the Solver
panel of the Simulation Parameters dialog box. Select one of the continuous
solvers (e.g., ode4) instead.

Multirate Filters
Multirate filters are those which alter the sample rate of the input signal
during the filtering process. Such filters are useful in both rate conversion and
filter bank applications.
The Multirate Filters library provides a number of blocks for multirate
applications:

• Dyadic Analysis Filter Bank

• Dyadic Synthesis Filter Bank
• FIR Decimation
• FIR Interpolation
• FIR Rate Conversion
• Wavelet Analysis
• Wavelet Synthesis

The DSP Blockset additionally provides a number of demos that make use of
the multirate filter blocks:

• Denoising (dspwdnois)
• Multistage Multirate Filtering Suite (dspmrf_menu)
• Interpolation of a Sinusoidal Signal (dspintrp)
• Sample Rate Conversion (dspsrcnv)
• Sigma-Delta A/D Converter (dspsdadc)
• Three-Channel Wavelet Transmultiplexer (dspwvtrnsmx)
• Wavelet Perfect Reconstruction Filter Bank (dspwpr1)
• Wavelet Reconstruction (dspwlet)

4-9
4 DSP Operations

Transforms
The Transforms library provides blocks for a number of transforms that are of
particular importance in DSP applications:

• Analytic Signal
• Complex Cepstrum
• DCT
• FFT
• IDCT
• IFFT
• Real Cepstrum

First and foremost among these are of course the FFT and IFFT blocks, which
respectively implement the fast Fourier transform and its inverse. These
blocks are discussed further in the next section.

Using the FFT and IFFT Blocks

This section provides the following two example models that use the FFT and
IFFT blocks:

• “Example: Using the FFT Block”

• “Example: Using the IFFT Block”

The first example loosely follows the example in the “Discrete Fourier
Transform” section of the Signal Processing Toolbox documentation, where you
can also find additional background information on these transform
operations.

Example: Using the FFT Block

In the model below, the Sine Wave block generates two frame-based sinusoids,
one at 15 Hz and the other at 40 Hz. The sinusoids are summed point-by-point
to generate the compound sinusoid

u = sin ( 30πt ) + sin ( 80πt )

which is then transformed to the frequency domain using an FFT block.

4-10
 Transforms

To build the model, make the following parameter settings:

• In the Sine Wave block, set:

- Amplitude = 1
- Frequency = [15 40]
- Phase offset = 0
- Sample time = 0.001
- Samples per frame = 128
• In the Matrix Sum block, set Sum along = Rows.
• In the Complex to Magnitude-Angle block, set Output = Magnitude.
• In the Vector Scope block, set:
- Input domain = Frequency in the Scope properties panel
- Amplitude scaling = Magnitude in the Axis properties panel
• Set the Stop time in the Parameters dialog box to inf, and start the
simulation by selecting Start from the Simulation menu.

The scope shows the two peaks at 0.015 and 0.04 kHz, as expected.

4-11
4 DSP Operations

Note that the three-block sequence of FFT, Complex to Magnitude-Angle, and

Vector Scope could be replaced by a single Spectrum Scope block, which
computes the magnitude FFT internally.
Other blocks that compute the FFT internally are the blocks in the Power
Spectrum Estimation library. See “Power Spectrum Estimation” on page 4-15
for more information about these blocks.

Example: Using the IFFT Block

In the model below, the Sine Wave block again generates two frame-based
sinusoids, one at 15 Hz and the other at 40 Hz. The sinusoids are summed
point-by-point to generate the compound sinusoid

u = sin ( 30πt ) + sin ( 80πt )

which is transformed to the frequency domain using an FFT block. The
frequency-domain signal is then immediately transformed back to the time
domain by the IFFT block, and the difference between the original time-domain
signal and transformed time-domain signal is plotted on the scope.

To build the model, make the following parameter settings (leave unlisted
parameters in their default settings):

• In the Sine Wave block, set:

- Amplitude = 1
- Frequency = [15 40]
- Phase offset = 0
- Sample time = 0.001
- Samples per frame = 128
• In the Matrix Sum block, set Sum along = Rows.
• In the FFT block, set Output in bit-reversed order =
• In the IFFT block, set:

4-12
 Transforms

- Input is in bit-reversed order =

- Input is conjugate symmetric =
• In the Sum block, set List of signs = |++.
• In the Gain block, set Gain = -1.
• In the Scope properties panel of the Vector Scope block, set
Input domain = Time
• Set the Stop time in the Parameters dialog box to inf, and start the
simulation by selecting Start from the Simulation menu.

The flat line on the scope suggests that there is no difference between the two
signals, and that the IFFT block has perfectly reconstructed the original
time-domain signal from the frequency-domain input.

More precisely, the two signals are identical to within round-off error, which
can be seen by selecting Autoscale from the right-click menu on the scope. The
enlarged trace shows that the differences between the two signals are on the
order of 10-15.

4-13
4 DSP Operations

4-14
 Power Spectrum Estimation

Power Spectrum Estimation

The Power Spectrum Estimation library provides a number of blocks for
spectral analysis. Many of them have correlates in the Signal Processing
Toolbox, which are shown in parentheses:

• Burg Method (pburg)

• Covariance Method (pcov)
• Magnitude FFT (periodogram)
• Modified Covariance Method (pmcov)
• Short-Time FFT
• Yule-Walker Method (pyulear)

See “Spectral Analysis” in the Signal Processing Toolbox documentation for an

overview of spectral analysis theory and a discussion of the above methods.
The DSP Blockset provides two demos that illustrate the spectral analysis
blocks:

• A Comparison of Spectral Analysis Techniques (dspsacomp)

• Spectral Analysis: Short-Time FFT (dspstfft)

4-15
4 DSP Operations

Linear Algebra
The Matrices and Linear Algebra library provides three large sublibraries
containing blocks for linear algebra:

• Linear System Solvers

• Matrix Factorizations
• Matrix Inverses

A third library, Matrix Operations, provides other essential blocks for working
with matrices. See “Multichannel Signals” on page 3-11 for more information
about matrix signals.
The following sections provide examples to help you get started with the linear
algebra blocks:

• “Solving Linear Systems”

• “Factoring Matrices”
• “Inverting Matrices”

Solving Linear Systems

The Linear System Solvers library provides the following blocks for solving the
system of linear equations AX = B:

• Autocorrelation LPC
• Cholesky Solver
• Forward Substitution
• LDL Solver
• Levinson-Durbin
• LU Solver
• QR Solver
• SVD Solver

Some of the blocks offer particular strengths for certain classes of problems.
For example, the Cholesky Solver block is particularly adapted for a square
Hermitian positive definite matrix A, whereas the Backward Substitution
block is particularly suited for an upper triangular matrix A.

4-16
 Linear Algebra

Example: LU Solver
In the model below, the LU Solver block solves the equation Ax = b, where

1 –2 3 1
A = 4 0 6 b = –2
2 –1 3 –1

and finds x to be the vector [-2 0 1]'.

To build the model, set the following parameters:

• In the DSP Constant block, set Constant value = [1 -2 3;4 0 6;2 -1 3].
• In the DSP Constant1 block, set Constant value = [1 -2 -1]'.

You can verify the solution by using the Matrix Multiply block to perform the
multiplication Ax, as shown in the model below.

Factoring Matrices
The Matrix Factorizations library provides the following blocks for factoring
various kinds of matrices:

• Cholesky Factorization
• LDL Factorization
• LU Factorization

4-17
4 DSP Operations

• QR Factorization
• Singular Value Decomposition

Some of the blocks offer particular strengths for certain classes of problems.
For example, the Cholesky Factorization block is particularly suited to
factoring a Hermitian positive definite matrix into triangular components,
whereas the QR Factorization is particularly suited to factoring a rectangular
matrix into unitary and upper triangular components.

Example: LU Factorization
In the model below, the LU Factorization block factors a matrix Ap into upper
and lower triangular submatrices U and L, where Ap is row equivalent to input
matrix A, where

1 –2 3
A = 4 0 6
2 –1 3

To build the model, in the DSP Constant block, set the Constant value
parameter to [1 -2 3;4 0 6;2 -1 3].
The lower output of the LU Factorization, P, is the permutation index vector,
which indicates that the factored matrix Ap is generated from A by
interchanging the first and second rows.

4 0 6
Ap = 1 –2 3
2 –1 3

The upper output of the LU Factorization, LU, is a composite matrix containing

the two submatrix factors, U and L, whose product LU is equal to Ap.

4-18
 Linear Algebra

4 0 6 1 0 0
U = 0 –2 1.5 L = 0.25 1 0
0 0 – 0.75 0.5 0.5 1

You can check that LU = Ap with the Matrix Multiply block, as shown in the
model below.

Inverting Matrices
The Matrix Inverses library provides the following blocks for inverting various
kinds of matrices:

• Cholesky Inverse
• LDL Inverse
• LU Inverse
• Pseudoinverse

Example: LU Inverse
In the model below, the LU Inverse block computes the inverse of input
matrix A, where

1 –2 3
A = 4 0 6
2 –1 3

and then forms the product A-1A, which yields the identity matrix of order 3,
as expected.

4-19
4 DSP Operations

To build the model, in the DSP Constant block, set the Constant value
parameter to [1 -2 3;4 0 6;2 -1 3].
As shown above, the computed inverse is

– 1 – 0.5 2
–1
A = 0 0.5 –1
0.6667 0.5 – 1.333

4-20
 Statistics

Statistics
The Statistics library provides fundamental statistical operations such as
minimum, maximum, mean, variance, and standard deviation. Most blocks in
the Statistics library support two types of operations:

• Basic operations
• Running operations

The blocks listed below toggle between basic and running modes using the
Running check box in the parameter dialog box:

• Histogram
• Mean
• RMS
• Standard Deviation
• Variance

An unchecked Running box means that the block is operating in basic mode,
while a checked Running box means that the block is operating in running
mode.
The Maximum and Minimum blocks are slightly different from the blocks
above, and provide a Mode parameter in the block dialog box to select the type
of operation. The Value and Index, Value, and Index options in the Mode
menu all specify basic operation, in each case enabling a different set of output
ports on the block. The Running option in the Mode menu selects running
operation.
The following sections explain how basic mode and running mode differ:

• “Basic Operations”
• “Running Operations”

The statsdem demo illustrates the operation of several blocks from the
Statistics library.

Basic Operations
A basic operation is one that processes each input independently of previous
and subsequent inputs. For example, in basic mode (with Value and Index

4-21
4 DSP Operations

selected, for example) the Maximum block finds the maximum value in each
column of the current input, and returns this result at the top output (Val).
Each consecutive Val output therefore has the same number of columns as the
input, but only one row. Furthermore, the values in a given output only depend
on the values in the corresponding input. The block repeats this operation for
each successive input.
This type of operation is exactly equivalent to the MATLAB command
val = max(u) % Equivalent MATLAB code

which computes the maximum of each column in input u.

The next section provides an example of a basic statistical operation.

Example: Sliding Windows

You can use the basic statistics operations in conjunction with the Buffer block
to implement basic sliding window statistics operations. A sliding window is
like a stencil that you move along a data stream, exposing only a set number of
data points at one time.
For example, you may want to process data in 128-sample frames, moving the
window along by one sample point for each operation. One way to implement
such a sliding window is shown in the model below.

The Buffer block’s Buffer size (Mo) parameter determines the size of the
window. The Buffer overlap (L) parameter defines the “slide factor” for the
window. At each sample instant, the window slides by Mo-L points. The Buffer
overlap is often Mo-1 (the same as the Delay Line block), so that a new statistic
is computed for every new signal sample.
To build the model, make the following settings:

• In the Signal From Workspace block, set:

- Signal = 1:256
- Sample time = 0.1
- Samples per frame = 1

4-22
 Statistics

• In the Buffer block, set:

- Output buffer size (per channel) = 128
- Buffer overlap = 127

Running Operations
A running operation is one that processes successive sample-based or
frame-based inputs, and computes a result that reflects both present and past
inputs. A reset port enables you to restart this tracking at any time. The
running statistic is computed for each input channel independently, so the
block’s output is the same size as the input.
For example, in running mode (Running selected from the Mode parameter)
the Maximum block outputs a record of the input’s maximum value over time.
The figure below illustrates how a Maximum block in running mode operates
on a frame-based 3-by-2 (two-channel) matrix input, u. The running maximum
is reset at t=2 by an impulse to the block’s optional Rst port.
In Rst Output

ch1 ch2 ch1 ch2

61 61
First
13 t=0 0 First output 63
input 39 69

–7 2 69
2 4 t=1 0 69
5 1 69
Simulation time

8 6 86
0 2 t=2 1 86 Reset
–1 5 86

–3 0 8 6
2 4 t=3 0 8 6
1 17 8 17

4-23
4 DSP Operations

DSP Blockset Demos Overview

You can access the DSP Blockset demos by typing
demos

at the MATLAB command line. In the Demos window that opens, expand the
Blocksets entry by double-clicking, and then click DSP to see the demos.
Explore all the demos to see how you can implement both basic and advanced
DSP algorithms with the DSP Blockset. You can also use the demos as a base
for building your own models. Simply select the section of the demo that you
want to build on and copy it into your own model.
The available demos are listed below by category.

Adaptive Processing Demos

• Equalization: Demonstrates adaptive channel equalization by using the
LMS algorithm to adaptively compute an estimate of an FIR equalization
filter.
• Noise canceller (using either LMS or RLS): These demos use either the LMS
or RLS algorithm to subtract noise from an input signal.
• Linear prediction: Uses the LMS adaptive FIR algorithm to adaptively
compute the linear prediction coefficients for a noisy input signal.
• Time-delay estimation: Uses the LMS adaptive FIR algorithm to adaptively
estimate the time delay for a noisy input signal.
• Tracking filter: Uses a Kalman filter to track the time-varying weights of a
nonstationary fifth order FIR filter.

Audio Processing Demos

• Dynamic range compression: Compresses the dynamic range of a signal by
modifying the range of the magnitude at each frequency bin. This nonlinear
spectral modification is followed by an overlap-add FFT algorithm for
reconstruction.
• Flanging: Introduces a “flanging” effect into a short segment of music.
• Reverberation: Uses the Integer Delay block to demonstrate the popular
reverberation audio effect.

4-24
 DSP Blockset Demos Overview

• LPC analysis and synthesis: Uses the Levinson solver and Time-Varying
Lattice Filter for low-bandwidth transmission of speech.
• Waveform coding: This set of demos uses a variety of modulation methods to
code a waveform using one bit per message sample:
- ADPCM (Adaptive Differential Pulse Code Modulation)
- CVSD (Continuously Variable Slope Delta-modulation)
- LDM (Linear Delta Modulation)
- Comparison of LDM, CVSD, and ADPCM

Communications Demos
• SSB modulation: Demonstrates single sideband (SSB) modulation in
sample-based and frame-based modes.
• WWV digital receiver: WWV is the call sign of a US Government radio
station that transmits frequency reference standards and time code
information with a timing accuracy of 10 microseconds and a frequency
accuracy of 1 part in 100 billion. This demo simulates the transmission of a
WWV signal and demonstrates implementation of the subsequent receiver
and decoder blocks. The receiver design serves as a simple example of the use
of Simulink, DSP Blockset, Stateflow® and Real-Time Workshop.

Filtering Demos
• Multirate filtering suite: Uses FIR decimation blocks in multiple stages to
filter with very short bandwidths and low computational loads.
• FIR interpolation: Uses the FIR Interpolation block to demonstrate
interpolation of a delayed sine wave signal.
• Overlap add/save: Demonstrates filtering of a sinusoid using the
Overlap-Add and Overlap-Save FFT blocks.
• Sample rate conversion: Illustrates the efficiency of the FIR rate conversion
block by comparing the block with the equivalent process of separate
upsampling, FIR filtering, and downsampling.

4-25
4 DSP Operations

Queues Demo
• Demo uses a Queue block with a system of selection switches to illustrate
pushing and popping elements from a queue.

Sigma-Delta A/D Conversion Demo

• Demo illustrates analog-to-digital conversion using a sigma-delta algorithm
implementation.

Sine Wave Generation Demo

• Demo compares different sine wave generation systems.

Spectral Analysis Demos

• Short-time FFT: Uses the Short-Time FFT block to compute and display a
spectrogram.
• Comparison of techniques: Uses the Vector Scope block to simultaneously
display spectral estimates computed by the Short-Time FFT, Burg Method,
and Modified Covariance Method blocks.

Statistical Functions Demo

• Demo illustrates the behavior of several running-statistics blocks that are
periodically reset every 100 input samples.

Wavelets Demos
• One-level PR filter bank: Uses the Dyadic Analysis and Dyadic Synthesis
blocks to implement a perfect reconstruction filter bank.
• Wavelet function: Uses a sequence of FIR interpolation blocks to reconstruct
a wavelet function from filter coefficients.
• Denoising: Uses Analysis and Synthesis blocks to remove noise from an
input signal.
• Wavelet transmultiplexer (WTM): Illustrates the perfect reconstruction
property of the discrete wavelet transform (DWT) by using a WTM to
reconstruct three independent combined signals transmitted over a single
communications link.

4-26
 5

DSP Block Reference

Features of the Online DSP Block Reference . . . . . 5-2
Main Sections of a Block Reference Page . . . . . . . . . 5-2
Ways to Access Online DSP Block Reference Pages . . . . . 5-4
Running Example Code in the MATLAB Help browser . . . 5-4
Running Example Models in the MATLAB Help browser . . 5-4

Blocks Supporting Code Generation . . . . . . . . . 5-6

Block Library List . . . . . . . . . . . . . . . . . 5-9

Block Library Hierarchy . . . . . . . . . . . . . . . . 5-9

Block Library Contents . . . . . . . . . . . . . . . . 5-10

5 DSP Block Reference

Features of the Online DSP Block Reference

The online DSP Blockset block reference section contains complete information
on every block in the DSP Blockset in a structured, accessible format. Use this
reference section when you need to find detailed information on a particular
block. See the following sections for more information:

• “Main Sections of a Block Reference Page”

- “About Tunable Parameters”
- “About Supported Data Types”
• “Ways to Access Online DSP Block Reference Pages”
• “Running Example Code in the MATLAB Help browser”
• “Running Example Models in the MATLAB Help browser”

To learn the basic concepts behind building DSP models with Simulink, see
Chapter 2, “Simulink and the DSP Blockset.” To find out about using blocks
together for common DSP tasks, see Chapter 3, “Working with Signals.”

Main Sections of a Block Reference Page

The block reference entries appear in alphabetical order and each contains
most of the following sections.

Section Description

“Purpose” The purpose of the block.

“Library” The library or libraries where the block can be found.

“Description” A description of the block’s use.

“Dialog Box” The block’s dialog box and parameters. Tunable

parameters are labeled “Tunable”. See the next section,
“About Tunable Parameters” for more information.

“Supported The data types supported by the block. See the following
Data Types” section, “About Supported Data Types” for more
information.

“See Also” A list of related blocks and functions.

5-2
 Features of the Online DSP Block Reference

About Tunable Parameters

Tunable parameters are block parameters whose settings you can change or
tune during a simulation. In the “Dialog Box” section of the block reference
pages, these parameters are marked “Tunable” in the parameter descriptions.
To tune a tunable parameter during a simulation, open the block parameters
dialog, change the parameter to the desired setting, then press the OK or
Apply button.
Parameters that are not labeled “Tunable” are not tunable. During a
simulation, the fields, pull-down menus, and check boxes of nontunable
parameters become gray and cannot be edited.

About Supported Data Types

Many DSP Blockset blocks can support all built-in data types, as well as
custom data types and the fixed-point data type. To see which data types a
particular block supports, check the “Supported Data Types” section of its
reference page.
Note that not all blocks support all of the following data types.

Data Types Supported by the DSP Blockset:

• Fixed-point data type
• Custom data types
• Simulink built-in data types (and commands for casting values to these data
types):
- Boolean — boolean
- Integer (8-,16-, or 32-bits) — int8, int16, int32
- Unsigned integer (8-,16-, or 32-bits) — uint8, uint16, uint32
- Single-precision floating point — single
- Double-precision floating point — double

Correctly Defining Custom Data Types. Custom data types are user-defined data
types. You must define your custom data types by following the guidelines in
the Custom Data Types section in the “Implementing Block Features” section
of the “Writing S-Functions” Simulink documentation. If you do not follow the
Simulink guidelines for creating custom data types, the DSP Blockset blocks
will not support your custom data types.

5-3
5 DSP Block Reference

Ways to Access Online DSP Block Reference Pages

There are several ways to access the reference pages:

• Click Help in a block dialog box.

• Right-click a block in a model, and select Help from the pop-up menu.
• Right-click a block in the Simulink Library Browser, and select Help from
the pop-up menu. (Open the library browser by typing simulink at the
MATLAB command line.)
• Type doc('block name') at the MATLAB command line.
• Expand the DSP Blockset entry in the Help browser, and select DSP Block
Reference, which is under Reference. (Open the Help browser by typing
doc at the MATLAB command line.)

Running Example Code in the MATLAB Help

browser
When viewing online reference pages in the MATLAB Help browser, you can
run example code without retyping it:

• Highlight the code.

• Right-click on the selection.
• Choose Evaluate Selection from the drop-down menu.

Running Example Models in the MATLAB Help

browser
When viewing online reference pages in the MATLAB Help browser, you can
run example models without rebuilding them (note the models may create new
variables in your workspace):

5-4
 Features of the Online DSP Block Reference

• Click on indicated links to bring up example models.

• Run the models as you would run any other model.

Open the following model by clicking here in the MATLAB Help browser.

5-5
5 DSP Block Reference

Blocks Supporting Code Generation

You can generate C code from models containing DSP Blockset blocks by using
the Real-Time Workshop. All DSP Blockset blocks support generic real-time
(GRT) code generation. Many blocks also support embedded real-time (ERT)
code generation, as indicated in the following table. See the Real-Time
Workshop documentation for more information on generating code from
Simulink models.

Note All DSP Blockset blocks support generic real-time (GRT) code
generation.

DSP Blockset Blocks Supporting ERT Code Generation:

Analytic Signal Autocorrelation

Biquadratic Filter Buffer

Check Signal Attributes Chirp

Complex Cepstrum Complex Exponential

Constant Diagonal Matrix Constant Ramp

Contiguous Copy Convert 1-D to 2-D

Convert 2-D to 1-D Convolution

Correlation Counter

Create Diagonal Matrix Cumulative Sum

dB Conversion dB Gain

DCT Delay Line

Difference Digital Filter Design

Direct-Form II Transpose Filter Discrete Impulse

5-6
 Blocks Supporting Code Generation

DSP Blockset Blocks Supporting ERT Code Generation:

Display Downsample

DSP Constant Dyadic Analysis Filter Bank

Dyadic Synthesis Filter Bank Edge Detector

Event-Count Comparator Extract Diagonal

Extract Triangular Matrix FFT

Filter Realization Wizard FIR Decimation

FIR Interpolation FIR Rate Conversion

Flip Frame Status Conversion

Histogram Identity Matrix

IFFT Inherit Complexity

Integer Delay Kalman Adaptive Filter

LMS Adaptive Filter Magnitude FFT

Matrix 1-Norm Matrix Concatenation

Matrix Multiply Matrix Product

Matrix Scaling Matrix Square

Matrix Sum Maximum

Mean Median

Minimum Multiport Selector

N-Sample Switch Normalization

Overlap-Add FFT Filter Overlap-Save FFT Filter

Pad Permute Matrix

Polynomial Evaluation Polynomial Stability Test

Quantizer Random Source

5-7
5 DSP Block Reference

DSP Blockset Blocks Supporting ERT Code Generation:

Real Cepstrum Repeat

RLS Adaptive Filter RMS

Sample and Hold Selector

Short-Time FFT Signal From Workspace

Signal To Workspace Sine Wave

Sort Standard Deviation

Submatrix Time Scope

Time-Varying Direct-Form II Time-Varying Lattice Filter

Transpose Filter

Toeplitz Transpose

Triggered Delay Line Triggered Signal From Workspace

Triggered To Workspace Unbuffer

Uniform Decoder Uniform Encoder

Unwrap Upsample

Variable Fractional Delay Variable Integer Delay

Variable Selector Variance

Wavelet Analysis Wavelet Synthesis

Window Function Zero Pad

5-8
 Block Library List

Block Library List

This section contains the following two subsections:

• “Block Library Hierarchy” – a structured list of the DSP Blockset libraries

• “Block Library Contents” – a listing of all DSP blocks, arranged by library

See “Alphabetical List of Blocks” on page 5-18 for an alphabetical listing of

blocks. The pages that follow that section contain reference information for all
blocks in the DSP Blockset, arranged in alphabetical order by block name.

Block Library Hierarchy

The DSP Blockset contains the following libraries and sublibraries:

• DSP Sinks
• DSP Sources
• Estimation
- Estimation: Linear Prediction
- Estimation: Parametric Estimation
- Estimation: Power Spectrum Estimation
• Filtering
- Filtering: Adaptive Filters
- Filtering: Filter Designs
- Filtering: Multirate Filter
• Math Functions
- Matrices and Linear Algebra
• Linear System Solvers
• Matrix Factorizations
• Matrix Inverses
• Matrix Operations
- Math Functions: Math Operations
- Math Functions: Polynomial Functions
• Quantizers
• Signal Management

5-9
5 DSP Block Reference

- Signal Management: Buffers

- Signal Management: Indexing
- Signal Management: Signal Attributes
- Signal Management: Switches and Counters
• Signal Operations
• Statistics
• Transforms

Use the Simulink Library Browser to access the blockset directly through the
above hierarchical library list.

Block Library Contents

The DSP blocks in each of these libraries are listed below. Simulink blocks that
appear in DSP Blockset libraries (such as the Display block in DSP Sinks) are
followed by the phrase “Simulink block” in parentheses.

DSP Sinks

Display (Simulink block) To Wave Device

Matrix Viewer To Wave File

Signal To Workspace Triggered To Workspace

Spectrum Scope Vector Scope

Time Scope (Simulink Block)

DSP Sources

Chirp Identity Matrix

Constant Diagonal Matrix Multiphase Clock

Constant Ramp N-Sample Enable

Counter Random Source

5-10
 Block Library List

DSP Sources (Continued)

DSP Constant Signal From Workspace

Discrete Impulse Sine Wave

From Wave Device Triggered Signal From Workspace

From Wave File Window Function

Estimation: Linear Prediction

Autocorrelation LPC

Estimation: Parametric Estimation

Burg AR Estimator Modified Covariance AR Estimator

Covariance AR Estimator Yule-Walker AR Estimator

Estimation: Power Spectrum Estimation

Burg Method Modified Covariance Method

Covariance Method Short-Time FFT

Magnitude FFT Yule-Walker Method

5-11
5 DSP Block Reference

Filtering: Adaptive Filters

Kalman Adaptive Filter RLS Adaptive Filter

LMS Adaptive Filter

Filtering: Filter Designs

Analog Filter Design Overlap-Add FFT Filter

Biquadratic Filter Overlap-Save FFT Filter

Digital Filter Design Direct-Form II Transpose Filter

Filter Realization Wizard Time-Varying Direct-Form II

Transpose Filter

Time-Varying Lattice Filter

Filtering: Multirate Filter

Dyadic Analysis Filter Bank FIR Rate Conversion

Dyadic Synthesis Filter Bank Wavelet Analysis

FIR Decimation Wavelet Synthesis

FIR Interpolation

5-12
 Block Library List

Math Functions: Matrices and Linear Algebra

Linear System Solvers

Autocorrelation LPC Levinson-Durbin

Cholesky Solver LU Solver

Forward Substitution QR Solver

LDL Solver SVD Solver

Math Functions: Matrices and Linear Algebra

Matrix Factorizations

Cholesky Factorization QR Factorization

LDL Factorization Singular Value Decomposition

LU Factorization

Math Functions: Matrices and Linear Algebra

Matrix Inverses

Cholesky Inverse LU Inverse

LDL Inverse Pseudoinverse

5-13
5 DSP Block Reference

Math Functions: Matrices and Linear Algebra

Matrix Operations

Constant Diagonal Matrix Matrix Scaling

Create Diagonal Matrix Matrix Square

Extract Diagonal Matrix Sum

Extract Triangular Matrix Permute Matrix

Identity Matrix Reciprocal Condition

Matrix Concatenation (Simulink Submatrix

block)

Matrix 1-Norm Toeplitz

Matrix Multiply Transpose

Matrix Product

Math Functions: Math Operations

Complex Exponential dB Gain

Cumulative Sum Normalization

dB Conversion Difference

Math Functions: Polynomial Functions

Least Squares Polynomial Fit Polynomial Stability Test

Polynomial Evaluation

5-14
 Block Library List

Quantizers

Quantizer (Simulink block) Uniform Encoder

Uniform Decoder

Signal Management: Buffers

Buffer Stack

Delay Line Triggered Delay Line

Queue Unbuffer

Signal Management: Indexing

Flip Submatrix

Multiport Selector Variable Selector

Selector (Simulink block)

Signal Management: Signal Attributes

Check Signal Attributes Convert 2-D to 1-D

Contiguous Copy Frame Status Conversion

Convert 1-D to 2-D Inherit Complexity

5-15
5 DSP Block Reference

Signal Management: Switches and Counters

Counter Multiphase Clock

Edge Detector N-Sample Enable

Event-Count Comparator N-Sample Switch

Signal Operations

Convolution Unwrap

Downsample Upsample

Integer Delay Variable Fractional Delay

Pad Variable Integer Delay

Repeat Window Function

Sample and Hold Zero Pad

Statistics

Autocorrelation Median

Correlation Minimum

Detrend RMS

Histogram Sort

Maximum Standard Deviation

Mean Variance

5-16
 Block Library List

Transforms

Analytic Signal IDCT

Complex Cepstrum IFFT

DCT Real Cepstrum

FFT

5-17
 Analog Filter Design

Purpose 5Analog Filter Design

Design and implement an analog filter.

Library Filtering / Filter Designs

Description The Analog Filter Design block designs and implements a Butterworth,
Chebyshev type I, Chebyshev type II, or elliptic filter in a highpass, lowpass,
bandpass, or bandstop configuration.
The input must be a sample-based scalar signal.
The design and band configuration of the filter are selected from the Design
method and Filter type pop-up menus in the dialog box. For each combination
of design method and band configuration, an appropriate set of secondary
parameters is displayed.

Filter Design Description

Butterworth The magnitude response of a Butterworth filter is

maximally flat in the passband and monotonic overall.
Chebyshev The magnitude response of a Chebyshev type I filter is
type I equiripple in the passband and monotonic in the
stopband.
Chebyshev The magnitude response of a Chebyshev type II filter is
type II monotonic in the passband and equiripple in the
stopband.
Elliptic The magnitude response of an elliptic filter is
equiripple in both the passband and the stopband.

The table below lists the available parameters for each design/band
combination. For lowpass and highpass band configurations, these parameters
include the passband edge frequency Ωp, the stopband edge frequency Ωs, the
passband ripple Rp, and the stopband attenuation Rs. For bandpass and
bandstop configurations, the parameters include the lower and upper
passband edge frequencies, Ωp1 and Ωp2, the lower and upper stopband edge
frequencies, Ωs1 and Ωs2, the passband ripple Rp, and the stopband

5-23
Analog Filter Design

attenuation Rs. Frequency values are in rad/s, and ripple and attenuation
values are in dB.

Lowpass Highpass Bandpass Bandstop

Butterworth Order, Ωp Order, Ωp Order, Ωp1, Ωp2 Order, Ωp1, Ωp2
Chebyshev Type I Order, Ωp, Rp Order, Ωp, Rp Order, Ωp1, Ωp2, Rp Order, Ωp1, Ωp2, Rp
Chebyshev Type II Order, Ωs, Rs Order, Ωs, Rs Order, Ωs1, Ωs2, Rs Order, Ωs1, Ωs2, Rs
Elliptic Order, Ωp, Rp, Rs Order, Ωp, Rp, Rs Order, Ωp1, Ωp2, Rp, Rs Order, Ωp1, Ωp2, Rp, Rs

The analog filters are designed using the Signal Processing Toolbox’s filter
design commands buttap, cheb1ap, cheb2ap, and ellipap, and are
implemented in state-space form. Filters of order 8 or less are implemented in
controller canonical form for improved efficiency.

Supported Double-precision floating point

Data Types

Dialog Box

The parameters displayed in the dialog box vary for different design/band
combinations. Only a portion of the parameters listed below are visible in the
dialog box at any one time.
Design method
The filter design method: Butterworth, Chebyshev type I, Chebyshev
type II, or Elliptic. Tunable.

5-24
 Analog Filter Design

Filter type
The type of filter to design: Lowpass, Highpass, Bandpass, or Bandstop.
Tunable.
Filter order
The order of the filter, for lowpass and highpass configurations. For
bandpass and bandstop configurations, the order of the final filter is twice
this value.
Passband edge frequency
The passband edge frequency, in rad/s, for the highpass and lowpass
configurations of the Butterworth, Chebyshev type I, and elliptic designs.
Lower passband edge frequency
The lower passband frequency, in rad/s, for the bandpass and bandstop
configurations of the Butterworth, Chebyshev type I, and elliptic designs.
Upper passband edge frequency
The upper passband frequency, in rad/s, for the bandpass and bandstop
configurations of the Butterworth, Chebyshev type I, or elliptic designs.
Stopband edge frequency
The stopband edge frequency, in rad/s, for the highpass and lowpass band
configurations of the Chebyshev type II design.
Lower stopband edge frequency
The lower stopband edge frequency, in rad/s, for the bandpass and
bandstop configurations of the Chebyshev type II design.
Upper stopband edge frequency
The upper stopband edge frequency, in rad/s, for the bandpass and
bandstop filter configurations of the Chebyshev type II design.
Passband ripple in dB
The passband ripple, in dB, for the Chebyshev Type I and elliptic designs.
Stopband attenuation in dB
The stopband attenuation, in dB, for the Chebyshev Type II and elliptic
designs. Tunable.

5-25
Analog Filter Design

References Antoniou, A. Digital Filters: Analysis, Design, and Applications. 2nd ed. New
York, NY: McGraw-Hill, 1993.

Supported Double-precision floating point

Data Types

See Also Digital Filter Design DSP Blockset

buttap Signal Processing Toolbox
cheb1ap Signal Processing Toolbox
cheb2ap Signal Processing Toolbox
ellipap Signal Processing Toolbox

See the following sections for related information:

• “Filter Designs” on page 4-4

• “Designing Continuous-Time Classical IIR Filters” on page 4-7

5-26
 Analytic Signal

Purpose 5Analytic Signal

Compute the analytic signal of a discrete-time input.

Library Transforms

Description The Analytic Signal block computes the complex analytic signal corresponding
to each channel of the real M-by-N input, u.

y = u + jH { u }
where j = – 1 and H{⋅} denotes the Hilbert transform. The real part of the
output in each channel is a replica of the real input in that channel; the
imaginary part is the Hilbert transform of the input. In the frequency domain,
the analytic signal retains the positive frequency content of the original signal
while zeroing-out negative frequencies and doubling the DC component.
The block computes the Hilbert transform using an equiripple FIR filter with
the order specified by the Filter order parameter, n. The linear phase filter is
designed using the Remez exchange algorithm, and imposes a delay of n/2 on
the input samples.
The output has the same dimension and frame status as the input.

Sample-Based Operation
When the input is sample-based, each of the M∗N matrix elements represents
an independent channel. Thus, the block computes the analytic signal for each
channel (matrix element) over time.

Frame-Based Operation
When the input is frame-based, each of the N columns in the matrix contains
M sequential time samples from an independent channel, and the block
computes the analytic signal for each channel over time.

Dialog Box

5-27
Analytic Signal

Filter order
The length of the FIR filter used to compute the Hilbert transform.

Supported Double-precision floating point

Data Types

5-28
 Autocorrelation

Purpose 5Autocorrelation
Compute the autocorrelation of a vector input.

Library Statistics

Description The Autocorrelation block computes the autocorrelation of each column

(channel) in an M-by-N input matrix u. Matrix inputs must be frame-based.
The result, y, is a frame-based (l+1)-by-N matrix whose jth column has
elements
M
y i, j = ∑ u*k, j u( k + i – 1 ), j 1 ≤ i ≤ (l + 1)
k=1

where ∗ denotes the complex conjugate, and l represents the maximum lag.
Note that y1,j is the zero-lag element in the jth column. When All positive lags
is selected, l=M. Otherwise, l is specified as a nonnegative integer by the
Maximum positive lag parameter.

Input u is zero when indexed outside of its valid range. When the input is real,
the output is real; otherwise, the output is complex. If the input is a
sample-based vector (row, column, or 1-D), the output is sample-based, with
the same shape as the input and length l+1. The Autocorrelation block does not
accept a sample-based full-dimension matrix input.
The Scaling parameter controls the scaling that is applied to the output. The
following options are available:

• None – Generates the raw autocorrelation, yi,j, without normalization.

• Biased – Generates the biased estimate of the autocorrelation.

biased y i, j
y i, j = --------
M
• Unbiased – Generates the unbiased estimate of the autocorrelation.

unbiased y i, j
y i, j = -------------
M–i
• Unity at zero-lag – Normalizes the estimate of the autocorrelation for each
channel so that the zero-lag sum is identically 1.

y 1, j = 1

5-29
Autocorrelation

Dialog Box

All positive lags

When selected, computes the autocorrelation over all M+1 positive lags.
Maximum positive lag
The maximum positive lag, l, for the autocorrelation. This parameter is
enabled when the All positive lags check box is unselected.
Scaling
The type of scaling for the autocorrelation: None, Biased, Unbiased, or
Unity at zero-lag. Tunable, except in Simulink’s external mode.

Supported Double-precision floating point

Data Types

See Also Correlation DSP Blockset

xcorr Signal Processing Toolbox

5-30
 Autocorrelation LPC

Purpose 5Autocorrelation LPC

Determine the coefficients of an Nth-order forward linear predictor.

Library Estimation / Linear Prediction

Description The Autocorrelation LPC block determines the coefficients of an N-step

forward linear predictor for the time-series in length-M input vector, u, by
minimizing the prediction error in the least-squares sense. A linear predictor
is an FIR filter that predicts the next value in a sequence from the present and
past inputs. This technique has applications in filter design, speech coding,
spectral analysis, and system identification.
The Autocorrelation LPC block can output the prediction error as polynomial
coefficients, reflection coefficients, or both. It can also output the prediction
error power. The length-M input, u, can be a scalar, 1-D vector, frame- or
sample-based column vector, or a sample-based row vector. Frame-based row
vectors are not valid inputs.
When Inherit prediction order from input dimensions is selected, the
prediction order, N, is inherited from the input dimensions. Otherwise, the
Prediction order parameter sets the value of N.

When Output(s) is set to A, port A is enabled. Port A outputs an (N+1)-by-1

column vector, a = [1 a2 a3 … aN+1]T, containing the coefficients of an
Nth-order moving average (MA) linear process that predicts the next value,
ûM+1, in the input time-series.

uˆ M + 1 = – ( a 2 u M ) – ( a 3 u M – 1 ) – L – ( a N + 1 u M – N + 1 )

When Output(s) is set to K, port K is enabled. Port K outputs a length-N

column vector whose elements are the prediction error reflection coefficients.
When Output(s) is set to A and K, both port A and K are enabled, and each port
outputs its respective column vector of prediction coefficients. The outputs at
both port A and K are always 1-D vectors.
When Output prediction error power (P) is selected, port P is enabled. The
prediction error power, a scalar, is output at port P.

5-31
Autocorrelation LPC

Algorithm The Autocorrelation LPC block computes the least-squares solution to

min n Uã – b
ã ∈ ℜ

where ⋅ indicates the 2-norm and

u1 0 L 0
u2 u1 O M
u2
M u2 O 0
u3
M
M O u1
a2 M
U = M M M u2 , ã = M , b = u
M
M M M M an + 1 0
uM M M M
M
0 O M M 0
M O O M
0 L 0 uM

Solving the least-squares problem via the normal equations

* *
U Uã = U b
leads to the system of equations

r 1 r *2 L r *n a2 –r2
r2 r1 O M a3 –r3
=
M O O r *2 M M
a
rn L r2 r1 n + 1 –rn + 1

where r = [r1 r2 r3 … rn+1]T is an autocorrelation estimate for u computed

using the Autocorrelation block, and * indicates the complex conjugate
transpose. The normal equations are solved in O(n2) operations by the
Levinson-Durbin block.

5-32
 Autocorrelation LPC

Note that the solution to the LPC problem is very closely related to the
Yule-Walker AR method of spectral estimation. In that context, the normal
equations above are referred to as the Yule-Walker AR equations.

Dialog Box

Output(s)
The type of prediction coefficients output by the block. The block can output
polynomial coefficients (A), reflection coefficients (K), or both (A and K).
Output prediction error power (P)
When selected, enables port P, which outputs the output prediction error
power.
Inherit prediction order from input dimensions
When selected, the block inherits the prediction order from the input
dimensions.
Prediction order (N)
The prediction order, N. This parameter is disabled when Inherit
prediction order from input dimensions is selected.

References Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall,
1996.
Ljung, L. System Identification: Theory for the User. Englewood Cliffs, NJ:
Prentice Hall, 1987. Pgs. 278-280.

5-33
Autocorrelation LPC

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood

Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

See Also Autocorrelation DSP Blockset

Levinson-Durbin DSP Blockset
Yule-Walker Method DSP Blockset
lpc Signal Processing Toolbox

5-34
 Backward Substitution

Purpose 5Backward Substitution

Solve the equation UX=B for X when U is an upper triangular matrix.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The Backward Substitution block solves the linear system UX=B by simple
backward substitution of variables, where U is the upper triangular M-by-M
matrix input to the U port, and B is the M-by-N matrix input to the B port. The
output is the solution of the equations, the M-by-N matrix X, and is always
sample-based.
The block uses only the elements in the upper triangle of input U; the lower
elements are ignored. When Force input to be unit-upper triangular is
selected, the block replaces the elements on the diagonal of U with ones. This
is useful when matrix U is the result of another operation, such as an LDL
decomposition, that uses the diagonal elements to represent the D matrix.
A length-M vector input at port B is treated as an M-by-1 matrix.

Dialog Box

Force input to be unit-upper triangular

Replaces the elements on the diagonal of U with 1s when selected. Tunable.

Supported Double-precision floating point

Data Types

See Also Cholesky Solver DSP Blockset

Forward Substitution DSP Blockset
LDL Solver DSP Blockset
Levinson-Durbin DSP Blockset
LU Solver DSP Blockset
QR Solver DSP Blockset

5-35
Backward Substitution

See “Solving Linear Systems” on page 4-16 for related information.

5-36
 Biquadratic Filter

Purpose 5Biquadratic Filter

Apply a cascade of biquadratic (second-order section) filters to the input.

Library Filtering / Filter Designs

Description The Biquadratic Filter block applies a cascade of biquadratic filters

independently to each input channel. Biquadratic filters are useful for reduced
precision implementations because the coefficients are bounded between ±2 for
typical minimum-phase designs. This may reduce scaling and coefficient
sensitivity problems.
The filter is constructed from L second-order sections, each having a quadratic
numerator and denominator.
L L
b 1k + b 2k z – 1 + b 3k z –2
H(z) = ∏ H k(z) = ∏ ----------------------------------------------------------
a 1k + a 2k z – 1 + a 3k z – 2
k=1 k=1

The figure below illustrates the structure of a 4th-order biquadratic filter (L=2)
with states vik, where k is the section number.

b11 b12
u( nT s) Σ Σ y( nT s)
v11 v12

z-1 z-1
b21 a21 b22 a22
Σ Σ
v21 v22

z-1 z-1
b31 a31 b32 a32
Σ Σ

Section 1, H1(z) Section 2, H2(z)

An M-by-N sample-based matrix input is treated as M∗N independent

channels, and an M-by-N frame-based matrix input is treated as N
independent channels. In both cases, the block filters each channel
independently over time, and the output has the same size and frame status as
the input.

5-37
Biquadratic Filter

The SOS matrix parameter specifies the filter coefficients as a second-order

section matrix of the type produced by the ss2sos and tf2sos functions in the
Signal Processing Toolbox.

b 11 b 21 b 31 a 11 a 21 a 31
b 12 b 22 b 32 a 12 a 22 a 32
a 11 = a 12 = … = a 1L = 1
M M M M M M
b 1L b 2L b 3L a 1L a 2L a 3L

This is an L-by-6 matrix whose rows contain the numerator and denominator
coefficients bik and aik of each second-order section in H(z). Use the ss2sos and
tf2sos functions to convert a state-space or transfer-function description of the
filter into the second-order section description used by this block. Note that the
filter uses a value of 1 for the zero-delay denominator coefficients (a11 to a1L)
regardless of the value specified in the SOS matrix parameter.
The Initial conditions parameter sets the initial filter states, and can be
specified in the following different forms:

• Scalar to be used for all filter states (v11, v12, ..., v1L, v21 v22, ..., v2L) in all
channels. An empty vector, [], is the same as the scalar value 0.
• Vector of length 2∗L (row or column) to initialize the filter states for all
channels.

v 11 v 21 v 12 v 22 … v 1L v 2L

H1( z) H2( z) HL( z)

Each pair of elements specifies v1k and v2k for second-order section k in every
channel.
• Matrix of dimension (2∗L)-by-N containing the initial filter states for each of
the N channels.

5-38
 Biquadratic Filter

ch1 ch2 chN

v 11 v 11 L v 11
H1 ( z )
ch1 ch2 chN
v 21 v 21 L v 21
ch1 ch2 chN
v 12 v 12 L v 12
H2 ( z )
ch1 ch2 chN
v 22 v 22 L v 22
M M O M
ch1 ch2 chN
v 1L v 1L L v 1L
HL ( z )
ch1 ch2 chN
v 2L v 2L L v 2L

Each pair of elements in a column specifies v1k and v2k for second-order
section k of the corresponding channel.

Dialog Box

SOS matrix
The second-order section matrix specifying the filter’s coefficients. This
matrix can be generated from state-space or transfer-function descriptions
by using the Signal Processing Toolbox functions ss2sos and tf2sos.
Initial conditions
The filter’s initial conditions, a scalar, vector, or matrix.

Supported Double-precision floating point

Data Types

5-39
Biquadratic Filter

See Also Direct-Form II Transpose Filter DSP Blockset

Filter Realization Wizard DSP Blockset
Time-Varying Direct-Form II Transpose Filter DSP Blockset
filter MATLAB
sosfilt Signal Processing Toolbox
ss2sos Signal Processing Toolbox
tf2sos Signal Processing Toolbox

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-40
 Buffer

Purpose 5Buffer
Buffer the input sequence to a smaller or larger frame size.

Library Signal Management / Buffers

Description The Buffer block redistributes the input samples to a new frame size, larger or
smaller than the input frame size. Buffering to a larger frame size yields an
output with a slower frame rate than the input, as illustrated below for scalar
input.
“fast-time” input “slow-time” output
(frame size = 1, sample period = T si) (frame size = 3, frame period = 3∗Tsi)

7 4 1
9 8 7 6 5 4 3 2 1 8 5 2
9 6 3

Buffering to a smaller frame size yields an output with a faster frame rate than
the input, as illustrated below for scalar output.
“slow-time” input “fast-time” output
(frame size = 3, frame period = 3∗Tsi) (frame size = 1, sample period = Tsi)

7 4 1
8 5 2 9 8 7 6 5 4 3 2 1
9 6 3

The block coordinates the output frame size and frame rate of nonoverlapping
buffers so that the sample period of the signal is the same at both the input and
output, Tso = Tsi.

Sample-Based Operation
Sample-based inputs are interpreted by the Buffer block as independent
channels of data. Thus, a sample-based length-N vector input is interpreted as
N independent samples.
In sample-based operation, the Buffer block creates frame-based outputs from
sample-based inputs. A sequence of sample-based length-N vector inputs (1-D,
2-D row, or 2-D column) is buffered into an Mo-by-N matrix, where Mo is
specified by the Output buffer size parameter (Mo > 1). That is, each input
vector becomes a row in the N-channel frame-based output matrix. When

5-41
Buffer

Mo=1, the input is simply passed through to the output, and retains the same
dimension.
Sample-based full-dimension matrix inputs are not accepted.
The Buffer overlap parameter, L, specifies the number of samples (rows) from
the current output to repeat in the next output, where L < Mo. For 0 ≤ L < Mo,
the number of new input samples that the block acquires before propagating
the buffered data to the output is the difference between the Output buffer
size and Buffer overlap, Mo-L.

The output frame period is (Mo-L)∗Tsi, which is equal to the input sequence
sample period, Tsi, when the Buffer overlap is Mo-1. For L < 0, the block
simply discards L input samples after the buffer fills, and outputs the buffer
with period (Mo-L)∗Tsi, which is longer than the zero-overlap case.
In the model below, the block buffers a four-channel sample-based input using
a Output buffer size of 3 and a Buffer overlap of 1.

ch2 ch3
ch1 ch4
Sample-based input ,
t=5 6 1 5 –6 sample period = Tsi
Tsi = 1
t=4 5 1 5 –5
Frame-based output ,
t=3 4 0 5 –4 frame period = (M o-L)∗Tsi
first
t=2 3 0 5 –3
first sample-based frame-based
t=1 2 1 5 –2 input output
ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4

t=0 1 1 5 –1
4 0 5 –4 2 1 5 –2 0 0 0 0 0000
5 1 5 –5 3 0 5 –3 1 1 5 –1 0000
6 1 5 –6 4 0 5 –4 2 1 5 –2 0000

t=6 t=4 t=2 t=0

(Mo=3, L=1)

Note that the input vectors do not begin appearing at the output until the
second row of the second matrix. This is due to the block’s latency (see
“Latency” below). The first output matrix (all zeros in this example) reflects the
block’s Initial conditions setting, while the first row of zeros in the second
output is a result of the one-sample overlap between consecutive output
frames.

5-42
 Buffer

You can use the rebuffer_delay function with a frame size of 1 to precisely
compute the delay (in samples) for sample-based signals. For the above
example,
d = rebuffer_delay(1,3,1)

d =
4

This agrees with the four samples of delay (zeros) per channel shown in the
figure above.

Frame-Based Operation
In frame-based operation, the Buffer block redistributes the samples in the
input frame to an output frame with a new size and rate. A sequence of Mi-by-N
matrix inputs is buffered into a sequence of Mo-by-N frame-based matrix
outputs, where Mo is the output frame size specified by the Output buffer size
parameter (i.e., the number of consecutive samples from the input frame to
buffer into the output frame). Mo can be greater or less than the input frame
size, Mi. Each of the N input channels is buffered independently.
The Buffer overlap parameter, L, specifies the number of samples (rows) from
the current output to repeat in the next output, where L < Mo. For 0 ≤ L < Mo,
the number of new input samples the block acquires before propagating the
buffered data to the output is the difference between the Output buffer size
and Buffer overlap, Mo-L.
The input frame period is Mi∗Tsi, where Tsi is the sample period. The output
frame period is (Mo-L)∗Tsi, which is equal to the sequence sample period when
the Buffer overlap is Mo-1. The output sample period is therefore related to
the input sample period by

( M o – L )T si
T so = -------------------------------
Mo

Negative Buffer overlap values are not permitted.

In the model below, the block buffers a two-channel frame-based input using a
Output buffer size of 3 and a Buffer overlap of 1.

5-43
Buffer

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2
5 1 1 1
6 1 2 1 51 30 11 00 00 00
7 0 3 0 61 40 21 00 00 00
8 0 4 0 70 51 30 11 00 00

t=4 t=0 (Mo=3, L=1) t=10 t=8 t=6 t=4 t=2 t=0

first input first output

Input frame period = 4∗Tsi Output frame period = (M o-L)∗Tsi

Note that the sequence is delayed by eight samples, which is the latency of the
block in Simulink’s multitasking mode for the parameter settings of this
example (see “Latency” below). The first eight output samples therefore adopt
the value specified for the Initial conditions, which is assumed here to be zero.
Use the rebuffer_delay function to determine the block’s latency for any
combination of frame size and overlap.

Latency Zero Latency

The Buffer block has zero tasking latency in Simulink’s single-tasking mode for
the following special cases:

• Scalar input and output (Mo = Mi = 1) with zero or negative Buffer overlap
(L ≤ 0)
• Scalar output (Mo = 1) with zero Buffer overlap (L = 0) for any input frame
size Mi
• Equal input and output frame sizes (Mo = Mi) with zero Buffer overlap
(L = 0)
• Input frame size an integer multiple of the output frame size (Mi/Mo = k, for
an integer value of k) with zero Buffer overlap (L = 0)

Zero tasking latency means that the first input sample (received at t=0)
appears as first output sample.

5-44
 Buffer

Nonzero Latency

Sample-Based Operation. For all cases of sample-based single-tasking operation

other than those listed above, the Buffer block’s buffer is initialized to the
value(s) specified by the Initial conditions parameter, and the block reads
from this buffer to generate the first D output samples, where


 Mo + L (L ≥ 0)
D = 
 Mo (L < 0)


If the Buffer overlap, L, is zero, the Initial conditions parameter can be a

scalar to be repeated across the first Mo output samples, or a length-Mo vector
containing the values of the first Mo output samples. For nonzero Buffer
overlap, the Initial conditions parameter must be a scalar.

Frame-Based Operation. For frame-based single-tasking operation and all

multitasking operation, use the rebuffer_delay function to compute the exact
delay (in samples) that the Buffer block introduces for a given combination of
buffer size and buffer overlap.
For general buffering between arbitrary frame sizes, the Initial conditions
parameter must be a scalar value, which is then repeated across all elements
of the initial output(s). However, in the special case where the input is 1-by-N
(and the block’s output is therefore an Mo-by-N matrix), Initial conditions can
be:

• An Mo-by-N matrix
• A length-Mo vector to be repeated across all columns of the initial output(s)
• A scalar to be repeated across all elements of the initial output(s)

In the special case where the output is 1-by-N (the result of unbuffering an
Mi-by-N frame-based matrix), Initial conditions can be:

• A vector containing Mi samples to output sequentially for each channel

during the first Mi sample times
• A scalar to be repeated across all elements of the initial output(s)

5-45
Buffer

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

Output buffer size

The number of consecutive samples, Mo, from each channel to buffer into
the output frame.
Buffer overlap
The number of samples, L, by which consecutive output frames overlap.
Initial conditions
The value of the block’s initial output for cases of nonzero latency; a scalar,
vector, or matrix.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-46
 Buffer

See Also Delay Line DSP Blockset

Unbuffer DSP Blockset
rebuffer_delay DSP Blockset

See “Buffering Sample-Based and Frame-Based Signals” on page 3-47 for

related information.

5-47
Burg AR Estimator

Purpose 5Burg AR Estimator

Compute an estimate of AR model parameters using the Burg method.

Library Estimation / Parametric Estimation

Description The Burg AR Estimator block uses the Burg method to fit an autoregressive
(AR) model to the input data by minimizing (least squares) the forward and
backward prediction errors while constraining the AR parameters to satisfy
the Levinson-Durbin recursion.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal, which is assumed to be the output of an AR system
driven by white noise. The block computes the normalized estimate of the AR
system parameters, A(z), independently for each successive input frame.

G G
H ( z ) = ------------ = -------------------------------------------------------------------------------
A(z) –1
1 + a ( 2 )z + … + a ( p + 1 )z
–p

When Inherit estimation order from input dimensions is selected, the

order, p, of the all-pole model is one less that the length of the input vector.
Otherwise, the order is the value specified by the Estimation order parameter
The Output(s) parameter allows you to select between two realizations of the
AR process:

• A – The top output, A, is a column vector of length p+1 with the same frame
status as the input, and contains the normalized estimate of the AR model
polynomial coefficients in descending powers of z,
[1 a(2) ... a(p+1)]

• K – The top output, K, is a column vector of length p with the same frame
status as the input, and contains the reflection coefficients (which are a
secondary result of the Levinson recursion).
• A and K – The block outputs both realizations.

The scalar gain, G, is provided at the bottom output (G).

5-48
 Burg AR Estimator

Dialog Box

Output(s)
The realization to output, model coefficients, reflection coefficients, or both.
Inherit estimation order from input dimensions
When selected, sets the estimation order p to one less than the length of the
input vector.
Estimation order
The order of the AR model, p. This parameter is enabled when Inherit
estimation order from input dimensions is not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

See Also Burg Method DSP Blockset

Covariance AR Estimator DSP Blockset
Modified Covariance AR Estimator DSP Blockset
Yule-Walker AR Estimator DSP Blockset
arburg Signal Processing Toolbox

5-49
Burg Method

Purpose 5Burg Method

Compute a parametric spectral estimate using the Burg method.

Library Estimation / Power Spectrum Estimation

Description The Burg Method block estimates the power spectral density (PSD) of the input
frame using the Burg method. This method fits an autoregressive (AR) model
to the signal by minimizing (least-squares) the forward and backward
prediction errors while constraining the AR parameters to satisfy the
Levinson-Durbin recursion.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal. The block’s output (a column vector) is the estimate of
the signal’s power spectral density at Nfft equally spaced frequency points in
the range [0,Fs), where Fs is the signal’s sample frequency.
When Inherit estimation order from input dimensions is selected, the order
of the all-pole model is one less that the input frame size. Otherwise, the order
is the value specified by the Estimation order parameter. The spectrum is
computed from the FFT of the estimated AR model parameters.
When Inherit FFT length from input dimensions is selected, Nfft is specified
by the frame size of the input, which must be a power of 2. When Inherit FFT
length from input dimensions is not selected, Nfft is specified as a power of 2
by the FFT length parameter, and the block zero pads or truncates the input
to Nfft before computing the FFT. The output is always sample-based.
The Burg Method and Yule-Walker Method blocks return similar results for
large frame sizes. The following table compares the features of the Burg
Method block to the Covariance Method, Modified Covariance Method, and
Yule-Walker Method blocks.

5-50
 Burg Method

Burg Covariance Modified Covariance Yule-Walker

Characteristics Does not apply Does not apply Does not apply Applies window to
window to data window to data window to data data

Minimizes the Minimizes the Minimizes the Minimizes the

forward and forward prediction forward and forward prediction
backward prediction error in the backward prediction error in the
errors in the least-squares sense errors in the least-squares sense
least-squares sense, least-squares sense (also called
with the AR “Autocorrelation
coefficients method”)
constrained to satisfy
the L-D recursion

Advantages High resolution for Better resolution than High resolution for Performs as well as
short data records Y-W for short data short data records other methods for
records (more large data records
accurate estimates)

Always produces a Able to extract Able to extract Always produces a

stable model frequencies from data frequencies from data stable model
consisting of p or more consisting of p or more
pure sinusoids pure sinusoids

Does not suffer

spectral line-splitting

Disadvantages Peak locations highly May produce unstable May produce unstable Performs relatively
dependent on initial models models poorly for short data
phase records

May suffer spectral Frequency bias for Peak locations Frequency bias for
line-splitting for estimates of sinusoids slightly dependent on estimates of sinusoids
sinusoids in noise, or in noise initial phase in noise
when order is very
large

Frequency bias for Minor frequency bias

estimates of sinusoids for estimates of
in noise sinusoids in noise

Conditions for Order must be less Order must be less Because of the biased
Nonsingularity than or equal to half than or equal to 2/3 estimate, the
the input frame size the input frame size autocorrelation
matrix is guaranteed
to positive-definite,
hence nonsingular

5-51
Burg Method

Examples The dspsacomp demo compares the Burg method with several other spectral
estimation methods.

Dialog Box

Inherit estimation order from input dimensions

When selected, sets the estimation order to one less than the length of the
input vector. Tunable.
Estimation order
The order of the AR model. This parameter is enabled when Inherit
estimation order from input dimensions is not selected.

Inherit FFT length from input dimensions

When selected, uses the input frame size as the number of data points, Nfft,
on which to perform the FFT. Tunable.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft
exceeds the input frame size, the frame is zero-padded as needed. This
parameter is enabled when Inherit FFT length from input dimensions is
not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Orfanidis, J. S. Optimum Signal Processing: An Introduction. 2nd ed.
New York, NY: Macmillan, 1985.

5-52
 Burg Method

Supported Double-precision floating point

Data Types

See Also Burg AR Estimator DSP Blockset

Covariance Method DSP Blockset
Modified Covariance Method DSP Blockset
Short-Time FFT DSP Blockset
Yule-Walker Method DSP Blockset
pburg Signal Processing Toolbox

See “Power Spectrum Estimation” on page 4-15 for related information.

5-53
Check Signal Attributes

Purpose 5Check Signal Attributes

Generate an error when the input signal does or does not match selected
attributes exactly.

Library Signal Management / Signal Attributes

Description The Check Signal Attributes block terminates the simulation with an error
when the input characteristics differ from those specified by the block
parameters.
When the Error if input parameter is set to Does not match attributes
exactly, the block generates an error only when the input possesses none of the
attributes specified by the other parameters. Signals that possess at least one
of the specified attributes are propagated to the output unaltered, and do not
generate an error.
When the Error if input parameter is set to Matches attributes exactly, the
block generates an error only when the input possesses all attributes specified
by the other parameters. Signals that do not possess all of the specified
attributes are propagated to the output unaltered, and do not generate an
error.

Signal Attributes
The Check Signal Attributes block can test for up to five different signal
attributes, as specified by the following parameters. When Ignore is selected
in any parameter, the block does not check the signal for the corresponding
attribute. For example, when Complexity is set to Ignore, neither real nor
complex inputs cause the block to generate an error. The attributes are:
• Complexity
Checks whether the signal is real or complex. (Note that this information can
also be displayed in a model by attaching a Probe block with Probe complex
signal selected, or by selecting Port data types from the model window’s
Format menu.)
• Frame status
Checks whether the signal is frame-based or sample-based. (Note that
Simulink displays sample-based signals using a single line, →, and
frame-based signals using a double line, ⇒.)

5-54
 Check Signal Attributes

• Dimensionality
Checks the dimension of signal for compliance (Is...) or noncompliance
(Is not...) with the attributes in the subordinate Dimension menu, which are
shown in the table below. See“Signal Dimension Nomenclature” on page 1-10
for a description of Simulink signal dimensions. M and N are positive
integers unless otherwise indicated below.

5-55
Check Signal Attributes

Dimensions Is... Is not...

1-D 1-D vector, M-by-N matrix,

1-D scalar 1-by-N matrix (row vector),
M-by-1 matrix (column
vector),
1-by-1 matrix (2-D scalar)

2-D M-by-N matrix, 1-D vector,

1-by-N matrix (row vector), 1-D scalar
M-by-1 matrix (column
vector),
1-by-1 matrix (2-D scalar)

Scalar 1-D scalar, 1-D vector with length>1,

(1-D or 2-D) 1-by-1 matrix (2-D scalar) M-by-N matrix with M>1
and/or N>1

Vector 1-D vector, M-by-N matrix with M>1

(1-D or 2-D) 1-D scalar, and N>1
1-by-N matrix (row vector),
M-by-1 matrix (column
vector),
1-by-1 matrix (2-D scalar)
Vector (1-D or 2-D) or scalar

Row Vector 1-by-N matrix (row vector), 1-D vector,

(2-D) 1-by-1 matrix (2-D scalar) 1-D scalar,
Row vector (2-D) or scalar M-by-N matrix with M>1

Column M-by-1 matrix (column 1-D vector,

Vector vector), 1-D scalar,
(2-D) 1-by-1 matrix (2-D scalar) M-by-N matrix with N>1
Column vector (2-D) or
scalar

5-56
 Check Signal Attributes

Dimensions Is... Is not...

(Continued)

Full matrix M-by-N matrix with M>1 1-D vector,

and N>1 1-D scalar,
1-by-N matrix (row vector),
M-by-1 matrix (column
vector),
1-by-1 matrix (2-D scalar)

Square M-by-N matrix with M=N, M-by-N matrix with M≠N,

matrix 1-D scalar, 1-D vector,
1-by-1 matrix (2-D scalar) 1-by-N matrix (row vector),
M-by-1 matrix (column
vector)

Note that when Signal dimensions is selected from the model window
Format menu, Simulink displays the size of a 1-D vector signal as an
unbracketed integer, and displays the dimension of a 2-D signal as a pair of
bracketed integers, [MxN]. Simulink does not display any size information for
a 1-D or 2-D scalar signal. Dimension information for a signal can also be
displayed in a model by attaching a Probe block with Probe signal
dimensions selected.
• Data type
Checks the signal data type for compliance (Is...) or noncompliance (Is not...)
with the attributes in the subordinate General data type menu, which are
shown in the table below. Any of the specific data types listed in the Is...

5-57
Check Signal Attributes

column below can be individually selected from the subordinate Specific

data type menu.

General data type Is... Is not...

Boolean boolean single, double, uint8, int8,

uint16, int16, uint32, int32,
fixed-point

Floating-point single, double boolean, uint8, int8, uint16,

int16, uint32, int32, fixed-point

Fixed-point fixed-point boolean, uint8, int8, uint16,

int16, uint32, int32, single,
double

Integer Signed integer boolean, single, double

int8, int16, int32
Unsigned integer
uint8, uint16,
uint32

Note that data type information can also be displayed in a model by selecting
Port data types from the model window’s Format menu.
• Sample mode
Checks whether the signal is discrete-time or continuous-time. (Note that
when Sample time colors is selected from the Format menu, Simulink
displays continuous-time signal lines in black or grey and discrete-time
signal lines in colors corresponding to the relative rate. When a Probe block
with Probe sample time enabled is attached to a continuous-time signal, the
block icon displays the string Ts:[0 x], where x is the sample time offset.
When a Probe block is attached to a discrete-time signal, the block icon
displays the string Ts:[t 0] for a sample-based signal or Tf:[t 0] for a
frame-based signal, where t is the nonzero sample period or frame period,
respectively. Frame-based signals are almost always discrete-time.)

5-58
 Check Signal Attributes

Dialog Box

Error if input
Specifies whether the block generates an error when the input possesses
none of the required attributes (Does not match attributes exactly), or
when the input possesses all of the required attributes (Matches
attributes exactly).

Complexity
The complexity for which the input should be checked, Real or Complex.
Frame status
The frame status for which the input should be checked, Sample-based or
Frame-based.

Dimensionality
Specifies whether the input should be checked for compliance (Is...) or
noncompliance (Is not...) with the attributes in the subordinate
Dimension menu.

Dimensions
The dimensions for which the input should be checked. This parameter is
available when Is... or Is not... is selected in the Dimensionality menu.

5-59
Check Signal Attributes

Data type
Specifies whether the input should be checked for compliance (Is...) or
noncompliance (Is not...) with the attributes in the subordinate General
data type menu.

General data type

The general data type for which the input should be checked. This
parameter is available when Is... or Is not... is selected in the Data type
menu, and enables the subordinate Specific data type parameter in most
cases.
Specific data type
The specific data type for which the input should be checked. This
parameter is available when Floating-point, Fixed-point, or Integer is
selected in the General data type menu.
Sample mode
The sample mode for which the input should be checked, Discrete or
Continuous.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

Convert 1-D to 2-D DSP Blockset
Convert 2-D to 1-D DSP Blockset
Data Type Conversion Simulink
Frame Status Conversion DSP Blockset
Inherit Complexity DSP Blockset
Probe Simulink
Reshape Simulink
Submatrix DSP Blockset

5-60
 Chirp

Purpose 5Chirp
Generate a swept-frequency cosine (chirp) signal.

Library DSP Sources

Description The Chirp block outputs a swept-frequency cosine (chirp) signal with unity
amplitude and continuous phase. To specify the desired output chirp signal,
you must define its instantaneous frequency function, also known as the output
frequency sweep. The frequency sweep can be linear, quadratic, or logarithmic,
and repeats once every Sweep time by default. See the following sections of
this reference page for more details:

• “Variables Used in This Reference Page” on page 5-61

• “Setting the Output Frame Status” on page 5-62
• “Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep
Mode” on page 5-62
• “Unidirectional and Bidirectional Sweep Modes” on page 5-63
• “Setting Instantaneous Frequency Sweep Values” on page 5-64
• “Block Computation Methods” on page 5-65
• “Cautions Regarding the Swept Cosine Sweep” on page 5-67
• “Examples” on page 5-68

Variables Used in This Reference Page

Refer to the following list for definitions of variables used in this reference
page.
f0 Initial frequency parameter (Hz)
fi(tg) Target frequency parameter (Hz)
tg Target time parameter (seconds)
Tsw Sweep time parameter (seconds)
φ0 Initial phase parameter (radians)
ψ(t) Phase of the chirp signal (radians)
fi(t) User-specified output instantaneous frequency function (Hz);
user-specified sweep
fi(actual)(t) Actual output instantaneous frequency function (Hz); actual
output sweep
ychirp(t) Output chirp function

5-61
Chirp

Setting the Output Frame Status

Use Samples per frame parameter to set the block’s output frame status, as
summarized in the table. The Sample time parameter sets the sample time of
both sample- and frame-based outputs.

Setting of Samples Per Frame Parameter Output Frame Status

1 Sample-based

n (any integer greater than 1) Frame-based, frame size n

Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep

Mode
The basic shape of the output instantaneous frequency sweep, fi(t), is set by the
Frequency sweep and Sweep mode parameters, described in the following
table.

Parameters for Possible Settings Parameter Description

Setting Sweep Shape

Frequency sweep Linear Determines whether the sweep frequencies vary

Quadratic linearly, quadratically, or logarithmically.
Logarithmic (Linear and swept cosine sweeps both vary
Swept cosine linearly.)
Sweep mode Unidirectional Determines whether the sweep is unidirectional
Bidirectional or bidirectional. For details, see “Unidirectional
and Bidirectional Sweep Modes”.

5-62
 Chirp

The following diagram illustrates the possible shapes of the frequency sweep
that you can obtain by setting the Frequency sweep and Sweep mode
parameters.

Possible Shapes of the Output Instantaneous Frequency Sweep

Quadratic and Logarithmic Sweeps

Swept Cosine and Linear Sweeps (Logarithmic sweeps cannot be negative.)
These diagrams apply
only to quadratic sweeps.

Positive Sweeps Negative Sweeps Positive Sweeps Negative Sweeps

( fi(tg) > f0 ) ( fi(tg) < f0 )
Unidirectional

fi(t) fi(t) fi(t) fi(t)

Sweeps

... ... ... ...

Tsw time Tsw time Tsw time Tsw time
Bidirectional

fi(t) fi(t) fi(t) fi(t)

Sweeps

... ... ... ...

Tsw time Tsw time Tsw time Tsw time

For information on how to set the frequency values in your sweep, see “Setting
Instantaneous Frequency Sweep Values”.

Unidirectional and Bidirectional Sweep Modes

The Sweep mode parameter determines whether your sweep is unidirectional
or bidirectional, which affects the shape of your output frequency sweep (see
“Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep Mode”

5-63
Chirp

on page 5-62). The following table describes the characteristics of

unidirectional and bidirectional sweeps.

Sweep mode Sweep Characteristics

Parameter
Settings

Unidirectional • Lasts for one Sweep time, Tsw

• Repeats once every Tsw
Bidirectional • Lasts for twice the Sweep time, 2*Tsw
• Repeats once every 2*Tsw
• First half is identical to its unidirectional counterpart.
• Second half is a mirror image of the first half.

The following diagram illustrates a linear sweep in both sweep modes. For
information on setting the frequency values in your sweep, see “Setting
Instantaneous Frequency Sweep Values”.

Unidirectional Linear Sweep Bidirectional Linear Sweep

Lasts for Tsw Lasts for 2*Tsw

fi(t) First half is identical to its unidirectional counterpart.

Second half is mirror image of first half.
fi(t)
fi(tg) ...
f0
fi(tg) ...
0 tg Tsw 2Tsw time
f0
Repeats every Tsw 0 tg Tsw 2Tsw 3Tsw 4Tsw time

Repeats every 2*Tsw

Setting Instantaneous Frequency Sweep Values

Set the following parameters to tune the frequency values of your output
frequency sweep:
• Initial frequency (Hertz), f0

5-64
 Chirp

• Target frequency (Hertz), fi(tg)

• Target time (seconds), tg

The following table summarizes the sweep values at specific times for all
Frequency sweep settings. For information on the formulas used to compute
sweep values at other times, see “Block Computation Methods”.

Table 5-1: Instantaneous Frequency Sweep Values

Frequency Sweep Value at t = 0 Sweep Value at t = tg Time When Sweep Value is Target
Sweep Frequency, fi(tg)

Linear f0 fi(tg) tg

Quadratic f0 fi(tg) tg

Logarithmic f0 + 1 fi(tg) tg

Swept cosine f0 2fi(tg) - f0 tg/2

Block Computation Methods

The Chirp block uses one of two formulas to compute the block output,
depending on the Frequency Sweep parameter setting. For details, see the
following sections:

• “Equations for Output Computation”

• “Output Computation Method for Linear, Quadratic, and Logarithmic
Frequency Sweeps”
• “Output Computation Method for Swept Cosine Frequency Sweep”

Equations for Output Computation. The following table shows the equations used by
the block to compute the user-specified output frequency sweep, fi(t), the block
output, ychirp(t), and the actual output frequency sweep, fi(actual)(t). The only
time the user-specified sweep is not the actual output sweep is when the
Frequency sweep parameter is set to Swept cosine.

Note The following equations apply only to unidirectional sweeps in which

fi(0) < fi(tg). To derive equations for other cases, you may find it helpful to

5-65
Chirp

examine the following table and the diagram in “Shaping the Frequency
Sweep by Setting Frequency Sweep and Sweep Mode” on page 5-62.

Table 5-2 contains the following variables:

• fi(t) — the user-specified frequency sweep

• fi(actual)(t) — the actual output frequency sweep, usually equal to fi(t)
• ychirp(t) — the Chirp block output
• ψ ( t ) — the phase of the chirp signal, where ψ ( 0 ) = 0 , and 2πf i ( t ) is the
derivative of the phase
1 dψ ( t )
f i ( t ) = ------ ⋅ ---------------
2π dt

• φ 0 — the Initial phase parameter value, where y chirp ( 0 ) = cos ( φ 0 )

Table 5-2: Equations Used by the Chirp Block for Unidirectional Positive Sweeps

Frequency Block Output Chirp Signal User-Specified β Actual Frequency

Sweep Frequency Sweep, fi(actual)(t)
Sweep, fi(t)

Linear y chirp ( t ) = cos ( ψ ( t ) + φ 0 ) f i(t) = f 0 + βt fi ( tg ) – f0 f (t) = f (t)

i ( actual ) i
β = --------------------------
tg

Quadratic Same as Linear f i(t) = f 0 + βt 2 fi ( tg ) – f0 f (t) = f (t)

i ( actual ) i
β = --------------------------
2
tg

Logarithmic Same as Linear f i(t) = f 0 + 10 βt log [ f ( t ) – f ] f (t) = f (t)

i g 0 i ( actual ) i
β = ----------------------------------------
t
Note fi(0) = f0 + 1 g
Where fi(tg) > f0

Swept cosine y ( t ) = cos ( 2πf ( t )t + φ ) Same as Linear Same as Linear f (t) = f (t) + βt
chirp i 0 i ( actual ) i

Output Computation Method for Linear, Quadratic, and Logarithmic Frequency Sweeps.
The derivative of the phase of a chirp function gives the instantaneous
frequency of the chirp function. The Chirp block uses this principle to calculate

5-66
 Chirp

the chirp output when the Frequency Sweep parameter is set to Linear,
Quadratic, or Logarithmic.

y chirp ( t ) = cos ( ψ ( t ) + φ 0 ) Linear, quadratic, or logarithmic chirp

signal with phase ψ ( t )

1 dψ ( t ) Phase derivative is instantaneous

f i ( t ) = ------ ⋅ ---------------
2π dt frequency (5-1)

For instance, if you want a chirp signal with a linear instantaneous frequency
sweep, you should set the Frequency Sweep parameter to Linear, and tune
the linear sweep values by setting other parameters appropriately. The block
will output a chirp signal, the phase derivative of which is the specified linear
sweep. This ensures that the instantaneous frequency of the output is the
linear sweep you desired. For equations describing the linear, quadratic, and
logarithmic sweeps, see “Equations for Output Computation” on page 5-65.

Output Computation Method for Swept Cosine Frequency Sweep. To generate the swept
cosine chirp signal, the block sets the swept cosine chirp output as follows.

y chirp ( t ) = cos ( ψ ( t ) + φ 0 ) = cos ( 2πf i ( t )t + φ 0 ) Swept cosine chirp

output (Equation 5-1
does not hold.)

Note that Equation 5-1 does not hold for the swept cosine chirp, so the
user-defined frequency sweep, fi(t), is not the actual output frequency sweep,
fi(actual)(t), of the swept cosine chirp. Thus, the swept cosine output may not
behave as you expect. To learn more about swept cosine chirp behavior, see
“Cautions Regarding the Swept Cosine Sweep” on page 5-67 and “Equations for
Output Computation” on page 5-65.

Cautions Regarding the Swept Cosine Sweep

If you want a linearly swept chirp signal, we recommend you use a linear
frequency sweep. Though a swept cosine frequency sweep also yields a linearly
swept chirp signal, the output may have unexpected frequency content. For
details, see the following two sections.

5-67
Chirp

Swept Cosine Instantaneous Output Frequency at the Target Time is not the Target Frequency.
The swept cosine sweep value at the Target time is not necessarily the Target
frequency. This is because the user-specified sweep is not the actual frequency
sweep of the swept cosine output, as noted in “Output Computation Method for
Swept Cosine Frequency Sweep” on page 5-67. See Table 5-1, Instantaneous
Frequency Sweep Values, for the actual value of the swept cosine sweep at the
Target time.

Swept Cosine Output Frequency Content May Greatly Exceed Frequencies in the Sweep. In
Swept cosine mode, you should not set the parameters so that 1/Tsw is very
large compared to the values of the Initial frequency and Target frequency
parameters. In such cases, the actual frequency content of the swept cosine
sweep may be closer to 1/Tsw, far exceeding the Initial frequency and Target
frequency parameter values.

Examples The first few examples demonstrate how to use the Chirp block’s main
parameters, how to view the output in the time domain, and how to view the
output spectrogram:

• “Example 1: Setting a Final Frequency Value for Unidirectional Sweeps”

• “Example 2: Bidirectional Sweeps”
• “Example 3: When Sweep Time is Greater Than Target Time”

Examples 4 and 5 illustrate Chirp block settings that may produce unexpected
outputs:
• “Example 4: Output Sweep with Negative Frequencies”
• “Example 5: Output Sweep with Frequencies Greater Than Half the
Sampling Frequency”

Example 1: Setting a Final Frequency Value for Unidirectional Sweeps. Often times, you
may want a unidirectional sweep for which you know the initial and final
frequency values. You can specify the final frequency of a unidirectional sweep
by setting Target time equal to Sweep time, in which case the Target
frequency becomes the final frequency in the sweep. The following model
demonstrates this method.
This technique may not work for swept cosine sweeps. For details, see
“Cautions Regarding the Swept Cosine Sweep” on page 5-67.

5-68
 Chirp

Open the Example 1 model by clicking here in the MATLAB Help Browser. You
can also rebuild the model yourself; see the following list for model parameter
settings (leave unlisted parameters in their default states).

Since Target time is set to equal Sweep time (1 second), the Target
frequency (25 Hertz) is the final frequency of the unidirectional sweep.
10 40

35

5 30
AMPLITUDE

FREQUENCY

25

0
20

15
−5
10

5
−10
0 1 2 3 4 5 6 0
Frame: 6 TIME (s) 0 1 2 3 4 5
TIME (s)
Run your model to see the time domain output, and then type the following
command to view the chirp output spectrogram.

5-69
Chirp

specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)

Chirp Block Parameters for Example 1

Frequency sweep Linear
Sweep mode Unidirectional
Initial frequency 0
Target frequency 25
Target time 1
Sweep time 1
Initial phase 0
Sample time 1/400
Samples per frame 400

Vector Scope Block Parameters for Example 1

Input domain Time
Time display span 6

Signal To Workspace Block Parameters for Example 1

Variable name dsp_examples_yout

Simulation Parameters Dialog Parameters for Example 1

Stop time 5

Example 2: Bidirectional Sweeps. Change the Sweep mode parameter in the

Example 1 model to Bidirectional, and leave all other parameters the same to
view the following bidirectional chirp. Note that in the bidirectional sweep, the
period of the sweep is twice the Sweep time (2 seconds), whereas it was one
Sweep time (1 second) for the unidirectional sweep in Example 1.

5-70
 Chirp

Open the Example 2 model by clicking here in the MATLAB Help Browser.
10 40

35

5 30
AMPLITUDE

FREQUENCY
25

0
20

15
−5
10

5
−10
0 1 2 3 4 5 6 0
Frame: 6 TIME (s) 0 1 2 3 4 5
TIME (s)

Run your model to see the time domain output, and then type the following
command to view the chirp output spectrogram.
specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)

Example 3: When Sweep Time is Greater Than Target Time. Setting Sweep time to 1.5
and leaving the rest of the parameters as in the Example 1 model gives the
following output. The sweep still reaches the Target frequency (25 Hertz) at
the Target time (1 second), but since Sweep time is greater than Target time,
the sweep continues on its linear path until one Sweep time (1.5 seconds) is
traversed.
Unexpected behavior may arise when you set Sweep time greater than Target
time; see “Example 4: Output Sweep with Negative Frequencies” for details.

5-71
Chirp

Open the Example 3 model by clicking here in the MATLAB Help Browser.
10 40

35

5 30
AMPLITUDE

FREQUENCY
25
0
20

15
−5
10

5
−10
0 1 2 3 4 5 6 0
Frame: 6 TIME (s) 0 1 2 3 4 5
Time (s)

Run your model to see the time domain output, and then type the following
command to view the chirp output spectrogram.
specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)

Example 4: Output Sweep with Negative Frequencies. Modify the Example 1 model by
changing Sweep time to 1.5, Initial frequency to 25, and Target frequency
to 0. The output chirp of this example may not behave as you expect because the
sweep contains negative frequencies between 1 and 1.5 seconds. The sweep
reaches the Target frequency of 0 Hertz at one second, then continues on its
negative slope, taking on negative frequency values until it traverses one
Sweep time (1.5 seconds).

The spectrogram may reflect negative sweep frequencies along the x-axis so
they appear to be positive, as in the one below. If you unexpectedly get a chirp
output with a spectrogram resembling the one following, your chirp’s sweep
may contain negative frequencies. See the next example for another possible
unexpected chirp output.

5-72
 Chirp

Open the Example 4 model by clicking here in the MATLAB Help Browser.
10 30

25
5
20
AMPLITUDE

FREQUENCY
0 15

10
−5

−10
0 1 2 3 4 5 6 0
0 1 2 3 4 5
Frame: 6 TIME (s) TIME (s)
Run your model to see the time domain output, and then type the following
command to view the chirp output spectrogram.
specgram(dsp_examples_yout,[0:.1:30],400,hamming(128),110);

Example 5: Output Sweep with Frequencies Greater Than Half the Sampling Frequency.
Modify the Example 1 model by changing the Target frequency parameter
to 275. The output chirp of this model may not behave as you expect because the
sweep contains frequencies greater than half the sampling frequency (200
Hertz), which causes aliasing. If you unexpectedly get a chirp output with a
spectrogram resembling the one following, your chirp’s sweep may contain
frequencies greater than half the sampling frequency. See the previous
example for another possible unexpected chirp output.

5-73
Chirp

Open the Example 5 model by clicking here in the MATLAB Help Browser.
10 200

180

160
5
140
AMPLITUDE

FREQUENCY
120
0
100

80

−5 60

40

20
−10
0 1 2 3 4 5 6 0
Frame: 6 TIME (s) 0 1 2 3 4 5
TIME (s)

Run your model to see the time domain output, and then type the following
command to view the chirp output spectrogram.
specgram(dsp_examples_yout,256,400,hamming(64),60)

5-74
 Chirp

Dialog Box

Frequency sweep
The type of output instantaneous frequency sweep, fi(t): Linear,
Logarithmic, Quadratic, or Swept cosine. Tunable.

Sweep mode
The directionality of the chirp signal: Unidirectional or Bidirectional.
Tunable.
Initial frequency (Hz)
For Linear, Quadratic, and Swept cosine sweeps, the initial frequency,
f0, of the output chirp signal. For Logarithmic sweeps, Initial frequency
is one less than the actual initial frequency of the sweep. Also, when the
sweep is Logarithmic, you must set the Initial frequency to be less than
the Target frequency. Tunable.

5-75
Chirp

Target frequency (Hz)

For Linear, Quadratic, and Logarithmic sweeps, the instantaneous
frequency, fi(tg), of the output at the Target time, tg. For a Swept cosine
sweep, Target frequency is the instantaneous frequency of the output at
half the Target time, tg/2. When Frequency sweep is Logarithmic, you
must set the Target frequency to be greater than the Initial frequency.
Tunable.
Target time (sec)
For Linear, Quadratic, and Logarithmic sweeps, the time, tg, at which
the Target frequency, fi(tg), is reached by the sweep. For a Swept cosine
sweep, Target time is the time at which the sweep reaches 2fi(tg) - f0. You
must set Target time to be no greater than Sweep time, T sw ≥ t g .
Tunable.
Sweep time (sec)
In Unidirectional Sweep mode, the Sweep time, Tsw, is the period of the
output frequency sweep. In Bidirectional Sweep mode, the Sweep time
is half the period of the output frequency sweep. You must set Sweep time
to be no less than Target time, T sw ≥ t g . Tunable.
Initial phase (radians)
The phase, φ 0 , of the cosine output at t=0; y chirp ( t ) = cos ( φ 0 ) . Tunable.
Sample time
The sample period, Ts, of the output. The output frame period is Mo∗Ts.
Samples per frame
The number of samples, Mo, to buffer into each output frame.

Supported Double-precision floating point

Data Types

See Also Signal From Workspace DSP Blockset

Signal Generator Simulink
Sine Wave DSP Blockset
chirp Signal Processing Toolbox
specgram Signal Processing Toolbox

5-76
 Chirp

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-77
Cholesky Factorization

Purpose 5Cholesky Factorization

Factor a square Hermitian positive definite matrix into triangular
components.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The Cholesky Factorization block uniquely factors the square Hermitian
positive definite input matrix S as
*
S = LL
where L is a lower triangular square matrix with positive diagonal elements
and L* is the Hermitian (complex conjugate) transpose of L. Only the diagonal
and upper triangle of the input matrix are used, and any imaginary component
of the diagonal entries is disregarded.
The block’s output is a composite matrix with lower triangle elements from L
and upper triangle elements from L*, and is always sample-based.

9 –1 2 3.00 – 0.33 0.67

–1 8 –5 – 0.33 2.81 – 1.70
2 –5 7 0.67 – 1.70 1.91

3.00 0 0
L = – 0.33 2.81 0
0.67 – 1.70 1.91

Note that L and L* share the same diagonal in the output matrix. Cholesky
factorization requires half the computation of Gaussian elimination
(LU decomposition), and is always stable.
The algorithm requires that the input be square and Hermitian positive
definite. When the input is not positive definite, the block reacts with the
behavior specified by the Non-positive definite input parameter. The
following options are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid factorization. A partial factorization will be present in the
upper left corner of the output.

5-78
 Cholesky Factorization

• Warning – Display a warning message in the MATLAB command window,

and continue the simulation. The output is not a valid factorization. A partial
factorization will be present in the upper left corner of the output.
• Error – Display an error dialog box and terminate the simulation.

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Inverse DSP Blockset
Cholesky Solver DSP Blockset
LDL Factorization DSP Blockset
LU Factorization DSP Blockset
QR Factorization DSP Blockset
chol MATLAB

See “Factoring Matrices” on page 4-17 for related information.

5-79
Cholesky Inverse

Purpose 5Cholesky Inverse

Compute the inverse of a Hermitian positive definite matrix using Cholesky
factorization.

Library Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description The Cholesky Inverse block computes the inverse of the Hermitian positive
definite input matrix S by performing Cholesky factorization.

–1 * –1
S = ( LL )

L is a lower triangular square matrix with positive diagonal elements and L*

is the Hermitian (complex conjugate) transpose of L. Only the diagonal and
upper triangle of the input matrix are used, and any imaginary component of
the diagonal entries is disregarded. Cholesky factorization requires half the
computation of Gaussian elimination (LU decomposition), and is always stable.
The output is always sample-based.
The algorithm requires that the input be Hermitian positive definite. When the
input is not positive definite, the block reacts with the behavior specified by the
Non-positive definite input parameter. The following options are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid inverse.
• Warning – Display a warning message in the MATLAB command window,
and continue the simulation. The output is not a valid inverse.
• Error – Display an error dialog box and terminate the simulation.

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

5-80
 Cholesky Inverse

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Cholesky Factorization DSP Blockset

Cholesky Solver DSP Blockset
LDL Inverse DSP Blockset
LU Inverse DSP Blockset
Pseudoinverse DSP Blockset
inv MATLAB

See “Inverting Matrices” on page 4-19 for related information.

5-81
Cholesky Solver

Purpose 5Cholesky Solver

Solve the equation SX=B for X when S is a square Hermitian positive definite
matrix.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The Cholesky Solver block solves the linear system SX=B by applying Cholesky
factorization to input matrix at the S port, which must be square (M-by-M) and
Hermitian positive definite. Only the diagonal and upper triangle of the matrix
are used, and any imaginary component of the diagonal entries is disregarded.
The input to the B port is the right-hand side M-by-N matrix, B. The output is
the unique solution of the equations, M-by-N matrix X, and is always
sample-based.
When the input is not positive definite, the block reacts with the behavior
specified by the Non-positive definite input parameter. The following options
are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid solution.
• Warning – Proceed with the computation and display a warning message in
the MATLAB command window. The output is not a valid solution.
• Error – Display an error dialog box and terminate the simulation.

A length-M vector input for right-hand side B is treated as an M-by-1 matrix.

Algorithm Cholesky factorization uniquely factors the Hermitian positive definite input
matrix S as
*
S = LL
where L is a lower triangular square matrix with positive diagonal elements.
The equation SX=B then becomes
*
LL X = B
which is solved for X by making the substitution Y = L*X, and solving the
following two triangular systems by forward and backward substitution,
respectively.

5-82
 Cholesky Solver

LY = B

*
L X = Y

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Factorization DSP Blockset
Cholesky Inverse DSP Blockset
LDL Solver DSP Blockset
LU Solver DSP Blockset
QR Solver DSP Blockset
chol MATLAB

See “Solving Linear Systems” on page 4-16 for related information.

5-83
Complex Cepstrum

Purpose 5Complex Cepstrum

Compute the complex cepstrum of an input.

Library Transforms

Description The Complex Cepstrum block computes the complex cepstrum of each channel
in the real-valued M-by-N input matrix, u. For both sample-based and
frame-based inputs, the block assumes that each input column is a frame
containing M consecutive samples from an independent channel. The block
does not accept complex-valued inputs.
The input is altered by the application of a linear phase term so that there is
no phase discontinuity at ±π radians. That is, each input channel is
independently zero padded and circularly shifted to have zero phase at
π radians.
The output is a real Mo-by-N matrix, where Mo is specified by the FFT length
parameter. Each output column contains the length-Mo complex cepstrum of
the corresponding input column.
y = cceps(u,Mo) % Equivalent MATLAB code

When the Inherit FFT length from input port dimensions check box is
selected, the output frame size matches the input frame size (Mo=M). In this
case, a sample-based length-M row vector input is processed as a single channel
(i.e., as an M-by-1 column vector), and the output is a length-M row vector. A
1-D vector input is always processed as a single channel, and the output is a
1-D vector.
The output is always sample-based, and the output port rate is the same as the
input port rate.

Dialog Box

5-84
 Complex Cepstrum

Inherit FFT length from input port dimensions

When selected, matches the output frame size to the input frame size.
FFT length
The number of frequency points at which to compute the FFT, which is also
the output frame size, Mo. This parameter is available when Inherit FFT
length from input port dimensions is not selected.

Supported Double-precision floating point

Data Types

See Also DCT DSP Blockset

FFT DSP Blockset
Real Cepstrum DSP Blockset
cceps Signal Processing Toolbox

5-85
Complex Exponential

Purpose 5Complex Exponential

Compute the complex exponential function.

Library Math Functions / Math Operations

Description The Complex Exponential block computes the complex exponential function for
each element of the real input, u.
ju
y = e = cos u + j sin u
where j = – 1 . The output is complex, with the same size and frame status as
the input.

Dialog Box

Supported Double-precision floating point

Data Types

See Also Math Function Simulink

Sine Wave DSP Blockset
exp MATLAB

5-86
 Constant Diagonal Matrix

Purpose 5Constant Diagonal Matrix

Generate a square, diagonal matrix.

Library DSP Sources,

Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Constant Diagonal Matrix block outputs a square diagonal matrix
constant. The Constant along diagonal parameter determines the values
along the matrix diagonal. This parameter can be a scalar to be repeated for all
elements along the diagonal, or a vector containing the values of the diagonal
elements. To generate the identity matrix, set the Constant along diagonal
to 1, or use the Identity Matrix block.
The output is frame-based when the Frame-based output check box is
selected; otherwise, the output is sample-based.

Dialog Box

Constant(s) along diagonal

The values of the elements along the diagonal, as a scalar or vector.
Tunable.
Frame-based output
Specifies frame-based output when selected. Tunable.
MATLAB commands for casting values to certain data types are provided
parentheses:

5-87
Constant Diagonal Matrix

Supported (MATLAB
( commands for casting values to certain data types are provided in
Data Types parentheses.)
Boolean (boolean)
8-, 16-, and 32-bit signed integer (int8, int16, int32)
8-, 16-, and 32-bit unsigned integer (uint8, uint16, uint32)
Single-precision floating point (single)
Double-precision floating point (double)

See Also Create Diagonal Matrix DSP Blockset

DSP Constant DSP Blockset
Identity Matrix DSP Blockset
diag MATLAB

See “Creating Signals Using Constant Blocks” on page 3-33 for related
information.

5-88
 Constant Ramp

Purpose 5Constant Ramp

Generate a ramp signal with length based on input dimensions.

Library DSP Sources

Description The Constant Ramp block generates the constant ramp signal
y = (0:L-1)*m + b

where m is the slope specified by the scalar Slope parameter, b is the y-intercept
specified by the scalar Offset parameter.
For a matrix input, the length L of the output ramp is equal to either the
number of rows or the number of columns in the input, as determined by the
Ramp length equals number of parameter. For a 1-D vector input, L is equal
to the length of the input vector. The output, y, is always a 1-D vector.

Dialog Box

Ramp length equals number of

The dimension of the input matrix that determines the length of the output
ramp, Rows or Columns.
Slope
The slope of the ramp, a scalar.
Offset
The y-intercept of the ramp, a scalar.

Supported Double-precision floating point

Data Types

5-89
Constant Ramp

See Also Create Diagonal Matrix DSP Blockset

Identity Matrix DSP Blockset
DSP Constant DSP Blockset

See “Creating Signals Using Constant Blocks” on page 3-33 for related
information.

5-90
 Contiguous Copy

Purpose 5Contiguous Copy

Create a discontiguous input in a contiguous block of memory (for RTW code
generation from blocks linked to versions of the DSP Blockset prior to 4.0).

Library Signal Management / Signal Attributes

Description The Contiguous Copy block copies the input to a contiguous block of memory,
and passes this new copy to the output. The output is identical to the input, but
is guaranteed to reside in a contiguous section of memory.
Because Simulink employs an efficient copy-by-reference method for
propagating data in a model, some operations produce outputs with
discontiguous memory locations. An example of such an operation is shown
below with the Simulink Selector block.
Memory addresses m1 m2 m3 m4 m5 m6 m7 m8
Memory contents u1 u2 u3 u4 u5 u6 u7 u8

m1
m2
m3
m6
m4
m3
m5
m7
m6
m7
m8

Vector of pointers to Vector of pointers to

contiguous memory discontiguous memory

Although this does not present a problem during simulation, blocks linked to
versions of the DSP Blockset prior to 4.0 may require contiguous inputs for
code-generation with the Real-Time Workshop (RTW). When such blocks are
used in a model intended for code generation, they should be preceded by the
Contiguous Copy block to ensure that their inputs are contiguous. The DSP
Blockset version 3.1 Autocorrelation block shown below is an example of one
that requires contiguous inputs for code generation.

5-91
Contiguous Copy

Original memory allocation New memory allocation

m1 m2 m3 m4 m5 m6 m7 m8 Memory addresses m9 m10 m11

u1 u2 u3 u4 u5 u6 u7 u8 Memory contents u6 u3 u7

m6 m9 v3.1

m3 m 10
m7 m 11

Vector of pointers to Vector of pointers to new

discontiguous memory contiguous memory

Dialog Box

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-92
 Convert 1-D to 2-D

Purpose 5Convert 1-D to 2-D

Reshape a 1-D or 2-D input to a 2-D matrix with the specified dimensions.

Library Signal Management / Signal Attributes

Description The Convert 1-D to 2-D block reshapes a length-Mi 1-D vector or an Mi-by-Ni
matrix to an Mo-by-No matrix, where Mo is specified by the Number of output
rows parameter, and No is specified by the Number of output columns
parameter.
y = reshape(u,Mo,No) % Equivalent MATLAB code

The input is reshaped columnwise, as shown in the two cases below. The
length-6 vector and the 2-by-3 matrix are both reshaped to the same 3-by-2
output matrix.

(u1 u2 u3 u4 u5 u6)
u1 u4
u2 u5
u3 u6
u1 u3 u5
u2 u4 u6

An error is generated if (Mo∗No) ≠ (Mi∗Ni). That is, the total number of input
elements must be conserved in the output.
The output is frame-based if the Frame-based output check box is selected;
otherwise, the output is sample-based.

Dialog Box

5-93
Convert 1-D to 2-D

Number of output rows

The number of rows, Mo, in the output matrix. Tunable.
Number of output columns
The number of rows, No, in the output matrix. Tunable.
Frame-based output
Creates a frame-based output when selected. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

Convert 2-D to 1-D DSP Blockset
Frame Status Conversion DSP Blockset
Reshape Simulink
Submatrix DSP Blockset

5-94
 Convert 2-D to 1-D

Purpose 5Convert 2-D to 1-D

Convert a 2-D matrix input to a 1-D vector.

Library Signal Management / Signal Attributes

Description The Convert 2-D to 1-D block reshapes an M-by-N matrix input to a 1-D vector
with length M∗N.
y = u(:) % Equivalent MATLAB code

The input is reshaped columnwise, as shown below for a 3-by-2 matrix.

u1 u4
u2 u5 (u1 u2 u3 u4 u5 u6)
u3 u6

The output is always sample-based.

Dialog Box

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

Convert 1-D to 2-D DSP Blockset
Frame Status Conversion DSP Blockset
Reshape Simulink
Submatrix DSP Blockset

5-95
Convert Complex DSP To Simulink

Purpose 5Convert Complex DSP To Simulink

Convert complex data from the DSP Blockset Version 2.2 format to the
Simulink Version 3 format.

Library Elementary Functions, in Math Functions

Description The Convert Complex DSP To Simulink block accepts complex data (scalar,
vector, matrix) in the DSP Blockset Version 2.2 format, and outputs the same
data in the Simulink Version 3 complex format. Only complex data should be
supplied to this block.
Blocks provided in Release 11 and later blocksets (e.g., Simulink Version 3.0,
DSP Blockset Version 3.0, Fixed Point Blockset Version 2.0) use the
Simulink Version 3 complex format, which is not compatible with the DSP
Blockset Version 2.2 complex format. To add a new block or subsystem
(Release 11 and later) to an existing model that uses the DSP Blockset Version
2.2 complex data format, precede it with the Convert Complex DSP To
Simulink block. If the new block or subsystem’s output is complex, you should
follow it with the complementary Convert Complex Simulink To DSP block
(unless the downstream blocks have already been updated to their Release 11
counterparts).
These convertor blocks are only needed for interfacing Version 3.0 blocks to the
complex-data section of a Version 2.2 or earlier model. Version 3.0 blocks can
be added to real-data sections of older models without any data format
conversion.

Note Within a section of model that uses the Version 2.2 complex format, you
should continue to use the complex port identifier (∗) as a guide to wiring
blocks. Outputs ports labeled with the ∗ symbol should only be connected to
input ports labeled with the ∗ symbol.

The following figure shows how you can use these two convertor blocks to
migrate part of a complex-data model to the Version 3.0 complex format while
letting other components continue to use the Version 2.2 complex-data format.

5-96
 Convert Complex DSP To Simulink

Existing (Version 2.2) complex-data

Subsystem B upgraded to Version 3.0 complex-data

(Subsystem A remains a
Version 2.2 implementation)

Subsystem A upgraded to Version 3.0 complex-data

(Subsystem B remains a
Version 2.2 implementation)

Dialog Box

Supported Double-precision floating point

Data Types

See Also Convert Complex Simulink To DSP DSP Blockset

5-97
Convert Complex Simulink To DSP

Purpose 5Convert Complex Simulink To DSP

Convert complex data from the Simulink Version 3 format to the DSP Blockset
Version 2.2 format.

Library Elementary Functions, in Math Functions

Description The Convert Complex Simulink To DSP block accepts complex data (scalar,
vector, matrix) in the Simulink Version 3 format, and outputs the same data in
the DSP Blockset Version 2.2 complex format. Only complex data should be
supplied to this block.
Blocks provided in Release 11 and later blocksets (e.g., Simulink Version 3.0,
DSP Blockset Version 3.0, Fixed Point Blockset Version 2.0) use the
Simulink Version 3 complex format, which is not compatible with the DSP
Blockset Version 2.2 complex format. To add a new block or subsystem
(Release 11 and later) to an existing model that uses the DSP Blockset Version
2.2 complex data format, precede it with the Convert Complex DSP To
Simulink block. If the new block’s output is complex, you should then follow it
with the Convert Complex Simulink To DSP block (unless the downstream
blocks have already been updated to their Release 11 counterparts).
These convertor blocks are only needed for interfacing Version 3.0 blocks to the
complex-data section of a Version 2.2 or earlier model. Version Version 3.0
blocks can be added to real-data sections of older models without any data
format conversion.

Note Within a section of model that uses the Version 2.2 complex format, you
should continue to use the complex port identifier (∗) as a guide to wiring
blocks. Outputs ports labeled with the ∗ symbol should only be connected to
input ports labeled with the ∗ symbol.

The following figure shows how you can use these two convertor blocks to
migrate part of a complex-data model to the Version 3.0 complex format while
letting other components continue to use the Version 2.2 complex-data format.

5-98
 Convert Complex Simulink To DSP

Existing (Version 2.2) complex-data

Subsystem B upgraded to Version 3.0 complex-data

(Subsystem A remains a
Version 2.2 implementation)

Subsystem A upgraded to Version 3.0 complex-data

(Subsystem B remains a
Version 2.2 implementation)

Dialog Box

Supported Double-precision floating point

Data Types

See Also Convert Complex DSP To Simulink DSP Blockset

5-99
Convolution

Purpose 5Convolution
Compute the convolution of two inputs.

Library Signal Operations

Description The Convolution block convolves corresponding columns (channels) of Mu-by-N

input matrix u and Mv-by-N input matrix v.

Frame-Based Inputs
Matrix inputs must be frame-based. The output, y, is a frame-based
(Mu+Mv-1)-by-N matrix whose jth column has elements
max ( M u, M v )

y i, j = ∑ u k, j v *( i – k + 1 ), j 1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

where ∗ denotes the complex conjugate. Inputs u and v are zero when indexed
outside of their valid ranges. When both inputs are real, the output is real;
when one or both inputs are complex, the output is complex.
When one input is a column vector (single channel) and the other is a matrix
(multiple channels), the single-channel input is independently convolved with
each channel of the multichannel input. For example, if u is a Mu-by-1 column
vector and v is an Mv-by-N matrix, the output is an (Mu+Mv-1)-by-N matrix
whose jth column has elements
max ( M u, M v )

y i, j = ∑ u k v (*i – k + 1 ), j 1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

Sample-Based Inputs
If u and v are sample-based vectors with lengths Mu and Mv, the Convolution
block performs the vector convolution
max ( M u, M v )

yi = ∑ u k v *( i – k + 1 ) 1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

5-100
 Convolution

The dimensions of the sample-based output vector are determined by the

dimensions of the input vectors:

• When both inputs are row vectors, or when one input is a row vector and the
other is a 1-D vector, the output is a 1-by-(Mu+Mv-1) row vector.
• When both inputs are column vectors, or when one input is a column vector
and the other is a 1-D vector, the output is a (Mu+Mv-1)-by-1 column vector.
• When both inputs are 1-D vectors, the output is a 1-D vector of length
Mu+Mv-1.

The Convolution block does not accept sample-based full-dimension matrix

inputs, or mixed sample-based row vector and column vector inputs.

Dialog Box

Supported Double-precision floating point

Data Types

See Also Correlation DSP Blockset

conv MATLAB

5-101
Correlation

Purpose 5Correlation
Compute the correlation along the columns of two inputs.

Library Statistics

Description The Correlation block computes the cross-correlation of corresponding columns

(channels) of the Mu-by-N input matrix u and Mv-by-N input matrix v. The
frame status of both inputs must be the same. The block does not accept
sample-based full-dimension matrix inputs or 2-D row vector inputs.

Frame-Based Inputs
Matrix inputs must be frame-based. The output, y, is a frame-based
(Mu+Mv-1)-by-N matrix whose jth column has elements
max ( M u, M v )

y i, j = ∑ u k, j v *( k + i – M ), j
v
1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

where ∗ denotes the complex conjugate. Inputs u and v are zero when indexed
outside of their valid ranges. When both inputs are real, the output is real;
when one or both inputs are complex, the output is complex.
When one input is a column vector (single channel) and the other is a matrix
(multiple channels), the single-channel input is independently cross-correlated
with each channel of the multichannel input. For example, if u is a Mu-by-1
column vector and v is an Mv-by-N matrix, the output is an (Mu+Mv-1)-by-N
matrix whose jth column has elements
max ( M u, M v )

y i, j = ∑ u k v *( k – i + M v ), j 1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

Sample-Based Inputs
Matrix inputs cannot be sample based, so all sample-based inputs are column
vectors or 1-D vectors. (the block does not support 2-D row vector inputs.) If u
and v are sample-based vectors with lengths Mu and Mv, the Correlation block
performs the vector cross-correlation

5-102
 Correlation

max ( M u, M v )

yi = ∑ u k v *( k – i + M v ) 1 ≤ i ≤ ( Mu + Mv – 1 )
k=1

The dimensions of the sample-based output vector are determined by the

dimensions of the input vectors:

• When both inputs are column vectors, or when one input is a column vector
and the other is a 1-D vector, the output is a (Mu+Mv-1)-by-1 column vector.
• When both inputs are 1-D vectors, the output is a 1-D vector of length
Mu+Mv-1.

The Correlation block does not accept sample-based full-dimension matrix

inputs or 2-D row vector inputs.

Dialog Box

Supported Double-precision floating point

Data Types

See Also Autocorrelation DSP Blockset

Convolution DSP Blockset
xcorr Signal Processing Toolbox

5-103
Counter

Purpose 5Counter
Count up or down through a specified range of numbers.

Library Signal Management / Switches and Counters

Description The Counter block increments or decrements an internal counter each time it
receives a trigger event at the Clk port. A trigger event at the Rst port resets
the counter to its initial state.
The input to the Rst port must be a real sample-based scalar. The input to the
Clk port can be a real sample-based scalar, or a real frame-based vector
(i.e., single channel). If both inputs are sample-based, they must have the same
sample period. If the Clk input is frame-based, the frame period must equal the
sample period of the Rst input.
The trigger event for both inputs is specified by the Count event pop-up menu,
and can be one of the following:
• Rising edge triggers a count or reset operation when the Clk or Rst input
rises from a negative value to zero or a positive value, or from zero to a
positive value.
• Falling edge triggers a count or reset operation when the Clk or Rst input
falls from a positive value to zero or a negative value, or from zero to a
negative value.
• Either edge triggers a count or reset operation when either a rising or falling
edge (as described above) occurs.
• Nonzero sample triggers a count or reset operation at each sample time that
the Clk or Rst input is not zero.
• Free running disables the Clk port, and enables the Samples per output
frame and Sample time parameters. The block increments or decrements
the counter at a constant interval, Ts, specified by the Sample time
parameter. See “Free-Running Operation” below.

At the start of the simulation, the block sets the counter to the value specified
by the Initial count parameter, which can be any integer in the range defined
by the Counter size parameter. The Counter size parameter allows you to
choose from three standard counter ranges, or to specify an arbitrary counter
limit:

• 8 bits specifies a counter with a range of 0 to 255.

5-104
 Counter

• 16 bits specifies a counter with a range of 0 to 65535.

• 32 bits specifies a counter with a range of 0 to 232-1.
• User defined enables the supplementary Maximum count parameter,
which allows you to specify an arbitrary integer as the upper count limit. The
range of the counter is then 0 to the Maximum count value.

Sample-Based Operation
The block operates in sample-based mode when the Clk input is a sample-based
scalar. Sample-based vectors and matrices are not accepted.
When the Count direction parameter is set to Up, a sample-based trigger
event at the Clk input causes the block to increment the counter by one. The
block continues incrementing the counter when triggered until the counter
value reaches the upper count limit (e.g., 255 for an 8-bit counter). At the next
Clk trigger event, the block resets the counter to 0, and resumes incrementing
the counter with the subsequent Clk trigger event.
When the Count direction parameter is set to Down, a sample-based trigger
event at the Clk input causes the block to decrement the counter by one. The
block continues decrementing the counter when triggered until the counter
value reaches 0. At the next Clk trigger event, the block resets the counter to
the upper count limit (e.g., 255 for an 8-bit counter), and resumes
decrementing the counter with the subsequent Clk trigger event.
Between triggering events the block holds the output at its most recent value.
The block resets the counter to its initial state when the trigger event specified
in the Count event menu is received at the optional Rst input. When trigger
events are received simultaneously at the Clk and Rst ports, the block first
resets the counter, and then increments or decrements appropriately. (If you
do not need to reset the counter during the simulation, you can disable the Rst
port by deselecting the Reset input check box.)
The Output pop-up menu provides three options for the output port
configuration of the block icon:

• Count configures the block icon to show a Cnt port, which produces the
current value of the counter as a sample-based scalar with the same sample
period as the inputs.
• Hit configures the block icon to show a Hit port. The Hit port produces zeros
while the value of the counter does not equal the integer Hit value

5-105
Counter

parameter setting. When the counter value does equal the Hit value setting,
the block generates a value of 1 at the Hit port. The output is sample-based
with the same sample period as the inputs.
• Count and Hit configures the block icon with both ports.

Frame-Based Operation
The block operates in frame-based mode when the Clk input is a frame-based
vector (i.e., single channel). Multichannel frame-based inputs are not accepted.
Frame-based operation is the same as sample-based operation, except that the
block increments or decrements the counter by the total number of trigger
events contained in the Clk input frame. A trigger event that is split across two
consecutive frames is counted in the frame that contains the conclusion of the
event. When a trigger event is received at the Rst port, the block first resets the
counter, and then increments or decrements the counter by the number of
trigger events contained in the Clk frame.
The Cnt and Hit outputs are sample-based scalars with sample period equal to
the Clk input frame period.

Free-Running Operation
The block operates in free-running mode when Free running is selected from
the Count event menu.
The Clk input port is disabled in this mode, and the block simply increments or
decrements the counter using the constant sample period specified by the
Sample time parameter, Ts. The Cnt output is a frame-based M-by-1 matrix
containing the count value at each of M consecutive sample times, where M is
specified by the Samples per output frame parameter. The Hit output is a
frame-based M-by-1 matrix containing the hit status (0 or 1) at each of those M
consecutive sample times. Both outputs have a frame period of M∗Ts.

Example In the model below, the Clk port of the Counter block is driven by Simulink’s
Pulse Generator block, and the Rst port is triggered by an N-Sample Enable
block. All of the Counter block’s inputs and outputs are multiplexed into a
single To Workspace block using a 4-port Mux block.

5-106
 Counter

To run the model, first select Simulation Parameters from the Simulation
menu, and set the Stop time to 30. Then adjust the block parameters as
described below. (Use the default settings for the Pulse Generator and To
Workspace blocks.)

• Set the N-Sample Enable block parameters as follows:

- Trigger count = 6
- Active level = High (1)
• Set the Counter block parameters as follows:
- Count direction = Down
- Count event = Rising edge
- Counter size = User defined
- Maximum count = 20
- Initial count = 5
- Output = Count and Hit
- Hit value = 4
- Reset input
• Set the Number of inputs parameter of the Mux block to 4.

The figure below shows the first 22 samples of the model’s four-column output,
yout. The first column is the Counter block’s Clk input, the second column is
the block’s Rst input, the third column is the block’s Cnt output, and the fourth
column is the block’s Hit output.

5-107
Counter

Clk Rst Cnt Hit

[1] [0] initial value [5] [0]

[0] [0] [5] [0]
[1] [0] [4] hit [1]
[0] [0] [4] [1]
[1] [0] [3] [0]
[0] [0] [3] [0]
[1] [1] reset [4] hit [1]
[0] [1] [4] [1]
[1] [1] [3] [0]
[0] [1] [3] [0]
[1] [1] [2] [0]
Simulation time

[0] [1] [2] [0]

[1] [1] [1] [0]
[0] [1] [1] [0]
[1] [1] [0] [0]
[0] [1] [0] [0]
[1] [1] max value [20] [0]
[0] [1] [20] [0]
[1] [1] [19] [0]
[0] [1] [19] [0]
[1] [1] [18] [0]
[0] [1] [18] [0]
...

...

...

...
You can see that the seventh input samples to both the Clk and Rst ports of the
Counter block represent trigger events (rising edges), so at this time step the
block first resets the counter to its initial value of 5, and then immediately
decrements the count to 4. When the counter reaches its minimum value of 0,
it rolls over to its maximum value of 20 with the following trigger event at the
Cnt port.

5-108
 Counter

Dialog Box

Count direction
The counter direction, Up or Down. Tunable, except in Simulink’s external
mode.
Count event
The type of event that triggers the block to increment, decrement, or reset
the counter when received at the Clk or Rst ports. Free running disables
the Clk port, and counts continuously with the period specified by the
Sample time parameter.

Counter size
The range of integer values the block should count through before recycling
to zero.
Maximum count
The counter’s maximum value when Counter size is set to User defined.
Tunable.

5-109
Counter

Initial count
The counter’s initial value at the start of the simulation and after reset.
Tunable, except in Simulink’s external mode.
Output
Selects the output port(s) to enable: Cnt, Hit, or both.
Hit value
The scalar value whose occurrence in the count should be flagged by a 1 at
the (optional) Hit output. This parameter is available when Hit or Count
and Hit are selected in the Output menu. Tunable, except in Simulink’s
external mode.
Reset input
Enables the Rst input port when selected.
Samples per output frame
The number of samples, M, in each output frame. This parameter is
available when Free running is selected in the Count event menu.
Sample time
The output sample period, Ts, in free-running mode. This parameter is
available when Free running is selected in the Count event menu.

Supported Double-precision floating point

Data Types

See Also Edge Detector DSP Blockset

N-Sample Enable DSP Blockset
N-Sample Switch DSP Blockset

5-110
 Covariance AR Estimator

Purpose 5Covariance AR Estimator

Compute an estimate of AR model parameters using the covariance method.

Library Estimation / Parametric Estimation

Description The Covariance AR Estimator block uses the covariance method to fit an
autoregressive (AR) model to the input data. This method minimizes the
forward prediction error in the least-squares sense.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal, which is assumed to be the output of an AR system
driven by white noise. The block computes the normalized estimate of the AR
system parameters, A(z), independently for each successive input frame.

G G
H ( z ) = ------------ = -------------------------------------------------------------------------------
A(z) –1
1 + a ( 2 )z + … + a ( p + 1 )z
–p

The order, p, of the all-pole model is specified by the Estimation order

parameter.
The top output, A, is a column vector of length p+1 with the same frame status
as the input, and contains the normalized estimate of the AR model coefficients
in descending powers of z,
[1 a(2) ... a(p+1)]

The scalar gain, G, is provided at the bottom output (G).

Dialog Box

Estimation order
The order of the AR model, p.

5-111
Covariance AR Estimator

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

See Also Burg AR Estimator DSP Blockset

Covariance Method DSP Blockset
Modified Covariance AR Estimator DSP Blockset
Yule-Walker AR Estimator DSP Blockset
arcov Signal Processing Toolbox

5-112
 Covariance Method

Purpose 5Covariance Method

Compute a parametric spectral estimate using the covariance method.

Library Estimation / Power Spectrum Estimation

Description The Covariance Method block estimates the power spectral density (PSD) of
the input using the covariance method. This method fits an autoregressive
(AR) model to the signal by minimizing the forward prediction error in the
least-squares sense. The order of the all-pole model is the value specified by the
Estimation order parameter, and the spectrum is computed from the FFT of
the estimated AR model parameters.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal. The block’s output (a column vector) is the estimate of
the signal’s power spectral density at Nfft equally spaced frequency points in
the range [0,Fs), where Fs is the signal’s sample frequency.
When Inherit FFT length from input dimensions is selected, Nfft is specified
by the frame size of the input, which must be a power of 2. When Inherit FFT
length from input dimensions is not selected, Nfft is specified as a power of 2
by the FFT length parameter, and the block zero pads or truncates the input
to Nfft before computing the FFT. The output is always sample-based.
See the Burg Method block reference for a comparison of the Burg Method,
Covariance Method, Modified Covariance Method, and Yule-Walker Method
blocks.

Dialog Box

Estimation order
The order of the AR model.

5-113
Covariance Method

Inherit FFT length from input dimensions

When selected, uses the input frame size as the number of data points, Nfft,
on which to perform the FFT. Tunable.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft
exceeds the input frame size, the frame is zero-padded as needed. This
parameter is enabled when Inherit FFT length from input dimensions is
not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

See Also Burg Method DSP Blockset

Covariance AR Estimator DSP Blockset
Short-Time FFT DSP Blockset
Modified Covariance Method DSP Blockset
Yule-Walker Method DSP Blockset
pcov Signal Processing Toolbox

See “Power Spectrum Estimation” on page 4-15 for related information.

5-114
 Create Diagonal Matrix

Purpose 5Create Diagonal Matrix

Create a square diagonal matrix from diagonal elements.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Create Diagonal Matrix block populates the diagonal of the M-by-M matrix
output with the elements contained in the length-M vector input, D. The
elements off the diagonal are zero.
A = diag(D) Equivalent MATLAB code

The output is always sample-based.

Dialog Box

Supported Double-precision floating point

Data Types

See Also Constant Diagonal Matrix DSP Blockset

Extract Diagonal DSP Blockset
diag MATLAB

5-115
Cumulative Sum

Purpose 5Cumulative Sum

Compute the cumulative sum of row or column elements.

Library Math Functions / Math Operations

Description The Cumulative Sum block computes the cumulative sum of the row or column
elements in the M-by-N input matrix u.

Columnwise Summing
When the Cumulative Sum along parameter is set to Columns, the block
computes the cumulative sum of the column elements.
y = cumsum(u) % Equivalent MATLAB code

The output is an M-by-N matrix whose jth column has elements

i
y i, j = ∑ u k, j 1≤i≤M
k=1

The frame status of the output is the same as the input. For sample-based
inputs, the first row of each successive output is the same as that of the
corresponding input. For convenience, length-M 1-D vector inputs are treated
as M-by-1 column vectors for column-wise summation, and the output is a
length-M 1-D vector.
For frame-based inputs, the first row of the first output is the same as that of
the first input, and the first row of each subsequent output contains the sum of
the first row of the current input (time t) and the last row of the previous output
(time t-Tf).

y 1, j ( t ) = u 1, j ( t ) + y M, j ( t – T f )

Rowwise Summing
When the Cumulative Sum along parameter is set to Rows, the block
computes the cumulative sum of the row elements.
y = cumsum(u,2) % Equivalent MATLAB code

The output is an M-by-N matrix whose ith row has elements

5-116
 Cumulative Sum

j
y i, j = ∑ u i, k 1≤j≤N
k=1

The frame status of the output is the same as the input. For both sample-based
and frame-based inputs, the first column of each successive output is the same
as that of the corresponding input. For convenience, length-N 1-D vector inputs
are treated as 1-by-N row vectors for row-wise summation, and the output is a
length-N 1-D vector.

Dialog Box

Cumulative Sum along

The dimension along which to compute the cumulative summations.
Columns specifies columnwise summation, while Rows specifies rowwise
summation.

Supported Double-precision floating point

Data Types

See Also Difference DSP Blockset

Matrix Sum DSP Blockset
cumsum MATLAB

5-117
dB Conversion

Purpose 5dB Conversion

Convert magnitude data to decibels (dB or dBm).

Library Math Functions / Math Operations

Description The dB Conversion block converts a linearly scaled power or amplitude input
to dB or dBm. The Input signal parameter specifies whether the input is a
power signal or a voltage signal, and the Convert to parameter controls the
scaling of the output. When selected, the Add eps to input to protect
against “log(0) = -inf” parameter adds a value of eps to all power and voltage
inputs. When this option is not enabled, zero-valued inputs produce -inf at the
output. The size and frame status of the output are the same as the input.

Power Inputs
Select Power as the Input signal parameter when the input, u, is a real,
nonnegative, power signal (units of watts). When the Convert to parameter is
set to dB, the block performs the dB conversion
y = 10*log10(u) % Equivalent MATLAB code

When the Convert to parameter is set to dBm, the block performs the dBm
conversion
y = 10*log10(u) + 30

The dBm conversion is equivalent to performing the dB operation after

converting the input to milliwatts.

Voltage Inputs
Select Amplitude as the Input signal parameter when the input, u, is a real
voltage signal (units of volts). The block uses the scale factor specified in ohms
by the Load resistance parameter, R, to convert the voltage input to units of
power (watts) before converting to dB or dBm. When the Convert to parameter
is set to dB, the block performs the dB conversion
y = 10*log10(abs(u)^2/R)

When the Convert to parameter is set to dBm, the block performs the dBm
conversion
y = 10*log10(abs(u)^2/R) + 30

5-118
 dB Conversion

The dBm conversion is equivalent to performing the dB operation after

converting the (abs(u)^2/R) result to milliwatts.

Dialog Box

Convert to
The logarithmic scaling to which the input is converted, dB or dBm.
Tunable.
Input signal
The type of input signal, Power or Amplitude. Tunable.
Load resistance
The scale factor used to convert voltage inputs to units of power. Tunable.
Add eps to input to protect against “log(0) = -inf”
When selected, adds eps to all input values (power or voltage). Tunable.

Supported Double-precision floating point

Data Types

See Also dB Gain DSP Blockset

Math Function Simulink
log10 MATLAB

5-119
dB Gain

Purpose 5dB Gain

Apply a gain specified in decibels.

Library Math Functions / Math Operations

Description The dB Gain block multiplies the input by the decibel values specified in the
Gain parameter. For an M-by-N input matrix u with elements uij, the Gain
parameter can be a real M-by-N matrix with elements gij to be multiplied
element-wise with the input, or a real scalar.
( g ij ⁄ k )
y ij = 10u ij

The value of k is 10 for power signals (select Power as the Input signal
parameter) and 20 for voltage signals (select Amplitude as the Input signal
parameter).
The value of the equivalent linear gain

lin ( g ij ⁄ k )
g ij = 10

is displayed in the block icon below the dB gain value. The size and frame
status of the output are the same as the input.

Dialog Box

Gain
The dB gain to apply to the input, a scalar or a real M-by-N matrix.
Tunable.
Input signal
The type of input signal: Power or Amplitude. Tunable.

5-120
 dB Gain

Supported Single-precision floating point

Data Types Double-precision floating point

See Also dB Conversion DSP Blockset

Math Function Simulink
log10 MATLAB

5-121
DCT

Purpose 5DCT
Compute the DCT of the input.

Library Transforms

Description The DCT block computes the unitary discrete cosine transform (DCT) of each
channel in the M-by-N input matrix, u.
y = dct(u) % Equivalent MATLAB code

For both sample-based and frame-based inputs, the block assumes that each
input column is a frame containing M consecutive samples from an
independent channel. The frame size, M, must be a power of two. To work with
other frame sizes, use the Zero Pad block to pad or truncate the frame size to a
power-of-two length.
The output is an M-by-N matrix whose lth column contains the length-M DCT
of the corresponding input column.
M
π ( 2m – 1 ) ( k – 1 )
y ( k, l ) = w ( k ) ∑ u ( m, l ) cos --------------------------------------------,
2M
k = 1, … , M
m=1

where

 1
 --------- , k=1

w(k) =  M
 2
 ----- , 2≤k≤M
 M

The output is always sample-based, and the output port rate and data type
(real/complex) are the same as those of the input port.
For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are processed as single channels (i.e., as M-by-1 column vectors),
and the output has the same dimension as the input.

5-122
 DCT

Dialog Box

Supported Double-precision floating point

Data Types

See Also Complex Cepstrum DSP Blockset

FFT DSP Blockset
IDCT DSP Blockset
Real Cepstrum DSP Blockset
dct Signal Processing Toolbox

5-123
Delay Line

Purpose 5Delay Line

Rebuffer a sequence of inputs with a one-sample shift.

Library Signal Management / Buffers

Description The Delay Line block buffers the input samples into a sequence of overlapping
or underlapping matrix outputs. In the most typical use (sample-based inputs),
each output differs from the preceding output by only one sample, as
illustrated below for scalar input.
(input sample period = Tsi) (output sample period = Tsi)

4 3 2 1 0 0 0
9 8 7 6 5 4 3 2 1 5 4 3 2 1 0 0
6 5 4 3 2 1 0

Note that the first output of the block in the example above is all zeros; this is
because the Initial Conditions parameter is set to zero. Due to the latency of
the Delay Line block, all outputs are delayed by one frame, the entries of which
are defined by the Initial Conditions parameter.

Sample-Based Operation
In sample-based operation, the Delay Line block buffers a sequence of
sample-based length-N vector inputs (1-D, row, or column) into a sequence of
overlapping frame-based Mo-by-N matrix outputs, where Mo is specified by the
Delay line size parameter (Mo>1). That is, each input vector becomes a row in
the frame-based output matrix.
At each sample time the new input vector is added in the last row of the output,
so each output overlaps the previous output by Mo-1 samples. Therefore, the
output sample period and frame period is the same as the input sample period
(Tso=Tsi, and Tfo=Tsi). When Mo=1, the input is simply passed through to the
output and retains the same dimension, but becomes frame-based. The latency
of the block always causes an initial delay in the output; the value of the first
output is specified by the Initial conditions parameter (see “Initial
Conditions” below). Sample-based full-dimension matrix inputs are not
accepted.
The Delay Line block’s sample-based operation is similar to that of a Buffer
block with Buffer size equal to Mo and Buffer overlap equal to Mo-1, except
that the Buffer block has a different latency.

5-124
 Delay Line

In the model below, the block operates on a sample-based input with a Delay
line size of 3.

ch2 ch3
ch1 ch4
Sample-based input,
t=5 6 1 5 –6 sample period = Tsi
Tsi = 1
t=4 5 1 5 –5
Frame-based output ,
t=3 4 0 5 –4 sample period = T si
first
t=2 3 0 5 –3
first sample-based frame-based
t=1 2 1 5 –2 input output

ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4

ch1
ch2
ch3
ch4
t=0 1 1 5 –1
1 1 5 –1 0 0 0 0 0 0 0 0 0000
2 1 5 –2 1 1 5 –1 0 0 0 0 0000
3 0 5 –3 2 1 5 –2 1 1 5 –1 0000

t=3 t=2 t=1 t=0

(Mo=3)
Tso = 1

The input vectors in the example above do not begin appearing at the output
until the second row of the second matrix due to the block’s latency (see “Initial
Conditions” below). The first output matrix (all zeros in this example) reflects
the block’s Initial conditions setting. As for any sample-based input, the
output frame rate and output sample rate are both equal to the input sample
rate.

Frame-Based Operation
In frame-based operation, the Delay Line block rebuffers a sequence of
frame-based Mi-by-N matrix inputs into a sequence of frame-based Mo-by-N
matrix outputs, where Mo is the output frame size specified by the Delay line
size parameter. Depending on whether Mo is greater than, less than, or equal
to the input frame size, Mi, the output frames can be underlapped or
overlapped. Each of the N input channels is rebuffered independently.
When Mo > Mi, the output frame overlap is the difference between the output
and input frame size, Mo-Mi. When Mo < Mi, the output is underlapped; the
Delay Line block discards the first Mi-Mo samples of each input frame so that
only the last Mo samples are buffered into the corresponding output frame.

5-125
Delay Line

When Mo = Mi, the output data is identical to the input data, but is delayed by
the latency of the block. Due to the block’s latency, the outputs are always
delayed by one frame, the entries of which are specified by the Initial
conditions (see “Initial Conditions” below).

The output frame period is equal to the input frame period (Tfo=Tfi). The output
sample period, Tso, is therefore equal to Tfi/Mo, or equivalently, Tsi(Mi/Mo)
In the model below, the block rebuffers a two-channel frame-based input with
a Delay line size of 3.
ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2
9 1 5 1 1 1
61 21 00
10 1 6 1 2 1
70 30 00
11 0 7 0 3 0
80 40 00
12 0 8 0 4 0
t=8 t=4 t=0 t=8 t=4 t=0
(Mo=3)

first input first output

Input frame period = 4∗Tsi Output frame period = Tsi

The first output frame in the example is a product of the latency of the Delay
Line block; it is all zeros because the Initial conditions is set to be zero. Since
the input frame size, 4, is larger than the output frame size, 3, only the last
three samples in each input frame are propagated to the corresponding output
frame. The frame periods of the input and output are the same, and the output
sample period is Tsi(Mi/Mo), or 4/3 the input sample period.

Initial Conditions
The Delay Line block’s buffer is initialized to the value specified by the
Initial condition parameter. The block outputs this buffer at the first
simulation step (t=0). If the block’s output is a vector, the Initial condition can
be a vector of the same size, or a scalar value to be repeated across all elements
of the initial output. If the block’s output is a matrix, the Initial condition can
be a matrix of the same size, a vector (of length equal to the number of matrix
rows) to be repeated across all columns of the initial output, or a scalar to be
repeated across all elements of the initial output.

5-126
 Delay Line

Dialog Box

Delay line size

The number of rows in output matrix, Mo.
Initial conditions
The value of the block’s initial output, a scalar, vector, or matrix.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

Triggered Delay Line DSP Blockset

See “Buffering Sample-Based and Frame-Based Signals” on page 3-47 for

related information.

5-127
Detrend

Purpose 5Detrend
Remove a linear trend from a vector.

Library Statistics

Description The Detrend block removes a linear trend from the length-M input vector, u,
by subtracting the straight line that best fits the data in the least-squares
sense.
The least-squares line, û = ax + b, is the line with parameters a and b that
minimizes the quantity
M
2
∑ ( ui – ûi )
i=1

for M evenly-spaced values of x, where ui is the ith element in the input vector.
The output, y = u–û, is an M-by-1 column vector (regardless of the input vector
dimension) with the same frame status as the input.

Dialog Box

Supported Double-precision floating point

Data Types

See Also Cumulative Sum DSP Blockset

Difference DSP Blockset
Least Squares Polynomial Fit DSP Blockset
Unwrap DSP Blockset
detrend MATLAB

5-128
 Difference

Purpose 5Difference
Compute the element-to-element difference along rows or columns.

Library Math Functions / Math Operations

Description The Difference block computes the difference between adjacent elements in
rows or columns of the M-by-N input matrix u.

Columnwise Differencing
When the Difference along parameter is set to Columns, the block computes
differences between adjacent column elements.
y = diff(u) % Equivalent MATLAB code

For sample-based inputs, the output is a sample-based (M-1)-by-N matrix

whose jth column has elements

y i, j = u i + 1 , j – u i, j 1 ≤ i ≤ (M – 1)

For convenience, length-M 1-D vector inputs are treated as M-by-1 column
vectors for columnwise differencing, and the output is 1-D.
For frame-based inputs, the output is a frame-based M-by-N matrix whose jth
column has elements

y i, j = u i + 1 , j – u i, j 2≤i≤M

The first row of the first output contains the difference between the first row of
the first input and zero. The first row of each subsequent output contains the
difference between the first row of the current input (time t) and the last row
of the previous input (time t-Tf).

y 1, j ( t ) = u M , j ( t – T f ) – u 1, j ( t )

Rowwise Differencing
When the Difference along parameter is set to Rows, the block computes
differences between adjacent row elements.
y = diff(u,[],2) % Equivalent MATLAB code

5-129
Difference

The output is an M-by-(N-1) matrix whose ith row has elements

y i, j = u i, j + 1 – u i, j 1 ≤ j ≤ (N – 1)

The frame status of the output is the same as the input. For convenience,
length-N 1-D vector inputs are treated as 1-by-N row vectors for rowwise
differencing, and the output is 1-D.

Dialog Box

Difference along
The dimension along which to compute element-to-element differences.
Columns specifies columnwise differencing, while Rows specifies rowwise
differencing. Tunable.

Supported Double-precision floating point

Data Types

See Also Cumulative Sum DSP Blockset

diff MATLAB

5-130
 Digital Filter Design

Purpose 5Digital Filter Design

Design and implement a variety of digital FIR and IIR filters.

Library Filtering / Filter Designs

Description The Digital Filter Design block implements a digital FIR or IIR filter that you
design using the Filter Design and Analysis Tool graphical user interface,
referred to as FDATool. The block applies the filter to a discrete-time input
signal and outputs the resulting signal.
To learn how to use FDATool, see the FDATool section of the Signal Processing
Toolbox documentation.

Input and Output Characteristics

The block filters each input channel independently over time, preserving the
input size, frame status, and dimension (1-D or 2-D). Depending on input
characteristics, the block considers the input’s channels as the input columns
or individual input elements:
• Sample-based input matrix — Each matrix element is a channel
• Frame-based input matrix — Each matrix column is a channel
• Unoriented 1-D input vector — Each vector element is a channel

Designing the Filter

Double-click the Digital Filter Design block to open FDATool. Use FDATool to
design or directly specify the filter coefficients of a digital FIR or IIR filter. See
the FDATool section of the Signal Processing Toolbox documentation to learn
how to use FDATool.

Tuning the Filter During Simulation

You can tune the filter specifications in FDATool during simulations as long as
your changes do not modify the filter length or filter order. The block’s filter
updates as soon as you apply any filter changes in FDATool.

5-131
Digital Filter Design

Dialog Box Double-click the block to open FDATool.

Supported Double-precision floating point

Data Types

5-132
 Digital Filter Design

See Also Analog Filter Design DSP Blockset

Window Function DSP Blockset
fdatool Signal Processing Toolbox
fvtool Signal Processing Toolbox
sptool Signal Processing Toolbox

5-133
Direct-Form II Transpose Filter

Purpose 5Direct-Form II Transpose Filter

Apply an IIR filter to the input.

Library Filtering / Filter Designs

Description The Direct-Form II Transpose Filter block applies a transposed direct-form II

IIR filter to the input.

u ( k) ...
b( m ) b(3) b(2) b(1)

Σ z-1
... Σ z-1 Σ z-1 Σ y( k)
zn-1(k) z 2 ( k) z1(k)
-a(n) -a(3) -a(2)
...

This is a canonical form that has the minimum number of delay elements. The
filter order is max(m,n)-1.
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and an M-by-N frame-based matrix input is treated as N
independent channels. In both cases, the block filters each channel
independently over time, and the output has the same size and frame status as
the input.
The filter is specified in the parameter dialog box by its transfer function,

–1 –( m – 1 )
B(z) b1 + b2 z + … + bm + 1 z
H ( z ) = ------------ = -----------------------------------------------------------------------------------
A(z) –1
a1 + a2 z + … + an + 1 z
–( n – 1 )

where the Numerator parameter specifies the vector of numerator coefficients,

[b(1) b(2) ... b(m)]

and the Denominator parameter specifies the vector of denominator

coefficients,
[a(1) a(2) ... a(n)]

The filter coefficients are normalized by a1.

5-134
 Direct-Form II Transpose Filter

Initial Conditions
In its default form, the filter initializes the internal filter states to zero, which
is equivalent to assuming past inputs and outputs are zero. The block also
accepts optional nonzero initial conditions for the filter delays. Note that the
number of filter states (delay elements) per input channel is
max(m,n)-1

The Initial conditions parameter may take one of four forms:

• Empty matrix
The empty matrix, [], causes a zero (0) initial condition to be applied to all
delay elements in each filter channel.
• Scalar
The scalar value is copied to all delay elements in each filter channel. Note
that a value of zero is equivalent to setting the Initial conditions parameter
to the empty matrix, [].
• Vector
The vector has a length equal to the number of delay elements in each filter
channel, max(m,n)-1, and specifies a unique initial condition for each delay
element in the filter channel. This vector of initial conditions is applied to
each filter channel.
• Matrix
The matrix specifies a unique initial condition for each delay element, and
can specify different initial conditions for each filter channel. The matrix
must have the same number of rows as the number of delay elements in the
filter, max(m,n)-1, and must have one column per filter channel.

5-135
Direct-Form II Transpose Filter

Dialog Box

Numerator
The filter numerator vector. Tunable; the numerator coefficients can be
adjusted while the simulation runs, but the vector length (i.e., the filter
order) must remain the same.
Denominator
The filter denominator vector. Tunable; the denominator coefficients can
be adjusted while the simulation runs, but the vector length (i.e., the filter
order) must remain the same.
Initial conditions
The filter’s initial conditions, a scalar, vector, or matrix.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

5-136
 Direct-Form II Transpose Filter

See Also Biquadratic Filter DSP Blockset

Discrete Filter Simulink
Filter Realization Wizard DSP Blockset
Time-Varying Direct-Form II Transpose Filter DSP Blockset
filter MATLAB

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-137
Discrete Impulse

Purpose 5Discrete Impulse

Generate a discrete impulse.

Library DSP Sources

Description The Discrete Impulse block generates an impulse (the value 1) at output
sample D+1, where D is specified by the Delay parameter (D ≥ 0). All output
samples preceding and following sample D+1 are zero.
When D is a length-N vector, the block generates an M-by-N matrix output
representing N distinct channels, where frame size M is specified by the
Samples per frame parameter. The impulse for the ith channel appears at
sample D(i)+1. For M=1, the output is sample-based; otherwise, the output is
frame-based.
The Sample time parameter value, Ts, specifies the output signal sample
period. The resulting frame period is M∗Ts.
The Data type parameter allows you to specify an output precision of double,
single, or Boolean. Note, however, that most of the blocks in the DSP Blockset
accept only double precision inputs. Use the Simulink Data Type Conversion
block to convert integer data types to double precision. See “Working with Data
Types” in the Simulink documentation for a complete discussion of data types,
as well as a list of Simulink blocks capable of reduced-precision operations.

Example Construct the model below.

Configure the Discrete Impulse block to generate a frame-based three-channel

output of type double, with impulses at samples 1, 4, and 6 of channels 1, 2,
and 3, respectively. Use a sample period of 0.25 and a frame size of 4. The
corresponding settings should be as follows:

• Delay = [0 3 5]
• Sample time = 0.25
• Samples per frame = 4
• Data type = Double

5-138
 Discrete Impulse

Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout(1:10,:)
ans =

1 0 0
0 0 0
0 0 0
0 1 0
0 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0

The block generates an impulse at sample 1 of channel 1 (first column), at

sample 4 of channel 2 (second column), and at sample 6 of channel 3 (third
column).

Dialog Box

Delay
The number of zero-valued output samples, D, preceding the impulse. A
length-N vector specifies an N-channel output. Tunable.

5-139
Discrete Impulse

Sample time
The sample period, Ts, of the output signal. The output frame period is
M∗Ts. Tunable.
Samples per frame
The number of samples, M, in each output frame. Tunable.
Data type
The precision of the output. Tunable.

Supported Single-precision floating point

Data Types Double-precision floating point

See Also Data Type Conversion Simulink

DSP Constant DSP Blockset
Multiphase Clock DSP Blockset
N-Sample Enable DSP Blockset
Signal From Workspace DSP Blockset
impz Signal Processing Toolbox

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-140
 Downsample

Purpose 5Downsample
Resample an input at a lower rate by deleting samples.

Library Signal Operations

Description The Downsample block resamples each channel of the Mi-by-N input at a rate
K times lower than the input sample rate by discarding K-1 consecutive
samples following each sample passed through to the output. The integer K is
specified by the Downsample factor parameter.
The Sample offset parameter delays the output samples by an integer number
of sample periods, D, where 0 ≤ D < (K-1), so that any of the K possible output
phases can be selected. For example, when you downsample the sequence
1, 2, 3, ... by a factor of 4, you can select from the following four phases.

Input Sequence Sample Offset, D Output Sequence (K=4)

1,2,3,... 0 0,1,5,9,13,17,21,25,...

1,2,3,... 1 0,2,6,10,14,18,22,26,...

1,2,3,... 2 0,3,7,11,15,19,23,27,...

1,2,3,... 3 0,4,8,12,16,20,24,28,...

The initial zero in each output sequence above is a result of the default zero
Initial condition parameter setting for this example. See “Latency” on
page 5-143 for more on the Initial condition parameter.

Sample-Based Operation
When the input is sample-based, the block treats each of the M∗N matrix
elements as an independent channel, and downsamples each channel over
time. The input and output sizes are identical.
The Sample-based mode parameter determines how the block represents the
new rate at the output. There are two available options:
• Allow multirate
When Allow multirate is selected, the sample period of the sample-based
output is K times longer than the input sample period (Tso = KTsi). The block
is therefore multirate.

5-141
Downsample

• Enforce single rate

When Enforce single rate is selected, the block forces the output sample
rate to match the input sample rate (Tso = Tsi) by repeating every Kth input
sample K times at the output. The block is therefore single-rate. (The block’s
operation when Enforce single rate is selected is similar to the operation of
a Sample and Hold block with a repeating trigger event of period KTsi.)

The setting of the Frame-based mode popup menu does not affect
sample-based inputs.

Frame-Based Inputs
When the input is frame-based, the block treats each of the N input columns as
a frame containing Mi sequential time samples from an independent channel.
The block downsamples each channel independently by discarding K-1 rows of
the input matrix following each row that it passes through to the output.
The Frame-based mode parameter determines how the block adjusts the rate
at the output to accommodate the reduced number of samples. There are two
available options:

• Maintain input frame size

The block generates the output at the slower (downsampled) rate by using a
proportionally longer frame period at the output port than at the input port.
For downsampling by a factor of K, the output frame period is K times longer
than the input frame period (Tfo = KTfi), but the input and output frame
sizes are equal.

The model below shows a single-channel input with a frame period of

1 second being downsampled by a factor of 4 to a frame period of 4 seconds.
The input and output frame sizes are identical.

5-142
 Downsample

• Maintain input frame rate

The block generates the output at the slower (downsampled) rate by using a
proportionally smaller frame size than the input. For downsampling by a
factor of K, the output frame size is K times smaller than the input frame
size (Mo = Mi/K), but the input and output frame rates are equal.
The model below shows a single-channel input of frame size 64 being
downsampled by a factor of 4 to a frame size of 16. The input and output
frame rates are identical.

The setting of the Sample-based mode popup menu does not affect
frame-based inputs.

Latency

Zero Latency. The Downsample block has zero tasking latency for the special
combinations of input signal sampling and parameter settings shown in the
table below. In all of these cases the block has single-rate operation.

Input Sampling Parameter Settings

Downsample factor parameter, K, is 1, or

Sample-based
Enforce single rate is selected (with D=0)

Downsample factor parameter, K, is 1, or

Frame-based
Maintain input frame rate is selected

Zero tasking latency means that the block propagates input sample D+1
(received at t=0) as the first output sample, followed by input sample D+1+K,
input sample D+1+2K, and so on. The Initial condition parameter value is not
used.

5-143
Downsample

Nonzero Latency. The Downsample block is multirate for most settings other
than those in the above table. The amount of latency for multirate operation
depends on input signal sampling and Simulink’s tasking mode, as shown in
the table below.

Multirate... Sample-Based Latency Frame-Based Latency

None, for D=0

Single-tasking One frame (Mi samples)
One sample, for D>0
Multitasking One sample One frame (Mi samples)

The only case of nonzero single-rate latency occurs in sample-based mode,

when Enforce single rate is selected with D > 0. The latency in this case is one
sample.
In all cases of one-sample latency, the initial condition for each channel appears
as the first output sample. Input sample D+1 appears as the second output
sample for each channel, followed by input sample D+1+K, input sample
D+1+2K, and so on. The Initial condition parameter can be an Mi-by-N matrix
containing one value for each channel, or a scalar to be applied to all signal
channels.
In all cases of one-frame latency, the Mi rows of the initial condition matrix
appear in sequence as the first Mi output rows. Input sample D+1 (i.e, row D+1
of the input matrix) appears in the output as sample Mi+1, followed by input
sample D+1+K, input sample D+1+2K, and so on. The Initial condition value
can be an Mi-by-N matrix, or a scalar to be repeated across all elements of the
Mi-by-N matrix. See the example below for an illustration of this case.
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Example Construct the frame-based model shown below.

5-144
 Downsample

Adjust the block parameters as follows:

• Configure the Signal From Workspace block to generate a two-channel

signal with frame size of 4 and sample period of 0.25 seconds. This
represents an output frame period of 1 second (0.25∗4). The first channel
should contain the positive ramp signal 1, 2, ..., 100, and the second channel
should contain the negative ramp signal -1, -2, ..., -100. The settings are:
- Signal = [(1:100)' (-1:-1:-100)']
- Sample time = 0.25
- Samples per frame = 4
• Configure the Downsample block to downsample the two-channel input by
decreasing the output frame rate by a factor of 2 relative to the input frame
rate. Set a sample offset of 1, and a 4-by-2 initial condition matrix of

11 – 11
12 – 12
13 – 13
14 – 14

- Downsample factor = 2
- Sample offset = 1
- Initial condition = [11 -11;12 -12;13 -13;14 -14]
- Frame-based mode = Maintain input frame size
• Configure the Probe blocks by deselecting the Probe width and Probe
complex signal check boxes (if desired).

This model is multirate because there are at least two distinct frame rates, as
shown by the two Probe blocks. To run this model in Simulink’s multitasking
mode, select Fixed-step and discrete from the Type controls in the Solver

5-145
Downsample

panel of the Simulation Parameters dialog box, and select MultiTasking from
the Mode parameter. Additionally, set the Stop time to 30.
Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout =

11 -11
12 -12
13 -13
14 -14
2 -2
4 -4
6 -6
8 -8
10 -10
12 -12
14 -14

Since we ran this frame-based multirate model in multitasking mode, the first
row of the initial condition matrix appears as the first output sample, followed
by the other three initial condition rows. The second row of the first input
matrix (i.e., row D+1, where D is the Sample offset) appears in the output as
sample 5 (i.e., sample Mi+1, where Mi is the input frame size).

Dialog Box

5-146
 Downsample

Downsample factor
The integer factor, K, by which to decrease the input sample rate.
Sample offset
The sample offset, D, which must be an integer in the range [0, K-1].
Initial condition
The value with which the block is initialized for cases of nonzero latency; a
scalar or matrix.
Sample-based mode
The method by which to implement downsampling for sample-based
inputs: Allow multirate (i.e, decrease the output sample rate), or Force
single-rate (i.e., force the output sample rate to match the input sample
rate by repeating every Kth input sample K times at the output).
Frame-based mode
The method by which to implement downsampling for frame-based inputs:
Maintain input frame size (i.e., decrease the frame rate), or Maintain
input frame rate (i.e., decrease the frame size).

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also FIR Decimation DSP Blockset

FIR Rate Conversion DSP Blockset
Repeat DSP Blockset
Sample and Hold DSP Blockset
Upsample DSP Blockset

5-147
DSP Constant

Purpose 5DSP Constant

Generate a discrete-time or continuous-time constant signal.

Library DSP Sources

Description The DSP Constant block generates a signal whose value remains constant
throughout the simulation. The Constant value parameter specifies the
constant to output, and can be any valid MATLAB expression that evaluates to
a scalar, vector, or matrix.
When a row vector or column vector is specified for the Constant value
parameter, and the Interpret vector parameters as 1-D check box is selected,
the dimension of the Constant value vector is disregarded, and the output is a
1-D vector. When the Interpret vector parameters as 1-D check box is not
selected, the output dimension is constrained to match the Constant value
dimension (row or column). When the Constant value is an M-by-N matrix
with M > 1 and N > 1, the output is always M-by-N.
When Sample mode is set to Continuous, the output is a continuous-time
signal. When Sample mode is set to Discrete, the Sample time and
Frame-based output parameters are enabled, and signal has the discrete
output period specified by the Sample time parameter.
When the Frame-based output check box is selected, the output is
frame-based; otherwise, the output is sample-based. Because a 1-D vector
signal cannot be frame-based, an active Frame-based output setting overrides
an active Interpret vector parameters as 1-D setting, and the output is a
frame-based column vector (regardless of the actual Constant value vector
dimension).

5-148
 DSP Constant

Dialog Box

Constant value
The constant to generate. Tunable; values entered here can be tuned, but
their dimensions must remain fixed.
Interpret vector parameters as 1-D
When selected, generates 1-D vector outputs for Constant value settings
with vector dimension; when unselected, generates 2-D vector outputs for
Constant value settings with vector dimension. An active Interpret
vector parameters as 1-D setting is overridden by an active Frame-based
output setting.

Sample mode
The sample mode of the output, Discrete for a discrete-time signal or
Continuous for a continuous-time signal.

Sample time
The discrete sample period for sample-based outputs. When the
Frame-based output parameter is checked, this parameter is named
Frame period, and is the discrete frame period for the frame-based output.
This parameter is enabled when Discrete is selected in the Sample mode
menu.
Frame-based output
Specifies frame-based output when selected. This parameter is enabled
when Discrete is selected in the Sample mode menu

5-149
DSP Constant

Supported (MATLAB commands for casting values to certain data types are provided in
Data Types parentheses.)
Boolean (boolean)
8-, 16-, and 32-bit signed integer (int8, int16, int32)
8-, 16-, and 32-bit unsigned integer (uint8, uint16, uint32)
Single-precision floating point (single)
Double-precision floating point (double)

See Also Constant Simulink

Signal From Workspace DSP Blockset

See “Creating Signals Using Constant Blocks” on page 3-33 for related
information.

5-150
 Dyadic Analysis Filter Bank

Purpose 5Dyadic Analysis Filter Bank

Decompose a signal into components of equal or logarithmically decreasing
frequency intervals and sample rates.

Library Filtering / Multirate Filters

Description The Dyadic Analysis Filter Bank block decomposes a broadband signal into a
collection of successively more bandlimited components by repeatedly dividing
the frequency range. The typical (asymmetric) n-level filter bank structure is
shown below.
Asymmetric Filter Bank, n Levels

u HP ↓2 2Ts y1

LP ↓2 HP ↓2 4Ts y2

LP ↓2 HP ↓2 8Ts y3

LP ↓2 ... HP ↓2 yn

Tsi = Ts LP ↓2 yn+1

HP: highpass filter with fc ≈ 1/2 Nyquist

Tso = (2k)Ts for output yk, 1 ≤ k ≤ n
LP: lowpass filter with fc ≈ 1/2 Nyquist
Tso = (2n)Ts for output yn+1
↓2: downsample by 2

At each level, the low-frequency output of the previous level is decomposed into
adjacent high- and low-frequency subbands by a highpass (HP) and lowpass
(LP) filter pair. Each of the two output subbands is half the bandwidth of the
input to that level (hence “dyadic”). The bandlimited output of each filter is
maximally decimated by a factor of 2 to preserve the bit rate of the original
signal. In wavelet applications (see below) the aliasing introduced by the
decimation stage can be exactly canceled in reconstruction.
The Lowpass FIR filter coefficients and Highpass FIR filter coefficients
parameters specify (respectively) the filter coefficients to be used for every
lowpass and highpass direct-form II transpose filter in the filter bank. The
values of these coefficients are typically computed using the wavelet family

5-151
Dyadic Analysis Filter Bank

functions in the Wavelet Toolbox (see the Wavelet Toolbox documentation for
more information).

Tree Structure
The Tree structure parameter specifies an asymmetric (or wavelet) tree, as
shown above, or a symmetric structure, as shown below. Note that the
symmetric structure decomposes both the high- and low-frequency subbands at
each level, whereas the asymmetric structure only decomposes the
low-frequency bands.

Asymmetric Tree. The asymmetric structure in the first figure (Tree structure
set to Asymmetric) has n+1 outputs, where n is the Number of levels
parameter value. The sample rate and bandwidth of the top output are half the
input sample rate and bandwidth. The sample rate and bandwidth of each
additional output (except the last) are half that of the output from the previous
level. In general, for an input with sample period Tsi = Ts, and bandwidth BW,
output yk has sample period Tso,k and bandwidth BWk.

 k
 ( 2 )T s (1 ≤ k ≤ n)
T so, k = 
 ( 2 n )T (k = n + 1)
 s

 BW
 ---------- (1 ≤ k ≤ n)
 2
k
BW k = 
 BW
---------- (k = n + 1)
 n
 2

Note that in frame-based mode, the change in the sample period of output yk is
reflected by its frame size, Mo,k, rather than by its frame rate.


 Mi
 ------- (1 ≤ k ≤ n)
 2
k
M o, k = 
 Mi
 ------- (k = n + 1)
n
 2


5-152
 Dyadic Analysis Filter Bank

The bottom two outputs (yn and yn+1) share the same sample period,
bandwidth, and frame size because they originate at the same tree level.

Symmetric Tree. The symmetric structure shown below (Tree structure set to
Symmetric) has 2n outputs, where n is the Number of levels parameter value.

Symmetric Filter Bank, n Levels

HP ↓2 y1

HP ↓2 ...
LP ↓2 y2

HP ↓2
HP ↓2 y3

LP ↓2 ...
LP ↓2 y4
u
HP ↓2 y5

HP ↓2 ...
LP ↓2 y6

LP ↓2
HP ↓2 y7

LP ↓2 ...

Tsi = Ts
LP ↓2 y2n

HP: highpass filter with fc ≈ 1/2 Nyquist

LP: lowpass filter with fc ≈ 1/2 Nyquist Tso = (2n)Ts for all 2n outputs
↓2: downsample by 2

The sample rate and bandwidth of every output are reduced by a factor of 2n
from the input sample rate and bandwidth. For an input with sample period
Tsi = Ts, and bandwidth BW, output yk has sample period Tso,k and
bandwidth BWk.
n n
T so, k = ( 2 )T s (1 ≤ k ≤ 2 )

BW n
BW k = ---------- (1 ≤ k ≤ 2 )
n
2

5-153
Dyadic Analysis Filter Bank

In frame-based mode, the sample period of output yk is reflected by its frame

size, Mo,k, rather than by its frame rate.

Mi n
M o, k = ------- (1 ≤ k ≤ 2 )
n
2

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block filters each channel independently over time. The
output at each port is the same size as the input, one output channel for each
input channel. As described earlier, for the asymmetric tree structure, each
output port has a different sample period.
The figure below shows the input and output sample periods for a 64-channel
sample-based input to a three-level filter bank. The input has a period of 1, so
the fastest output has a period of 2.

Tso = 2

Tso = 4
Tsi = 1
Tso = 8

Tso = 8

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block filters each channel independently over time. The input frame
size Mi must be a multiple of 2n, and n is the number of filter bank levels. For
example, a frame size of 8 would be appropriate for a three-level tree (23=8).
The number of columns in each output is the same as the number of columns
in the input.
Each output port has the same frame period as the input. The reduction in the
output sample rates results from the smaller output frame sizes, as shown in
the example below for a four-channel input to a three-level asymmetric tree.

5-154
 Dyadic Analysis Filter Bank

Tso = 1/32)

Tfi = 1 Tso = 1/16)

Tsi = 1/64 Tfo = 1
Tso = 1/8)

Tso = 1/8)

Applications

Wavelets. The primary application for dyadic analysis filter banks is coding for
data compression using wavelets.
At the transmitting end, the output of the dyadic analysis filter bank is fed to
a lossy compression scheme, which typically assigns the number of bits for each
filter bank output in proportion to the relative energy in that frequency band.
This represents the more powerful signal components by a greater number of
bits than the less powerful signal components.

lossy
decoding
coding

At the receiving end, the transmission is decoded and fed to a dyadic synthesis
filter bank to reconstruct the original signal. The filter coefficients of the
complementary analysis and synthesis stages are designed to cancel aliasing
introduced by the filtering and resampling.

Scalograms. When the magnitudes in each of the subband signals yk, 1 ≤ k ≤ n,

are plotted across the full bandwidth of the original signal, the result is a
scalogram. This is the equivalent of a spectrogram with constant Q, where

fy
k
Q = -------------
-
BW y k

and f y is the midpoint frequency of the band occupied by output yk. The
k
frequency axis of a scalogram therefore has logarithmic divisions like those
shown below, where Fs is the sample rate (1/Ts).

5-155
Dyadic Analysis Filter Bank

Fs/16 Fs/8 Fs/4 Fs/2 Fs

Fs/32
Fs/64
Fs/128
Fs/256
0

Latency

Zero Latency. The Dyadic Analysis Filter Bank block has no tasking latency for
frame-based operation, which is always single-rate. The block therefore
analyzes the first input sample (received at t=0) to produce the first output
sample at each port.

Nonzero Latency. The Dyadic Analysis Filter Bank block has tasking latency
only for sample-based operation, which is always multirate. As shown in the
table below, the amount of latency, D, depends on the structure (symmetric or
asymmetric) of the n-level tree used by the block.

Multirate... Symmetric Tree Asymmetric Tree

Single-tasking One sample 2n-1 samples

Multitasking One sample 2n-1 samples

In the above cases, the block repeats a zero initial condition in each channel for
the first D output samples. For example, in single-tasking mode, the
asymmetric tree structure generates 2n-1 zero-valued output samples at each
port in each channel before propagating the first analyzed input sample
(computed from the input received at t=0).
See “Excess Algorithmic Delay (Tasking Latency)” in Chapter 3 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

5-156
 Dyadic Analysis Filter Bank

Dialog Box

Lowpass FIR filter coefficients

A vector of filter coefficients (descending powers of z) to be shared by all the
lowpass filters in the filter bank.
Highpass FIR filter coefficients
A vector of filter coefficients (descending powers of z) to be shared by all the
highpass filters in the filter bank.
Number of levels
The number of filter bank levels. An n-level asymmetric structure has n+1
outputs; an n-level symmetric structure has 2n outputs.
Tree structure
The structure of the filter bank, Asymmetric (wavelet) or Symmetric.

References Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter

Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.
Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA:
Wellesley-Cambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ:
Prentice Hall, 1993.

5-157
Dyadic Analysis Filter Bank

Supported Double-precision floating point (double)

Data Types

See Also Dyadic Synthesis Filter Bank DSP Blockset

Wavelet Analysis DSP Blockset

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

• “Multirate Filters” on page 4-9

5-158
 Dyadic Synthesis Filter Bank

Purpose 5Dyadic Synthesis Filter Bank

Reconstruct a signal from its multirate bandlimited components.

Library Filtering / Multirate Filters

Description The Dyadic Synthesis Filter Bank block typically reconstructs a signal that
was decomposed by the Dyadic Analysis Filter Bank block. The reconstruction
or synthesis process is the inverse of the analysis process, and restores the
original signal by upsampling, filtering, and summing the bandlimited inputs
in stages corresponding to the analysis process. The typical (asymmetric)
n-level filter bank structure is shown below.
Asymmetric Filter Bank, n Levels

u1 2Ts ↑2 HP Σ y

u2 4Ts ↑2 HP Σ ↑2 LP

u3 8Ts ↑2 HP Σ ↑2 LP

un ↑2 HP Σ ... ↑2 LP

un+1 ↑2 LP Tso = Ts

HP: highpass filter with fc ≈ 1/2 Nyquist

Tsi = (2k)Ts for input uk, 1 ≤ k ≤ n
LP: lowpass filter with fc ≈ 1/2 Nyquist
Tsi = (2n)Ts for input un+1
↑2: upsample by 2

At each level, the two bandlimited inputs (one low-frequency, one

high-frequency, both with the same sample rate) are upsampled by a factor of 2
to match the sample rate of the input to the next stage. They are then filtered
by a highpass (HP) and lowpass (LP) filter pair with coefficients calculated to
cancel (in the subsequent summation) the aliasing introduced in the
corresponding dyadic analysis filter stage. The output from each
(upsample-filter-sum) level has twice the bandwidth and twice the sample rate
of the input to that level (hence “dyadic”).
The Lowpass FIR filter coefficients and Highpass FIR filter coefficients
parameters specify (respectively) the filter coefficients to be used for every

5-159
Dyadic Synthesis Filter Bank

highpass and lowpass direct-form II transpose filter in the filter bank. The
values of these coefficients are typically computed together with the dyadic
analysis coefficients using the wavelet family functions in the Wavelet Toolbox
(see the Wavelet Toolbox documentation for more information).

Tree Structure
The Tree structure parameter specifies an asymmetric (or wavelet) tree, as
shown above, or a symmetric structure, as shown below. Note that the
symmetric structure reconstructs a signal that was symmetrically decomposed
by the Dyadic Analysis Filter Bank block (i.e., both the high- and low-frequency
subbands were divided at each level). The asymmetric structure reconstructs a
signal that was asymmetrically decomposed by the Dyadic Analysis Filter
Bank block (i.e., only the low-frequency subbands were divided at each level).

Asymmetric Tree. The asymmetric structure in the first figure (Tree structure
set to Asymmetric) has n+1 inputs, where n is the Number of levels
parameter value. The sample rate and bandwidth of the output are twice the
sample rate and bandwidth of the top input. The sample rate and bandwidth
of each additional input (except the last) should be half that of the input to the
previous level.

T si, k + 1 = 2T si, k 1≤k<n

BW k
BW k + 1 = ------------- 1≤k<n
2

The bottom two inputs (un and un+1) should have the same sample rate and
bandwidth since they are processed by the same level.

T si, n + 1 = T si, n

BW n + 1 = BW n

Note that in frame-based mode, the change in the sample period of input uk is
reflected by its frame size, Mi,k, rather than by its frame rate.

M i, k
M i, k + 1 = ------------ 1≤k<n
2

5-160
 Dyadic Synthesis Filter Bank

M i, n + 1 = M i, n

Symmetric Tree. The symmetric structure shown below (Tree structure set to
Symmetric) has 2n inputs, where n is the Number of levels parameter value.
Symmetric Filter Bank, n Levels

u1 ↑2 HP
Σ ... ↑2 HP
u2 ↑2 LP
Σ ↑2 HP
u3 ↑2 HP
Σ ... ↑2 LP
u4 ↑2 LP
Σ y
u5 ↑2 HP
Σ ... ↑2 HP
u6 ↑2 LP
Σ ↑2 LP
u7 ↑2 HP
Σ ... ↑2 LP
Tso = Ts
u2n ↑2 LP
HP: highpass filter with fc ≈ 1/2 Nyquist
LP: lowpass filter with fc ≈ 1/2 Nyquist
Tsi = (2n)Ts for all 2n inputs ↑2: upsample by 2

The sample rate and bandwidth of the output are a factor of 2n higher than the
sample rate and bandwidth of the inputs, which are all equal.

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block filters each channel independently over time. The
output is the same size as the input at each port, one output channel for each
input channel. As described earlier, for the asymmetric tree structure, each
input port has a different sample period.

5-161
Dyadic Synthesis Filter Bank

The figure below shows the input and output sample periods for the four
64-channel sample-based inputs to a three-level filter bank. The fastest input
has a period of 2, so the output period is 1.

Tsi = 2

Tsi = 4
Tso = 1
Tsi = 8

Tsi = 8

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block filters each channel independently over time. The number of
columns in the output is the same as the number of columns in the input.
All inputs must have the same frame period, which is also the output frame
period. The different input sample rates should be represented by the input
frame sizes: If the input to the top port has frame size Mi, the input to the
second-from-top port should have frame size Mi/2, the input to the
third-from-top port should have frame size Mi/4, and so on. The input to the
bottom port should have the same frame size as the second-from-bottom port.
The increase in the sample rate of the output is also represented by its frame
size, which is twice the largest input frame size.
The relationship between sample periods, frame periods, and frame sizes is
shown below for a four-channel frame-based input to a three-level filter bank.

(Tsi=1/32)

(Tsi=1/16) Tfo = 1
Tfi = 1
Tso = 1/64
(Tsi=1/8)

(Tsi=1/8)

5-162
 Dyadic Synthesis Filter Bank

Applications
The primary application for asymmetric dyadic synthesis filter banks is coding
for compression using wavelets.
At the transmitting end, the output of a dyadic analysis filter bank is fed to a
lossy compression scheme, which typically assigns the number of bits for each
filter bank output in proportion to the relative energy in that frequency band.
This represents the more powerful signal components by a greater number of
bits than the less powerful signal components.

lossy
decoding
coding

At the receiving end, the transmission is decoded and fed to the dyadic
synthesis filter bank to reconstruct the original signal. The filter coefficients of
the complementary analysis and synthesis stages are designed to cancel
aliasing introduced by the filtering and resampling.

Latency

Zero Latency. The Dyadic Synthesis Filter Bank block has no tasking latency for
frame-based operation, which is always single-rate. The block therefore uses
the first input samples (received at t=0) to synthesize the first output sample.

Nonzero Latency. The Dyadic Synthesis Filter Bank block has tasking latency
only for sample-based operation, which is always multirate. As shown in the
table below, the amount of latency, D, depends on the structure (symmetric or
asymmetric) of the n-level tree used by the block.

Multirate... Symmetric Tree Asymmetric Tree

Single-tasking None 2n-2 samples

Multitasking 2n samples 2n samples

In the above cases, the block repeats a zero initial condition in each channel for
the first D output samples. For example, in single-tasking mode the

5-163
Dyadic Synthesis Filter Bank

asymmetric tree structure generates 2n-2 zero-valued output samples in each

channel before propagating the first synthesized output sample (computed
from the inputs received at t=0).
See “Excess Algorithmic Delay (Tasking Latency)” in Chapter 3 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

Lowpass FIR filter coefficients

A vector of filter coefficients (descending powers of z) to be shared by all the
lowpass filters in the filter bank.
Highpass FIR filter coefficients
A vector of filter coefficients (descending powers of z) to be shared by all the
highpass filters in the filter bank.
Number of levels
The number of filter bank levels. An n-level asymmetric structure has n+1
inputs; an n-level symmetric structure has 2n inputs.
Tree structure
The structure of the filter bank, Asymmetric (wavelet) or Symmetric.

References Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter

Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.

5-164
 Dyadic Synthesis Filter Bank

Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA:

Wellesley-Cambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ:
Prentice Hall, 1993.

Supported Double-precision floating point (double)

Data Types

See Also Dyadic Analysis Filter Bank DSP Blockset

Wavelet Synthesis DSP Blockset

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

• “Multirate Filters” on page 4-9

5-165
Edge Detector

Purpose 5Edge Detector

Detect a transition of the input from zero to a nonzero value.

Library Signal Management / Switches and Counters

Description The Edge Detector block generates an impulse (the value 1) in a given output
channel when the corresponding channel of the input transitions from zero to
a nonzero value. Otherwise, the block generates zeros in each channel.
The output has the same dimension and sample rate as the input. If the input
is frame-based, the output is frame-based; otherwise, the output is
sample-based. For frame-based input, an edge that is split across two
consecutive frames (i.e., a zero at the bottom of the first frame, and a nonzero
value at the top of the following frame) is counted in the frame that contains
the nonzero value.

Example In the model below, the Edge Detector block locates the edges (zero to nonzero
transitions) in a two-channel frame-based input with frame size 3. The two
input channels are horizontally concatenated with the two output channels to
create the four-channel workspace variable yout.

Adjust the block parameters as described below. (Use the default settings for
the To Workspace block.)

• Set the Signal From Workspace block parameters as follows:

- Signal = [(-5:5) ; 0 1 0 0 2 0 0 0 3 0 0]'
- Sample time = 1
- Samples per frame = 3
• Set the Matrix Concatenation block parameters as follows:
- Number of inputs = 2
- Concatenation method = Horizontal
As shown below, the block finds edges at sample 7 in channel 1, and at samples
2, 5, and 9 in channel 2.

5-166
 Edge Detector

Input Output

ch1 ch2 ch1 ch2

First –5 0 00
input First output
–4 1 01 ch2 edge

–3 0 00
–2 0 00

–1 2 01 ch2 edge
0 0 00

1 0 10 ch1 edge
Simulation time

2 0 00

3 3 01 ch2 edge
4 0 00

5 0 00
0 0 00

Dialog Box

Supported Double-precision floating point

Data Types

See Also Counter DSP Blockset

Event-Count Comparator DSP Blockset

5-167
Event-Count Comparator

Purpose 5Event-Count Comparator

Detect threshold crossing of accumulated nonzero inputs.

Library Signal Management / Switches and Counters

Description The Event-Count Comparator block records the number of nonzero inputs to
the Data port during the period that the block is enabled by a high signal (the
value 1) at the interval (Int) port. Both inputs must be scalars, and the Int
input must be sample-based.
When the number of accumulated nonzero inputs first equals the Event
threshold setting, the block waits one additional sample interval, and then
sets the output high (1). The block holds the output high until recording is
restarted by a low-to-high (0-to-1) transition at the Int port.
If the input to the Data port is frame-based, the output is frame-based;
otherwise, the output is sample-based.

Example In the model below, the Event-Count Comparator block (Event threshold = 3)
detects two threshold crossings in the input to the Data port, one at sample 4
and one at sample 12.

All inputs and outputs are multiplexed into the workspace variable yout,
whose contents are shown in the figure below. The two left columns in the
illustration show the inputs to the Data and Int ports, the center column shows
the state of the block’s internal counter, and the right column shows the block’s
output.

5-168
 Event-Count Comparator

Data Int Nonzero count Output

[0] [0] [0] [0]

[1] [1] start count [1] [0]
[2] [1] [2] [0]
[3] [1] [3] equals threshold [0]
[4] [1] [4] exceeds threshold [1]
[5] [1] [5] [1]
[0] [0] stop count [5] [1]
[0] [0] [5] [1]
[0] [1]
restart count, [0] [0]
[5] [1] [1] [0]
[4] [1] [2] [0]
[3] [1] [3] equals threshold [0]
[2] [1] [4] exceeds threshold [1]
[1] [1] [5] [1]
[0] [0] stop count [5] [1]
...

...

...

...
Dialog Box

Event threshold
The value against which to compare the number of nonzero inputs.
Tunable.

Supported Double-precision floating point

Data Types

See Also Counter DSP Blockset

Edge Detector DSP Blockset

5-169
Extract Diagonal

5Extract Diagonal

Purpose Extract the main diagonal of the input matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Extract Diagonal block populates the 1-D output vector with the elements
on the main diagonal of the M-by-N input matrix A.
D = diag(A) Equivalent MATLAB code

The output vector has length min(M,N), and is always sample-based.

Dialog Box

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Constant Diagonal Matrix DSP Blockset

Create Diagonal Matrix DSP Blockset
Extract Triangular Matrix DSP Blockset
diag MATLAB

5-170
 Extract Triangular Matrix

Purpose 5Extract Triangular Matrix

Extract the lower or upper triangle from an input matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Extract Triangular Matrix block creates a triangular matrix output from
the upper or lower triangular elements of an M-by-N input matrix. A length-M
1-D vector input is treated as an M-by-1 matrix.
The Extract parameter selects between the two components of the input:

• Upper – Copies the elements on and above the main diagonal of the input
matrix to an output matrix of the same size. The first row of the output
matrix is therefore identical to the first row of the input matrix. The
elements below the main diagonal of the output matrix are zero.
• Lower – Copies the elements on and below the main diagonal of the input
matrix to an output matrix of the same size. The first column of the output
matrix is therefore identical to the first column of the input matrix. The
elements above the main diagonal of the output matrix are zero.

The output has the same frame status as the input.

Example The example below shows the extraction of upper and lower triangles from a
5-by-3 input matrix.

1 2 3 1 2 3
4 5 6 0 5 6
7 8 9 0 0 9
10 11 12 0 0 0
13 14 15 0 0 0

1 2 3 1 0 0
4 5 6 4 5 0
7 8 9 7 8 9
10 11 12 10 11 12
13 14 15 13 14 15

5-171
Extract Triangular Matrix

Dialog Box

Extract
The component of the matrix to copy to the output, upper triangle or lower
triangle. Tunable, except in Simulink’s external mode.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Autocorrelation LPC DSP Blockset

Cholesky Factorization DSP Blockset
Constant Diagonal Matrix DSP Blockset
Extract Diagonal DSP Blockset
Forward Substitution DSP Blockset
LDL Factorization DSP Blockset
LU Factorization DSP Blockset
tril MATLAB
triu MATLAB

5-172
 FFT

Purpose 5FFT
Compute the FFT of the input.

Library Transforms

Description The FFT block computes the fast Fourier transform (FFT) of each channel in
the M-by-N or length-M input, u, where M must be a power of two. To work
with other input sizes, use the Zero Pad block to pad or truncate the length-M
dimension to a power-of-two length. The output is always complex-valued and
sample-based (it is unoriented 1-D vectors for unoriented inputs).
y = fft(u,M) % Equivalent MATLAB code

The kth entry of the lth output channel, y(k, l), is the kth point of the M-point
discrete Fourier transform (DFT) of the lth input channel.
M
y ( k, l ) = ∑ u ( m, l )e – j 2π ( m – 1 ) ( k – 1 ) ⁄ M k = 1 , …, M (5-2)
m=1

For information on block output characteristics and how to configure the block
computation methods, see the following sections:

• “Input and Output Characteristics” on page 5-173

• “Ordering Output Column Entries (Output in bit-reversed order
Parameter)” on page 5-176
• “Selecting the Twiddle Factor Computation Method” on page 5-177
• “Optimizing the Table of Trigonometric Values” on page 5-178
• “Algorithms Used for FFT Computation” on page 5-179
• “Example” on page 5-179

Input and Output Characteristics

The following table describes all valid block input types, their corresponding
outputs, and the dimension along which the block computes the DFT.

Note For M-by-N and length-M inputs, M must be a power of two. To work
with other input sizes, use the Zero Pad block to pad or truncate the length-M

5-173
FFT

dimension to a power-of-two length. Also, to get valid outputs, your inputs

must be in linear order.

Valid Block Inputs Dimension Along Corresponding Block Output Characteristics

• Real- or complex-valued Which Block Output port rate = input port rate
Computes DFT
• Must be in linear order
• M must be a power of two

Frame-based M-by-N Column • Sample-based

matrix • Complex-valued
Sample-based M-by-N Column • Same dimensions as input
matrix, M ≠ 1 • Each column (each row for sample-based
row inputs) contains the M-point DFT of the
Sample-based 1-by-M row Row
corresponding input channel in linear or
vector
bit-reversed order.

Unoriented length-M 1-D Vector Unoriented, length-M, complex-valued 1-D

vector vector containing M-point DFT of input in
linear or bit-reversed order

5-174
 FFT

Click here in the MATLAB Help Browser to open a Simulink model based on
the following diagram.

Effects of Block Input’s Size, Dimension, and Frame Status on Block Output

1 2 3 10 20 30
2 4 6 – 2 + 2i – 4 + 4i – 6 + 6i
Frame-based 4-by-3 input Sample-based 4-by-3 output –2 –4 –6
3 6 9
4 8 12 – 2 – 2i – 4 – 4i – 6 – 6i
Compute FFT of each column

1 2 3 10 20 30
2 4 6 – 2 + 2i – 4 + 4i – 6 + 6i
Sample-based 4-by-3 nonrow input Sample-based 4-by-3 output –2 –4 –6
3 6 9
4 8 12 – 2 – 2i – 4 – 4i – 6 – 6i
Compute FFT of each column

1234 Sample-based 1-by-4 row vector input Sample-based 1-by-4 output 10 – 2 + 2i – 2 – 2 – 2i

Compute FFT of the row

( 1, 2, 3, 4 ) Unoriented length-4 1-D vector input Unoriented length-4 1-D vector output ( 10, – 2 + 2i, – 2, – 2 – 2i )

Compute FFT of the vector

5-175
FFT

Ordering Output Column Entries (Output in bit-reversed order Parameter)

Set the Output in bit-reversed order parameter as follows to indicate the
ordering of the output’s column elements. For a definition of bit-reversed
ordering, see “Description of Bit-Reversed Ordering” on page 5-177.

Parameter Setting Ordering of Output Output Column Entries

Channel Elements

Linear order kth column element is the DFT of the

(See the following corresponding input column at the kth
note.) frequency.

Bit-reversed order kth column element is the DFT of the

corresponding input column at the rth
frequency, where r is the bit reversed
value of k.

Note Linearly ordering the output requires extra data sorting manipulation,
so in some situations it may be better to output in bit-reversed order as
illustrated in the example, “Use of Outputs in Bit-Reversed Order” on
page 5-179.

The next diagram illustrates the difference between linear and bit-reversed
outputs. Note that output values in linear and bit-reversed order are the same;
only the order in which they appear in the columns differs.
Input must be Output in Output in
in linear order linear order bit-reversed order
1 36 w0 w0 36 wk is the kth frequency at which
2 – 4 + 9.7i w1 w4 –4
the block computes the FFT. For an
3 – 4 + 4i w2 w2 – 4 + 4i
Output can – 4 + 1.7i w3 w6 – 4 – 4i N-point FFT,
4
be ordered
wk = 2πk/N
5 –4 w4 w1 – 4 + 9.7i
k = 0, 1, ..., N-1
6 in two ways – 4 – 1.7i w5 w5 – 4 – 1.7i
7 – 4 – 4i w6 w3 – 4 + 1.7i
8 – 4 – 9.7i w7 w7 – 4 – 9.7i
and indicate the
Bit reverse the frequencies at which the block
frequency indices computes the FFT to get the output

5-176
 FFT

Description of Bit-Reversed Ordering. Two numbers are bit-reversed values of each

other when the binary representation of one is the mirror image of the binary
representation of the other. For example, in a three-bit system, one and four
are bit-reversed values of each other, since the three-bit binary representation
of one, 001, is the mirror image of the three-bit binary representation of four,
100.
The sequence 0, 1, 2, 3, 4, 5, 6, 7, is in linear order. To put the sequence in
bit-reversed order, replace each element in the linearly ordered sequence with
its bit-reversed counterpart. You can do this by translating the sequence into
its binary representation (with the minimum number of bits), then finding the
mirror image of each binary entry, and translating the sequence back to its
decimal representation. The resulting sequence is the original linearly ordered
sequence in bit-reversed order.

Find mirror image of each entry

Linear Order Bit-Reversed Order
(In a three-bit system)
0 000 000 0
1 001 100 4
2 Translate to 010 010 Translate back 2
3 011 110 6
4 binary 100 001 to decimal 1
5 representation 101 101 representation 5
6 110 011 3
7 111 111 7

Selecting the Twiddle Factor Computation Method

The Twiddle factor computation parameter determines how the block
computes the necessary sine and cosine terms to calculate the term

5-177
FFT

e –j 2π ( m – 1 ) ( k – 1 ) ⁄ M in Equation 5-2. This parameter has two settings, each

with its advantages and disadvantages, as described in the following table.

Twiddle factor computation Sine and Cosine Computation Effect on Block Performance
Parameter Setting Method

Table lookup The block computes and stores The block usually runs much
the trigonometric values before more quickly, but requires
the simulation starts, and extra memory for storing the
retrieves them during the precomputed trigonometric
simulation. When you generate values. You can optimize the
code from the block, the table for memory
processor running the generated consumption or speed, as
code stores the trigonometric described in “Optimizing the
values computed by the block, Table of Trigonometric
and retrieves the values during Values” below.
code execution.

Trigonometric fcn The block computes sine and The block usually runs more
cosine values during the slowly, but does not need
simulation. When you generate extra data memory. For code
code from the block, the generation, the block
processor running the generated requires a support library to
code computes the sine and emulate the trigonometric
cosine values while the code functions, increasing the size
runs. of the generated code.

Optimizing the Table of Trigonometric Values

When you set the Twiddle factor computation parameter to Table lookup,
you need to set the Optimize table for parameter. This parameter optimizes

5-178
 FFT

the table of trigonometric values for speed or memory by varying the number
of table entries as summarized in the following table.

Optimize table for Number of Table Memory Required

Parameter Setting Entries for N-Point FFT for Single-Precision
512-Point FFT

Speed 3N/4 1536 bytes

Memory N/4 + 1 516 bytes

Algorithms Used for FFT Computation

Depending on whether the block input is real- or complex-valued, and whether
you want the output in linear or bit-reversed order, the block uses one or more
of the following algorithms as summarized in the next table:

• Radix-2 decimation-in-time (DIT) algorithm

• Radix-2 decimation-in-frequency (DIF) algorithm
• Half-length algorithm
• Double-signal algorithm

Input Complexity Output Ordering Algorithms Used for FFT Computation

Complex Linear or Radix-2 DIT

bit-reversed

Real Linear Radix-2 DIT in conjunction with the half-length and

double-signal algorithms when possible

Real Bit-reversed Radix-2 DIF in conjunction with the half-length and

double-signal algorithms when possible

Example Use of Outputs in Bit-Reversed Order. The FFT block runs more quickly when it
outputs in bit-reversed order. You can often use an output in bit-reversed order
when your model also uses the IFFT block (the IFFT block allows you to
indicate whether its input is in bit-reversed or linear order). For instance, set
the FFT block to output in bit-reversed order when you want to filter or

5-179
FFT

convolve signals by taking the FFT of time domain data, multiplying

frequency-domain data, and inputting the product to an IFFT block.
The following model shows the implementation of the Overlap-Save FFT Filter
block. The implementation uses the FFT block in conjunction with an IFFT
block, so the FFT block is set to output in bit-reversed order, and the IFFT
block is set to accept inputs in bit-reversed order. Note that the bitrevorder
function is used to reorder a vector processed with the FFT outputs.
Click here in the MATLAB Help browser to open the demo model.
Alternatively, type the following command in MATLAB.
olapfilt % Open the following demo model

To see the implementation of the Overlap-Save FFT Filter block, right-click on

the Overlap-Save FFT Filter block, and select Look under mask. Look under
the mask of the Overlap-Add FFT Filter block as well, which also uses an FFT
block that outputs in bit-reversed order.

Implementation of the Overlap-Save FFT Filter Block

FFT block set to output

in bit-reversed order. IFFT block set to accept
bitrevorder function used to inputs in bit-reversed
comply with ordering of FFT output order

5-180
 FFT

Dialog Box

Twiddle factor computation

Computation method of the term e – j 2π ( m – 1 ) ( k – 1 ) ⁄ M in Equation 5-2. In
Table lookup mode, the block computes and stores the sine and cosine
values before the simulation starts. In Trigonometric fcn mode, the block
computes the sine and cosine values during the simulation. See “Selecting
the Twiddle Factor Computation Method” on page 5-177.
Optimize table for
Optimization of the table of sine and cosine values for Speed or Memory.
Active only when Twiddle factor computation is set to Table lookup. See
“Selecting the Twiddle Factor Computation Method” on page 5-177.
Output in bit-reverse order
Order of the output channel elements relative to the ordering of the input
elements. When checked, the output channel elements are in bit-reversed
order relative to the input ordering. Otherwise, the output column
elements are linearly ordered relative to the input ordering. See “Ordering
Output Column Entries (Output in bit-reversed order Parameter)” on
page 5-176.

Supported Single-precision floating point Table lookup mode only

Data Types Double-precision floating point All modes

5-181
FFT

See Also Complex Cepstrum DSP Blockset

DCT DSP Blockset
IFFT DSP Blockset
Pad DSP Blockset
Zero Pad DSP Blockset
bitrevorder Signal Processing Toolbox
fft Signal Processing Toolbox
ifft Signal Processing Toolbox

5-182
 Filter Realization Wizard

Purpose 5Filter Realization Wizard

Automatically construct filter realizations using Sum, Gain, and Unit Delay
blocks.

Library Filtering / Filter Designs

Description The Filter Realization Wizard is a tool for automatically creating filter
realizations with specific architectures. The Wizard’s interface allows you to
specify the filter’s structure and coefficients, the type of data to be filtered, and
optimization criteria for the design. The Wizard then builds the specified filter
as a subsystem composed of Sum, Gain, and Unit Delay blocks. You can specify
the name of the subsystem (“Filter” is the default) and whether it is placed in
the current model or in a new model.
The Architecture panel in the Wizard’s interface allows you to select from the
following realizations.

Architecture Parameters

Direct-Form I Numerator, denominator

Direct-Form II Numerator, denominator

Symmetric FIR Coefficients

Lattice (AR) Lattice coefficients

Lattice (MA) Lattice coefficients

Lattice (ARMA) Lattice coefficients, ladder coefficients

The Optimization panel in the Wizard’s interface lets you choose to optimize
for zero and unity gains. Zero-gain optimization removes zero-gain paths from
the filter structure, and unity-gain optimization substitutes a wire (short
circuit) for unity gains.
Type a name for the new filter block in the Block Name text field, and select
where the block should be placed from the Destination pop-up menu. Within
a model, the Filter subsystem operates on a sample-based signal (similar to
Simulink’s Discrete Filter block), filtering each channel over time. Double-click
on the subsystem to open it; you can then modify the gains or the filter
structure to suit your needs.

5-183
Filter Realization Wizard

Fixed-Point Options
By default, the filter constructed by the Filter Realization Wizard operates
using the Simulink standard double-precision arithmetic. If you have the
Fixed-Point Blockset installed on your system, you have the additional option
of building the filter to operate using single-precision or fixed-point arithmetic.
Select the option you want from the Data Type panel:

• Built-in data types

The filter is constructed using the standard Simulink Sum, Gain, and Unit
Delay blocks, and operates in any precision supported by Simulink
(e.g., double-precision, single-precision, Boolean, etc.). This is the default.
• Single
The filter is constructed using the Sum, Gain, and Unit Delay blocks from
the Fixed-Point Blockset. The blocks are configured for single-precision
arithmetic.
• Fixed-Point
The filter is constructed using the Sum, Gain, and Unit Delay blocks from
the Fixed-Point Blockset. The Sum and Gain blocks are configured for
fixed-point arithmetic using the options specified in the Fixed-Point panel
of the Filter Realization Wizard. These options include:
- Format (Signed or Unsigned)
- Word size
- Radix pos
- Overflow (Wrap or Saturate)
- Rounding (Zero, Nearest, Ceiling, or Floor)
For information on these parameters, see the Fixed-Point Blockset
documentation.

Examples The examples below illustrate some of the common architectures available
through the Filter Realization Wizard:

• Example 1: Direct Form II

• Example 2: Second Order Sections
• Example 3: Nth Order Sections
• Example 4: ARMA Lattice

5-184
 Filter Realization Wizard

Example 1: Direct Form II

Design an fourth-order, quarter-band, lowpass Butterworth filter:

1 At the MATLAB command line, compute the filter coefficients by entering

[b,a] = butter(4,.25);

2 Launch the Filter Realization Wizard by double-clicking on the icon in the

Filter Realizations library.
3 Configure the Wizard to use b and a as the numerator and denominator of a
Direct-Form II structure:
- Select Direct-Form II from the Type menu.
- Type b in the Numerator text field.
- Type a in the Denominator text field.
4 Type a name for the new filter subsystem in the Block Name field. The
example uses Butter LPF.
The GUI with these settings is shown below.

5 Press the Build button to create the specified filter subsystem in a new
model window.

5-185
Filter Realization Wizard

6 Double-click the new Butter LPF block to see the Direct-Form II filter
realization that the Wizard created.

Example 2: Second Order Sections

Design an eighth-order, quarter-band, lowpass Butterworth filter using
second-order sections (SOS):

1 At the MATLAB command line, compute the second-order sections by

entering
[a,b,c,d] = butter(4,.25);
sos = ss2sos(a,b,c,d);

2 Configure the Wizard to use sos as the numerator of a Direct-Form II

structure:
- Select Direct-Form II from the Type menu.
- Type sos in the Numerator text field.
- Leave the Denominator text field blank.

5-186
 Filter Realization Wizard

3 Type a name for the new filter subsystem in the Block Name field. The
example uses Butter SOS.
4 Press the Build button to create the specified filter subsystem in a new
model window.
5 Double-click the new Butter SOS block to see the Direct-Form II filter
realization that the Wizard created.

Note that in a subsystem with the Direct-Form I or II architecture, the filter

sections are connected using From and Goto blocks rather than being directly
wired together. This makes it easier to recognize and move filter sections in the
model window independently of each other.

Example 3: Nth Order Sections

Design a lowpass Butterworth filter using Nth order cascades:

1 At the MATLAB command line, compute the coefficients for the Nth order
sections by entering
[b1,a1] = butter(4,.25);
[b2,a2] = butter(3,.25);

2 Configure the Wizard to use these coefficient vectors as the numerator and
denominator of a Direct-Form II structure:
- Select Direct-Form II from the Type menu.
- Type {b1,b2} in the Numerator text field. Note that the numerator
coefficient vector for each section is entered as an element in a cell array.
Since this is a two-section filter, a two-cell array is specified in the

5-187
Filter Realization Wizard

Numerator field. The two filter sections do not need to have the same
order.
- Type {a1,a2} in the Denominator text field. Note that the denominator
coefficient vector for each section is also entered as an element in a cell
array. Since this is a two-section filter, a two-cell array is specified in the
Denominator field.
3 Type a name for the new filter subsystem in the Block Name field. The
example uses Butter Sections.
4 Press the Build button to create the specified filter subsystem in a new
model window.
5 Double-click the new Butter Sections block to see the Direct-Form II filter
realization that the Wizard created.

Example 4: ARMA Lattice

Design a fourth-order, quarter-band, lowpass Butterworth filter using an
ARMA lattice:

1 At the MATLAB command line, compute the lattice and ladder coefficients
(k and v, respectively) for the ARMA filter.
[b,a] = butter(4,.25);

5-188
 Filter Realization Wizard

[k,v] = tf2latc(b,a);

Configure the Wizard to use k and v as the coefficients of the

lattice design:

- Select Lattice (ARMA) from the Type menu.

- Type k in the Lattice Coeffs text field.
- Type v in the Ladder Coeffs text field.
2 Type a name for the new filter subsystem in the Block Name field. The
example uses Butter Lattice.
3 Press the Build button to create the specified filter subsystem in a new
model window.
4 Double-click the new Butter Lattice block to see the ARMA filter realization
that the Wizard created.

5-189
Filter Realization Wizard

Dialog Box

The parameters displayed in the Architecture panel vary for different

selections in the Type menu. Only a portion of the parameters listed below are
visible in the wizard at any one time.
Type
The filter architecture: Direct-Form I, Direct-Form II, Symmetric FIR,
Lattice (MA), Lattice (AR), Lattice (ARMA).

Numerator
The numerator coefficients for the direct-form I and II structures, specified
as a vector or variable name.
Denominator
The denominator coefficients for the direct-form I and II structures,
specified as a vector or variable name.
Coefficients
The coefficients for the symmetric FIR structure, specified as a vector or
variable name.

5-190
 Filter Realization Wizard

Lattice Coeffs
The lattice coefficients for the lattice MA/AR/ARMA structures, specified
as a vector or variable name.
Ladder Coeffs
The ladder coefficients for the lattice ARMA structure, specified as a vector
or variable name.
Optimize for zero gains
Enables zero-gain optimization (when checked) by removing zero-gain
paths from the filter structure.
Optimize for unity gains
Enables unity-gain optimization (when checked) by substituting a wire
(short circuit) for unity gains.
Destination
The location where the new filter block should be created.
Block name
The name of the new filter block.
Build
Generate the filter.
Data type
The precision of the data that the filter will process. Built-in data types,
when selected, configures the block to build the filter using
double-precision Simulink blocks. Single precision and Fixed-point
configure the block to build the filter using Fixed-Point Blockset blocks.
Fixed-point
Options for fixed-point filter construction. See the Fixed-Point Blockset
documentation.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

5-191
Filter Realization Wizard

Supported Fixed-point Supported only when you install the

Data Types Fixed-Point Blockset
Single-precision floating point Supported only when you install the
Fixed-Point Blockset
Double-precision floating point

See Also Biquadratic Filter DSP Blockset

Direct-Form II Transpose Filter DSP Blockset
Discrete Filter Simulink
Time-Varying Direct-Form II Transpose Filter DSP Blockset
Time-Varying Lattice Filter DSP Blockset
filter MATLAB

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-192
 FIR Decimation

Purpose 5FIR Decimation

Filter and downsample an input signal.

Library Filtering / Multirate Filters

Description The FIR Decimation block resamples the discrete-time input at a rate K times
slower than the input sample rate, where the integer K is specified by the
Decimation factor parameter. This process consists of two steps:

• The block filters the input data using a direct-form II transpose FIR filter.
• The block downsamples the filtered data to a lower rate by discarding K-1
consecutive samples following every sample retained.

The FIR Decimation block implements the above FIR filtering and
downsampling steps together using a polyphase filter structure, which is more
efficient than straightforward filter-then-decimate algorithms. The output of
the decimator is the first phase of the polyphase filter.
The FIR filter coefficients parameter specifies the numerator coefficients of
the FIR filter transfer function H(z).
–1 –( m – 1 )
H ( z ) = B ( z ) = b1 + b2 z + … + bm z

The length-m coefficient vector, [b(1) b(2) ... b(m)], can be generated by
one of the filter design functions in the Signal Processing Toolbox, such as the
fir1 function used in the example below. The filter should be lowpass with
normalized cutoff frequency no greater than 1/K. All filter states are internally
initialized to zero.

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block decimates each channel over time. The output sample
period is K times longer than the input sample period (Tso = KTsi), and the
input and output sizes are identical.

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block decimates each channel over time. The Framing parameter
determines how the block adjusts the rate at the output to accommodate the
reduced number of samples. There are two available options:

5-193
FIR Decimation

• Maintain input frame size

The block generates the output at the slower (decimated) rate by using a
proportionally longer frame period at the output port than at the input port.
For decimation by a factor of K, the output frame period is K times longer
than the input frame period (Tfo = KTfi), but the input and output frame
sizes are equal.

The example below shows a single-channel input with a frame period of 1

second (Sample time = 1/64 and Samples per frame = 64 in the Signal
From Workspace block) being decimated by a factor of 4 to a frame period of 4
seconds. The input and output frame sizes are identical.

• Maintain input frame rate

The block generates the output at the slower (decimated) rate by using a
proportionally smaller frame size than the input. For decimation by a factor
of K, the output frame size is K times smaller than the input frame size
(Mo = Mi/K), but the input and output frame rates are equal. The input frame
size, Mi, must be a multiple of the decimation factor, K.
The example below shows a single-channel input of frame size 64 being
decimated by a factor of 4 to a frame size of 16. The block’s input and output
frame rates are identical.

5-194
 FIR Decimation

Latency

Zero Latency. The FIR Decimation block has zero tasking latency for all
single-rate operations. The block is single-rate for the particular combinations
of sampling mode and parameter settings shown in the table below.

Sampling Mode Parameter Settings

Sample-based Decimation factor parameter, K, is 1.

Decimation factor parameter, K, is 1, or

Frame-based
Framing parameter is Maintain input frame rate.

Note that in sample-based mode, single-rate operation occurs only in the trivial
case of factor-of-1 decimation.
The block also has zero latency for sample-based multirate operations in
Simulink’s single-tasking mode. Zero tasking latency means that the block
propagates the first filtered input sample (received at t=0) as the first output
sample, followed by filtered input samples K+1, 2K+1, and so on.

Nonzero Latency. The FIR Decimation block is multirate for all settings other
than those in the above table. The amount of latency for multirate operation
depends on Simulink’s tasking mode and the block’s sampling mode, as shown
in the table below.

Multirate... Sample-Based Latency Frame-Based Latency

Single-tasking None One frame (Mi samples)

Multitasking One sample One frame (Mi samples)

In cases of one-sample latency, a zero initial condition appears as the first

output sample in each channel. The first filtered input sample appears as the
second output sample, followed by filtered input samples K+1, 2K+1, and so on.
In cases of one-frame latency, the first Mi output rows contain zeros, where Mi
is the input frame size. The first filtered input sample (first filtered row of the
input matrix) appears in the output as sample Mi+1, followed by filtered input

5-195
FIR Decimation

samples K+1, 2K+1, and so on. See the example below for an illustration of this
case.
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Examples Example 1
Construct the frame-based model shown below.

Adjust the block parameters as follows:

• Configure the Signal From Workspace block to generate a two-channel

signal with frame size of 4 and sample period of 0.25. This represents an
output frame period of 1 (0.25∗4). The first channel should contain the
positive ramp signal 1, 2, ..., 100, and the second channel should contain the
negative ramp signal -1, -2, ..., -100.
- Signal = [(1:100)' (-1:-1:-100)']
- Sample time = 0.25
- Samples per frame = 4
• Configure the FIR Decimation block to decimate the two-channel input by
decreasing the output frame rate by a factor of 2 relative to the input frame
rate. Use a third-order filter with normalized cutoff frequency, fn0, of 0.25.
(Note that fn0 satisfies fn0 ≤ 1/K.)
- FIR filter coefficients = fir1(3,0.25)
- Downsample factor = 2
- Framing = Maintain input frame size

5-196
 FIR Decimation

The filter coefficient vector generated by fir1(3,0.25) is

[0.0386 0.4614 0.4614 0.0386]

or, equivalently,
–1 –2 –3
H ( z ) = B ( z ) = 0.0386 + 0.04614z + 0.04614z + 0.0386z
• Configure the Probe blocks by deselecting the Probe width, Probe complex
signal, and Probe signal dimensions check boxes (if desired).

This model is multirate because there are at least two distinct sample rates, as
shown by the two Probe blocks. To run this model in Simulink’s multitasking
mode, select Fixed-step and discrete from the Type controls in the Solver
panel of the Simulation Parameters dialog box, and select MultiTasking from
the Mode parameter. Also set the Stop time to 30.
Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout =

0 0
0 0
0 0
0 0
0.0386 -0.0386
1.5000 -1.5000
3.5000 -3.5000
5.5000 -5.5000
7.5000 -7.5000
9.5000 -9.5000
11.5000 -11.5000

Since we ran this frame-based multirate model in multitasking mode, the first
four (Mi) output rows are zero. The first filtered input matrix row appears in
the output as sample 5 (i.e., sample Mi+1).

Example 2
The dspmrf_menu demo illustrates the use of the FIR Decimation block in a
number of multistage multirate filters.

5-197
FIR Decimation

Dialog Box

FIR filter coefficients

The lowpass FIR filter coefficients, in descending powers of z.
Decimation factor
The integer factor, K, by which to decrease the sample rate of the input
sequence.
Framing
For frame-based operation, the method by which to implement the
decimation; reduce the output frame rate, or reduce the output frame size.

Supported Double-precision floating point

Data Types

See Also Direct-Form II Transpose Filter DSP Blockset

Downsample DSP Blockset
FIR Interpolation DSP Blockset
FIR Rate Conversion DSP Blockset
decimate Signal Processing Toolbox
fir1 Signal Processing Toolbox
fir2 Signal Processing Toolbox
firls Signal Processing Toolbox
remez Signal Processing Toolbox

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

5-198
 FIR Decimation

• “Multirate Filters” on page 4-9

5-199
FIR Interpolation

Purpose 5FIR Interpolation

Upsample and filter an input signal.

Library Filtering / Multirate Filters

Description The FIR Interpolation block resamples the discrete-time input at a rate
L times faster than the input sample rate, where the integer L is specified by
the Interpolation factor parameter. This process consists of two steps:

• The block upsamples the input to a higher rate by inserting L-1 zeros
between samples.
• The block filters the upsampled data with a direct-form II transpose FIR
filter.

The FIR Interpolation block implements the above upsampling and FIR
filtering steps together using a polyphase filter structure, which is more
efficient than straightforward upsample-then-filter algorithms.
The FIR filter coefficients parameter specifies the numerator coefficients of
the FIR filter transfer function H(z).
–1 –( m – 1 )
H ( z ) = B ( z ) = b1 + b2 z + … + bm z

The coefficient vector, [b(1) b(2) ... b(m)], can be generated by one of the
filter design functions in the Signal Processing Toolbox (such as fir1), and
should have a length greater than the interpolation factor (m>L). The filter
should be lowpass with normalized cutoff frequency no greater than 1/L. All
filter states are internally initialized to zero.

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block interpolates each channel over time. The output
sample period is L times shorter than the input sample period (Tso = Tsi/L), and
the input and output sizes are identical.

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block decimates each channel over time. The Framing parameter
determines how the block adjusts the rate at the output to accommodate the
added samples. There are two available options:

5-200
 FIR Interpolation

• Maintain input frame size

The block generates the output at the faster (interpolated) rate by using a
proportionally shorter frame period at the output port than at the input port.
For interpolation by a factor of L, the output frame period is L times shorter
than the input frame period (Tfo = Tfi/L), but the input and output frame
sizes are equal.

The example below shows a single-channel input with a frame period of 1

second (Sample time = 1/64 and Samples per frame = 64 in the Signal
From Workspace block) being interpolated by a factor of 4 to a frame period
of 0.25 seconds. The input and output frame sizes are identical.

• Maintain input frame rate

The block generates the output at the faster (interpolated) rate by using a
proportionally larger frame size than the input. For interpolation by a factor
of L, the output frame size is L times larger than the input frame size
(Mo = Mi∗L), but the input and output frame rates are equal.
The example below shows a single-channel input of frame size 16 being
interpolated by a factor of 4 to a frame size of 64. The block’s input and
output frame rates are identical.

5-201
FIR Interpolation

Latency

Zero Latency. The FIR Interpolation block has zero tasking latency for all
single-rate operations. The block is single-rate for the particular combinations
of sampling mode and parameter settings shown in the table below.

Sampling Mode Parameter Settings

Sample-based Interpolation factor parameter, L, is 1.

Interpolation factor parameter, L, is 1, or

Frame-based
Framing parameter is Maintain input frame rate.

Note that in sample-based mode, single-rate operation occurs only in the trivial
case of factor-of-1 interpolation.
The block also has zero latency for sample-based multirate operations in
Simulink’s single-tasking mode. Zero tasking latency means that the block
propagates the first filtered input (received at t=0) as the first input sample,
followed by L-1 interpolated values, the second filtered input sample, and so
on.

Nonzero Latency. The FIR Interpolation block is multirate for all settings other
than those in the above table. The amount of latency for multirate operation
depends on Simulink’s tasking mode and the block’s sampling mode, as shown
in the table below.

Multirate... Sample-Based Latency Frame-Based Latency

Single-tasking None One frame (Mi samples)

Multitasking One sample One frame (Mi samples)

In cases of one-sample latency, a zero initial condition appears as the first

output sample in each channel, followed immediately by the first filtered input
sample, L-1 interpolated values, and so on.
In cases of one-frame latency, the first Mi output rows contain zeros, where Mi
is the input frame size. The first filtered input sample (first filtered row of the

5-202
 FIR Interpolation

input matrix) appears in the output as sample Mi+1, followed by L-1

interpolated values, the second filtered input sample, and so on. See the
example below for an illustration of this case.
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Example Example 1
Construct the frame-based model shown below.

Adjust the block parameters as follows.

• Configure the Signal From Workspace block to generate a two-channel

signal with frame size of 4 and sample period of 0.25. This represents an
output frame period of 1 (0.25∗4). The first channel should contain the
positive ramp signal 1, 2, ..., 100, and the second channel should contain the
negative ramp signal -1, -2, ..., -100.
- Signal = [(1:100)' (-1:-1:-100)']
- Sample time = 0.25
- Samples per frame = 4
• Configure the FIR Interpolation block to interpolate the two-channel input
by increasing the output frame rate by a factor of 2 relative to the input
frame rate. Use a third-order filter (m=3) with normalized cutoff
frequency, fn0, of 0.25. (Note that fn0 and m satisfy fn0 ≤ 1/L and m > L.)
- FIR filter coefficients = fir1(3,0.25)
- Interpolation factor = 2
- Framing = Maintain input frame size

5-203
FIR Interpolation

The filter coefficient vector generated by fir1(3,0.25) is

[0.0386 0.4614 0.4614 0.0386]

or, equivalently,
–1 –2 –3
H ( z ) = B ( z ) = 0.0386 + 0.04614z + 0.04614z + 0.0386z
• Configure the Probe blocks by deselecting the Probe width, Probe complex
signal, and Probe signal dimensions check boxes (if desired).

This model is multirate because there are at least two distinct sample rates, as
shown by the two Probe blocks. To run this model in Simulink’s multitasking
mode, select Fixed-step and discrete from the Type controls in the Solver
panel of the Simulation Parameters dialog box, and select MultiTasking from
the Mode parameter. Also set the Stop time to 30.
Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout =

0 0
0 0
0 0
0 0
0.0386 -0.0386
0.4614 -0.4614
0.5386 -0.5386
0.9614 -0.9614
1.0386 -1.0386

Since we ran this frame-based multirate model in multitasking mode, the first
four (Mi) output rows are zero. The first filtered input matrix row appears in
the output as sample 5 (i.e., sample Mi+1). Every second row is an interpolated
value.

Example 2
The dspintrp demo provides another simple example, and the dspmrf_menu
demo illustrates the use of the FIR Interpolation block in a number of
multistage multirate filters.

5-204
 FIR Interpolation

Dialog Box

FIR filter coefficients

The FIR filter coefficients, in descending powers of z.
Interpolation factor
The integer factor, L, by which to increase the sample rate of the input
sequence.
Framing
For frame-based operation, the method by which to implement the
interpolation: increase the output frame rate, or increase the output frame
size.

Supported Double-precision floating point

Data Types

See Also FIR Decimation DSP Blockset

FIR Rate Conversion DSP Blockset
Upsample DSP Blockset
fir1 Signal Processing Toolbox
fir2 Signal Processing Toolbox
firls Signal Processing Toolbox
interp Signal Processing Toolbox
remez Signal Processing Toolbox

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

5-205
FIR Interpolation

• “Multirate Filters” on page 4-9

5-206
 FIR Rate Conversion

Purpose 5FIR Rate Conversion

Upsample, filter, and downsample an input signal.

Library Filtering / Multirate Filters

Description The FIR Rate Conversion block resamples the discrete-time input to a period
K/L times the input sample period, where the integer K is specified by the
Decimation factor parameter and the integer L is specified by the
Interpolation factor parameter. The resampling process consists of the
following steps:

• The block upsamples the input to a higher rate by inserting L-1 zeros
between input samples.
• The upsampled data is passed through a direct-form II transpose FIR filter.
• The block downsamples the filtered data to a lower rate by discarding K-1
consecutive samples following each sample retained.

K and L must be relatively prime integers; that is, the ratio K/L cannot be
reducible to a ratio of smaller integers. The FIR Rate Conversion block
implements the above three steps together using a polyphase filter structure,
which is more efficient than straightforward upsample-filter-decimate
algorithms. The output of the interpolator is the first filter phase, while the
output of the decimator is the last filter phase. When both K and L are greater
than 1, the resulting output is the last decimation phase from the first
interpolation phase.
The FIR filter coefficients parameter specifies the numerator coefficients of
the FIR filter transfer function H(z).
–1 –( m – 1 )
H ( z ) = B ( z ) = b1 + b2 z + … + bm z

The coefficient vector, [b(1) b(2) ... b(m)], can be generated by one of the
filter design functions in the Signal Processing Toolbox (such as fir1), and
should have a length greater than the interpolation factor (m>L). The filter
should be lowpass with normalized cutoff frequency no greater than
min(1/L,1/K). All filter states are internally initialized to zero.

5-207
FIR Rate Conversion

Frame-Based Operation
This block accepts only frame-based inputs. An Mi-by-N frame-based matrix
input is treated as N independent channels, and the block resamples each
channel independently over time.
The Interpolation factor, L, and Decimation factor, K, must satisfy the
relation

K Mi
---- = --------
L Mo

for an integer output frame size Mo. The simplest way to satisfy this
requirement is to let the Decimation factor equal the input frame size, Mi.
The output frame size, Mo, is then equal to the Interpolation factor. This
change in the frame size, from Mi to Mo, produces the desired rate conversion
while leaving the output frame period the same as the input (Tfo = Tfi).

FIR Rate Conversion (One-channel input) Input: Output:

Decimation factor: 4 4-by-1 3-by-1
Interpolation factor: 3 Tfi = 3 Tfo = 3

first input frame first non-zero output

17 13 9 5 1
5.17 3.84 2.50 1.17 0.04
18 14 10 6 2
5.61 4.30 2.94 1.61 0.29
19 15 11 7 3
6.05 4.72 3.39 2.05 0.72
20 16 12 8 4
t=12 t=9 t=6 t=3 t=0
t=12 t=9 t=6 t=3 t=0
Tfo = 3
Tfi = 3

Latency
The FIR Rate Conversion block has no tasking latency. The block propagates
the first filtered input (received at t=0) as the first output sample.

Examples The dspsrcnv demo compares sample rate conversion performed by the FIR
Rate Conversion block with the same conversion performed by a cascade of
Upsample, Direct-Form II Transpose Filter, and Downsample blocks.

5-208
 FIR Rate Conversion

Diagnostics An error is generated if the relation between K and L shown above is not
satisfied.
(Input port width)/(Output port width) must equal the
(Decimation factor)/(Interpolation factor).

A warning is generated if L and K are not relatively prime; that is, if the ratio
L/K can be reduced to a ratio of smaller integers.
Warning: Integer conversion factors are not relatively prime in
block 'modelname/FIR Rate Conversion (Frame)'. Converting ratio
L/M to l/m.

The block scales the ratio to be relatively prime, and continues the simulation.

Dialog Box

Interpolation factor
The integer factor, L, by which to upsample the signal before filtering.
FIR filter coefficients
The FIR filter coefficients, in descending powers of z.
Decimation factor
The integer factor, K, by which to downsample the signal after filtering.

References Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter

Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.

5-209
FIR Rate Conversion

Supported Double-precision floating point

Data Types

See Also Downsample DSP Blockset

FIR Decimation DSP Blockset
FIR Interpolation DSP Blockset
Upsample DSP Blockset
fir1 Signal Processing Toolbox
fir2 Signal Processing Toolbox
firls Signal Processing Toolbox
remez Signal Processing Toolbox
upfirdn Signal Processing Toolbox

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

• “Multirate Filters” on page 4-9

5-210
 Flip

Purpose 5Flip
Flip the input vertically or horizontally.

Library Signal Management / Indexing

Description The Flip block vertically or horizontally reverses the M-by-N input matrix, u.
The output always has the same dimension and frame status as the input.
When Columns is selected from the Flip along menu, the block vertically flips
the input so that the first row of the input is the last row of the output.
y = flipud(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs are treated as M-by-1 column
vectors for vertical flipping.
When Rows is selected from the Flip along menu, the block horizontally flips
the input so that the first column of the input is the last column of the output.
y = fliplr(u) % Equivalent MATLAB code

For convenience, length-N 1-D vector inputs are treated as 1-by-N row vectors
for horizontal flipping. The output always has the same dimension and frame
status as the input.

Dialog Box

Flip along
The dimension along which to flip the input. Columns specifies vertical
flipping, while Rows specifies horizontal flipping. Tunable

5-211
Flip

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Selector Simulink

Transpose DSP Blockset
Variable Selector DSP Blockset
flipud MATLAB
fliplr MATLAB

5-212
 Forward Substitution

Purpose 5Forward Substitution

Solve the equation LX=B for X when L is a lower triangular matrix.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The Forward Substitution block solves the linear system LX=B by simple
forward substitution of variables, where L is the lower triangular M-by-M
matrix input to the L port, and B is the M-by-N matrix input to the B port. The
output is the solution of the equations, the M-by-N matrix X, and is always
sample-based.
The block only uses the elements in the lower triangle of input L; the upper
elements are ignored. When Force input to be unit-lower triangular is
selected, the block replaces the elements on the diagonal of L with ones. This
is useful when matrix L is the result of another operation, such as an LDL
decomposition, that uses the diagonal elements to represent the D matrix.
A length-M vector input at port B is treated as an M-by-1 matrix.

Dialog Box

Force input to be unit-lower triangular

Replaces the elements on the diagonal of L with 1s when selected. Tunable.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Solver DSP Blockset
LDL Solver DSP Blockset
Levinson-Durbin DSP Blockset
LU Solver DSP Blockset
QR Solver DSP Blockset

5-213
Forward Substitution

See “Solving Linear Systems” on page 4-16 for related information.

5-214
 Frame Status Conversion

Purpose 5Frame Status Conversion

Specify the frame status of the output, sample-based or frame-based.

Library Signal Management / Signal Attributes

Description The Frame Status Conversion block passes the input through to the output,
and sets the output frame status to the Output signal parameter, which can
be either Frame-based or Sample-based. The output frame status can also be
inherited from the signal at the Ref (reference) input port, which is made
visible by selecting the Inherit output frame status from Ref input port
check box.
If the Output signal parameter setting or the inherited signal’s frame status
differs from the input frame status, the block changes the input frame status
accordingly, but does not otherwise alter the signal. In particular, the block
does not rebuffer or resize 2-D inputs. Because 1-D vectors cannot be
frame-based, if the input is a length-M 1-D vector, and the Output signal
parameter is set to Frame-based, the output is a frame-based M-by-1 matrix
(i.e., a single channel).
If the Output signal parameter or the inherited signal’s frame status matches
the input frame status, the block passes the input through to the output
unaltered.

Dialog Box

Inherit output frame status from Ref input port

When selected, enables the Ref input port from which the block inherits the
output frame status. Tunable.
Output signal
The output frame status, Frame-based or Sample-based. Tunable.

5-215
Frame Status Conversion

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Check Signal Attributes DSP Blockset

Convert 1-D to 2-D DSP Blockset
Convert 2-D to 1-D DSP Blockset
Inherit Complexity DSP Blockset

5-216
 From Wave Device

Purpose 5From Wave Device

Read audio data from a standard audio device in real-time.
(Windows 95/98/NT only)

Library DSP Sources

Description The From Wave Device block reads audio data from a standard Windows audio
device in real-time. It is compatible with most popular Windows hardware,
including Sound Blaster cards. (Models that contain both this block and the To
Wave Device block require a duplex-capable sound card.)
The Use default audio device parameter allows the block to detect and use the
system’s default audio hardware. This option should be selected on systems
that have a single sound device installed, or when the default sound device on
a multiple-device system is the desired source. In cases when the default sound
device is not the desired input source, deselect Use default audio device, and
enter the desired device identification number in the Audio device ID
parameter. The device ID is an integer value that the block associates with the
sound device. A three-device system, for example, has device ID numbers of
1, 2, and 3.

If the audio source contains two channels (stereo), the Stereo check box should
be selected. If the audio source contains a single channel (mono), the Stereo
check box should be deselected. For stereo input, the block’s output is an
M-by-2 matrix containing one frame (M consecutive samples) of audio data
from each of the two channels. For mono input, the block’s output is an M-by-1
matrix containing one frame (M consecutive samples) of audio data from the
mono input. The frame size, M, is specified by the Samples per frame
parameter. For M=1, the output is sample-based; otherwise, the output is
frame-based.
The amplitude of the input from the sound device should be in the range ±1.
Values outside this range are clipped to the nearest allowable value. If the
audio signal is saturating at ±1, you can reduce the microphone gain from the
Multimedia Properties window (available through the Windows 95/98/NT
Control Panel). The audio data is processed in uncompressed PCM (pulse code
modulation) format, and should typically be sampled at one of the standard
Windows audio device rates: 8000, 11025, 22050, or 44100 Hz. You can select
one of these rates from the Sample rate parameter. To specify a different rate,
select the User-defined option and enter a value in the User-defined sample
rate parameter.

5-217
From Wave Device

The Sample Width (bits) parameter specifies the number of bits used to
represent the signal samples read by the audio device. Two settings are
available:

• 8 – allocates 8 bits to each sample, allowing a resolution of 256 levels

• 16 – allocates 16 bits to each sample, allowing a resolution of 65536 levels

The 16-bit sample width setting requires more memory but yields better
fidelity. The output from the block is independent of the Sample Width (bits)
setting, and is always double precision.

Buffering
Since the audio device accepts real-time audio input, Simulink must read a
continuous stream of data from the device throughout the simulation. Delays
in reading data from the audio hardware can result in hardware errors or
distortion of the signal. This means that the From Wave Device block must in
principle read data from the audio hardware as quickly as the hardware itself
acquires the signal. However, the block often cannot match the throughput rate
of the audio hardware, especially when the simulation is running from within
Simulink rather than as generated code. (Simulink operations are generally
slower than comparable hardware operations, and execution speed routinely
varies during the simulation as the host operating system services other
processes.) The block must therefore rely on a buffering strategy to ensure that
signal data can be read on schedule without losing samples.
At the start of the simulation, the audio device begins writing the input data to
a (hardware) buffer with a capacity of Tb seconds. The From Wave Device block
immediately begins pulling the earliest samples off the buffer (first in, first out)
and collecting them in length-M frames for output. As the audio device
continues to append inputs to the bottom of the buffer, the From Wave Device
block continues to pull inputs off the top of the buffer at the best possible rate.
The following figure shows an audio signal being acquired and output with a
frame size of 8 samples. The buffer of the sound board is approaching its
five-frame capacity at the instant shown, which means that the hardware is
adding samples to the buffer more rapidly than the block is pulling them off. (If

5-218
 From Wave Device

the signal sample rate was 8 kHz, this small buffer could hold approximately
0.005 second of data.)

Hardware execution rate is Simulink execution rate varies.

board

No delays Simulation delay

Hardware buffer with
5-frame capacity

If the simulation throughput rate is higher than the hardware throughput

rate, the buffer remains empty throughout the simulation. If necessary, the
From Wave Device block simply waits for new samples to become available on
the buffer (the block does not interpolate between samples). More typically, the
simulation throughput rate is lower than the hardware throughput rate, and
the buffer tends to fill over the duration of the simulation.

Troubleshooting
If the buffer size is too small in relation to the simulation throughput rate, the
buffer may fill before the entire length of signal is processed. This usually
results in a device error or undesired device output. When this problem occurs,
you can choose to either increase the buffer size or the simulation throughput
rate:

• Increase the buffer size

The Queue duration parameter specifies the duration of signal, Tb (in
real-time seconds), that can be buffered in hardware during the simulation.
Equivalently, this is the maximum length of time that the block’s data
acquisition can lag the hardware’s data acquisition. The number of frames
buffered is approximately
Tb Fs
-------------
M

where Fs is the sample rate of the signal and M is the number of samples per
frame. The required buffer size for a given signal depends on the signal

5-219
From Wave Device

length, the frame size, and the speed of the simulation. Note that increasing
the buffer size may increase model latency.
• Increase the simulation throughput rate
Two useful methods for improving simulation throughput rates are
increasing the signal frame size and compiling the simulation into native
code:
- Increase frame sizes (and convert sample-based signals to frame-based
signals) throughout the model to reduce the amount of block-to-block
communication overhead. This can drastically increase throughput rates
in many cases. However, larger frame sizes generally result in greater
model latency due to initial buffering operations.
- Generate executable code with Real Time Workshop. Native code runs
much faster than Simulink, and should provide rates adequate for
real-time audio processing.
More general ways to improve throughput rates include simplifying the model,
and running the simulation on a faster PC processor. See “Delay and Latency”
on page 3-85 of this book, and “Improving Simulation Performance and
Accuracy” in the Simulink documentation, for other ideas on improving
simulation performance.

Dialog Box

5-220
 From Wave Device

Sample rate (Hz)

The sample rate of the audio data to be acquired. Select one of the standard
Windows rates or the User-defined option.
User-defined sample rate (Hz)
The (nonstandard) sample rate of the audio data to be acquired.
Sample width (bits)
The number of bits used to represent each signal sample.
Stereo
Specifies stereo (two-channel) inputs when checked, mono (one-channel)
inputs when unchecked. Stereo output is M-by-2; mono output is M-by-1.
Samples per frame
The number of audio samples in each successive output frame, M.
Queue duration (seconds)
The length of signal (in seconds) to buffer to the hardware at the start of
the simulation.
Use default audio device
Reads audio input from the system’s default audio device when selected.
Deselect to enable the Audio device ID parameter and manually enter a
device ID number. Tunable.
Audio device ID
The number of the audio device from which to read the audio output. In a
system with several audio devices installed, a value of 1 selects the first
audio card, a value of 2 selects the second audio card, and so on. Select
Use default audio device if the system has only a single audio card
installed. Tunable.

Supported Double-precision floating point

Data Types

See Also From Wave File DSP Blockset

To Wave Device DSP Blockset

See “Importing WAV Files” on page 3-71 for related information.

5-221
From Wave File

Purpose 5From Wave File

Read audio data from a Microsoft Wave (.wav) file. (Windows 95/98/NT only)

Library DSP Sources

Description The From Wave File block reads audio data from a Microsoft Wave (.wav) file
and generates a double-precision signal with amplitudes in the range ±1. The
audio data must be in uncompressed PCM (pulse code modulation) format.
y = wavread('filename') % Equivalent MATLAB code

The File name parameter can specify an absolute or relative path to the file. If
the file is on the MATLAB path or in the current directory (the directory
returned by typing pwd at the MATLAB command line), you need only specify
the file’s name. You do not need to specify the.wav extension in either case.
If the audio file contains two channels (stereo), the block’s output is an M-by-2
matrix containing one frame (M consecutive samples) of audio data from each
of the two channels. If the audio file contains a single channel (mono), the
block’s output is an M-by-1 matrix containing one frame (M consecutive
samples) of mono audio data. The frame size, M, is specified by the Samples
per frame parameter. For M=1, the output is sample-based; otherwise, the
output is frame-based.
The output frame period, Tfo, is

M
T fo = ------ ,
Fs

where Fs is the data sample rate in Hz.

To reduce the required number of file accesses, the block acquires L consecutive
samples from the file during each access, where L is specified by the Minimum
number of samples for each read from file parameter (L ≥ M). For L < M, the
block instead acquires M consecutive samples during each access. Larger
values of L result in fewer file accesses, which reduces run-time overhead.
The block icon shows the name, sample rate (in Hz), number of channels
(1 or 2), and sample width (in bits) of the data in the specified audio file. All
sample rates are supported; the sample width must be either 8 or 16 bits.

5-222
 From Wave File

Dialog Box

File name
The path and name of the file to read. Paths can be relative or absolute.
Samples per output frame
The number of samples in each output frame, M.
Minimum number of samples for each read from file
The number of consecutive samples to acquire from the file with each file
access, L. Tunable.

Supported Double-precision floating point

Data Types

See Also From Wave Device DSP Blockset

Signal From Workspace DSP Blockset
To Wave File DSP Blockset
wavread MATLAB

See “Importing WAV Files” on page 3-71 for related information.

5-223
Histogram

Purpose 5Histogram
Generate the histogram of an input or sequence of inputs.

Library Statistics

Description The Histogram block computes the frequency distribution of the elements in
each column of the input, or tracks the frequency distribution in a sequence of
inputs over a period of time. The Running histogram parameter selects
between basic operation and running operation, described below.
The block sorts the elements of each column into the number of discrete bins
specified by the Number of bins parameter, n.
y = hist(u,n) % Equivalent MATLAB code

Complex inputs are sorted by their magnitudes.

The histogram value for a given bin represents the frequency of occurrence of
the input values bracketed by that bin. The upper-boundary of the
highest-valued bin is specified by the Maximum value of input parameter,
BM, and the lower-boundary of the lowest-valued bin is specified by the
Minimum value of input parameter, Bm. The bins have equal width of

BM – Bm
∆ = -----------------------
n
and centers located at

B m +  k + ---  ∆
1
k = 0, 1, 2, …, n – 1
 2

Input values that fall on the border between two bins are sorted into the
lower-valued bin; that is, each bin includes its upper boundary. For example, a
bin of width 4 centered on the value 5 contains the input value 7, but not the
input value 3. Input values greater than the Maximum value of input
parameter or less than Minimum value of input parameter are sorted into the
highest-valued or lowest-valued bin, respectively.

Basic Operation
When the Running histogram check box is not selected, the block computes
the frequency distribution of each column in the M-by-N input u independently
at each sample time.

5-224
 Histogram

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output, y, is a sample-based n-by-N matrix whose jth column is the
histogram for the data in the jth column of u. When the Normalized check box
is selected, the block scales each column of the output so that sum(y(:,j)) is 1.

Running Operation
When the Running histogram check box is selected, the block computes the
frequency distributions in a time-sequence of M-by-N inputs by creating N
persistent histograms to which successive inputs are continuously added. For
frame-based inputs, this is equivalent to a persistent histogram for each
independent channel.
As in basic operation, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.
The output is a sample-based n-by-N matrix whose jth column reflects the
current state of the jth histogram. The block resets the running histogram (by
emptying all bins of all histograms) when the scalar input at the optional Rst
port is nonzero. (The Rst port can be disabled by deselecting the Reset port
check box.)

Example The model below illustrates the Histogram block’s basic operation for a
single-channel input, u, where
u = [0 -2 6 -12 2 5 4 3 0 4 3 -2 -3 -2 -9]'

The parameter settings for the Histogram block are:

• Minimum value of input = -10

• Maximum value of input = 10
• Number of bins = 5

5-225
Histogram

• Normalized =
• Running histogram =

The resulting bin width is 4, as shown below.

Input
Minimum value of input = -10
0 Maximum value of input = 10
–2 Number of bins = 5
6 Output
– 12
2 2
5 4
4
3
3
0 6
4 0
3
–2
6
–3
# of occurrences

5
–2
-2 4
–9
-2 2 4
-9 -2 0 3
-12 -3 0 3

-8 -4 0 4 8

Dialog Box

Minimum value of input

The lower boundary, Bm, of the lowest-valued bin.

5-226
 Histogram

Maximum value of input

The upper boundary, BM, of the highest-valued bin.
Number of bins
The number of bins, n, in the histogram.
Normalized
Normalizes the output vector (1-norm) when selected. Tunable, except in
Simulink’s external mode.
Running histogram
Enables running operation when selected.
Reset port
Enables the Rst input port when selected.

Supported Double-precision floating point

Data Types

See Also Sort DSP Blockset

hist MATLAB

5-227
IDCT

Purpose 5IDCT
Compute the IDCT of the input.

Library Transforms

Description The IDCT block computes the inverse discrete cosine transform (IDCT) of each
channel in the M-by-N input matrix, u.
y = idct(u) % Equivalent MATLAB code

For both sample-based and frame-based inputs, the block assumes that each
input column is a frame containing M consecutive samples from an
independent channel. The frame size, M, must be a power-of-two. To work with
other frame sizes, use the Zero Pad block to pad or truncate the frame size to a
power-of-two length.
The output is an M-by-N matrix whose lth column contains the length-M IDCT
of the corresponding input column.

M
π ( 2m – 1 ) ( k – 1 )
y ( m, l ) = ∑ w ( k )u ( k, l ) cos -------------------------------------------
2M
-, m = 1, …, M
k=1

where

 1
 --------- , k=1

w(k) =  M
 2
 ----- , 2≤k≤M
 M

The output is always frame-based, and the output sample rate and data type
(real/complex) are the same as those of the input.
For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are processed as single channels (i.e., as M-by-1 column vectors),
and the output has the same dimension as the input.

5-228
 IDCT

Dialog Box

Supported Double-precision floating point

Data Types

See Also DCT DSP Blockset

IFFT DSP Blockset
idct Signal Processing Toolbox

5-229
Identity Matrix

Purpose 5Identity Matrix

Generate a matrix with ones on the main diagonal and zeros elsewhere.

Library DSP Sources,

Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Identity Matrix block generates a rectangular matrix with ones on the
main diagonal and zeros elsewhere.
When the Inherit input port attributes from input port check box is selected,
the input port is enabled, and an M-by-N matrix input generates a
sample-based M-by-N matrix output with the same sample period. The values
in the input matrix are ignored.
y = eye([M N]) % Equivalent MATLAB code

When the Inherit input port attributes from input port check box is not
selected, the input port is disabled, and the dimensions of the output matrix are
determined by the Matrix size parameter. A scalar value, M, specifies an
M-by-M identity matrix, while a two-element vector, [M N], specifies an
M-by-N unit-diagonal matrix. The output is sample-based, and has the sample
period specified by the Sample time parameter.

Example Set Matrix size to [3 6] to generate the 3-by-6 unit-diagonal matrix below.

1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0

5-230
 Identity Matrix

Dialog Box

Inherit input port attributes from input port

Enables the input port when selected. The output inherits its dimensions
and sample period from the input.
Matrix size
The number of rows and columns in the output matrix: a scalar M for a
square M-by-M output, or a vector [M N] for an M-by-N output. This
parameter is disabled when Inherit input port attributes from input
port is selected.
Sample time
The discrete sample period of the output. This parameter is disabled when
Inherit input port attributes from input port is selected.

Supported Double-precision floating point

Data Types

See Also Constant Diagonal Matrix DSP Blockset

DSP Constant DSP Blockset
eye MATLAB

See “Creating Signals Using Constant Blocks” on page 3-33 for related
information.

5-231
IFFT

Purpose 5IFFT
Compute the IFFT of the input.

Library Transforms

Description The IFFT block computes the inverse fast Fourier transform (IFFT) of each
channel in the M-by-N or length-M input, u, where M must be a power of two.
To work with other input sizes, use the Zero Pad block to pad or truncate the
length-M dimension to a power-of-two length. The output is always
frame-based, and each output column contains the M-point inverse discrete
Fourier transform (IDFT) of the corresponding input channel.
y = ifft(u,M) % Equivalent MATLAB code

The kth entry of the lth output channel, y(k, l), is the kth point of the M-point
IDFT of the lth input channel.
M
1
y(k, l) = -----
M ∑ u ( m, l )e j2π ( m – 1 ) ( k – 1 ) ⁄ M k = 1, … , M (5-3)
m=1

You can choose to output a scaled version of the input’s IDFT, M ⋅ y(k, l) , by
setting the parameter Skip normalization by transform length, N.
M

M ⋅ y(k, l) = ∑ u ( m, l )e j2π ( m – 1 ) ( k – 1 ) ⁄ M k = 1, … , M (5-4)

m=1

For information on block output characteristics and how to configure the block
computation methods, see the following sections:

• “Input and Output Characteristics” on page 5-233

• “Conjugate Symmetric Input” on page 5-235
• “Inputs in Bit-Reversed Order” on page 5-236
• “Selecting the Twiddle Factor Computation Method” on page 5-236
• “Optimizing the Table of Trigonometric Values” on page 5-236
• “Algorithms Used for IFFT Computation” on page 5-236
• “Example” on page 5-237

5-232
 IFFT

Input and Output Characteristics

The following table describes all valid block input types, their corresponding
outputs, and the dimension along which the block computes the IDFT.

Note For M-by-N and length-M inputs, M must be a power of two. To work
with other input sizes, use the Zero Pad block to pad or truncate the length-M
dimension to a power-of-two length. To get valid outputs, you must correctly
set the Input is in bit-reversed order parameter to indicate the ordering of
the block input. When the input is conjugate symmetric and you want to get a
real-valued output, set the Input is conjugate symmetric parameter.

5-233
IFFT

Valid Block Inputs Dimension Along Corresponding Block Output

• Must be complex-valued Which Block Characteristics
Computes IDFT Output port rate = input port rate
• M must be a power of two
• In linear or bit-reversed
order

Frame-based M-by-N matrix Column The following output characteristics apply

to all valid block inputs:
Sample-based M-by-N Column
matrix, M ≠ 1 • Frame-based
• Complex-valued unless you set the Input
Sample-based 1-by-M row Row is conjugate symmetric parameter
vector when your input is conjugate-symmetric,
1-D length-M vector Vector in which case the output is real-valued
• Same dimension as input (for 1-D inputs,
output is a length-M column)
• Each column (each row for sample-based
row inputs) contains the M-point IDFT of
the corresponding input channel in linear
order. If the parameter Skip normaliza-
tion by transform length, N is set, rath-
er than computing the IDFT, the block
computes a scaled version of the IDFT
given by Equation 5-4.

5-234
 IFFT

Click here in the MATLAB Help Browser to open a Simulink model based on
the following diagram.

Effects of Block Input Size, Dimension, and Frame Status on Block Output

1 2 3 2.5 5 7.5
2 4 6 – 0.5 – 0.5i – 1 – i – 1.5 – 1.5i
Frame-based 4-by-3 input Frame-based 4-by-3 output – 0.5 –1 – 1.5
3 6 9
4 8 12 – 0.5 + 0.5i – 1 + i – 1.5 + 1.5i
Compute IFFT of each column

1 2 3 2.5 5 7.5
2 4 6 – 0.5 – 0.5i – 1 – i – 1.5 – 1.5i
Sample-based 4-by-3 nonrow input Frame-based 4-by-3 output – 0.5 –1 – 1.5
3 6 9
4 8 12 – 0.5 + 0.5i – 1 + i – 1.5 + 1.5i
Compute IFFT of each column

1234 Sample-based 1-by-4 row vector input Frame-based 1-by-4 output 2.5 – 0.5 – 0.5i – 0.5 – 0.5 + 0.5i

Compute IFFT of the row

2.5
( 1, 2, 3, 4 ) – 0.5 – 0.5i
Unoriented length-4 1-D vector input Frame-based 4-by-1 output – 0.5
– 0.5 + 0.5i
Compute IFFT of the vector

Conjugate Symmetric Input

When the block input is conjugate symmetric and you want real-valued
outputs, set the Input is conjugate symmetric parameter, which also
optimizes the block’s computation method. A common source of conjugate
symmetric data is the FFT block, which yields conjugate symmetric output
when its input is real-valued.

Note If the IFFT block input is conjugate symmetric but you do not set the
Input is conjugate symmetric parameter, you do not get a real-valued
output. Instead, you get a complex-valued output with small imaginary parts.

5-235
IFFT

The block output is invalid if you set this parameter when the input is not
conjugate symmetric.

Inputs in Bit-Reversed Order

When the block input is in bit-reversed order, you must set the parameter
Input is in bit-reversed order to get a valid output. The block output is invalid
if you set this parameter when the input is not in bit-reversed order. A common
source of bit-reversed inputs is the FFT block, as illustrated in the FFT block
example, “Use of Outputs in Bit-Reversed Order” on page 5-179.
For a definition of bit-reversed and linear order, see the FFT block reference
page section, “Description of Bit-Reversed Ordering” on page 5-177.

Selecting the Twiddle Factor Computation Method

The FFT block and IFFT block both have a parameter, Twiddle factor
computation. Setting this parameter in the IFFT block is very similar to
setting it in the FFT block. For details, see the FFT block reference page
section, “Selecting the Twiddle Factor Computation Method” on page 5-177.

Optimizing the Table of Trigonometric Values

The FFT block and IFFT block both have a parameter, Optimize table for.
Setting this parameter in the IFFT block is very similar to setting it in the FFT
block. For details, see the FFT block reference page section, “Optimizing the
Table of Trigonometric Values” on page 5-178.

Algorithms Used for IFFT Computation

Depending on whether the block input is real- or complex-valued and conjugate
symmetric, the block uses one or more of the following algorithms as
summarized in the next table:

• Radix-2 decimation-in-time (DIT) algorithm

• Half-length algorithm
• Double-signal algorithm

5-236
 IFFT

Input Complexity Other Parameter Algorithms Used for FFT Computation

Settings

Complex not applicable Radix-2 DIT

Real Radix-2 DIT

Real Radix-2 DIT in conjunction with the half-length

and double-signal algorithms when possible

Example For an example of how to optimize computations when using both the IFFT
block and FFT block in the same model, see the FFT block reference page
example, “Use of Outputs in Bit-Reversed Order” on page 5-179.

Dialog Box

Twiddle factor computation

Computation method of the term e j2π ( m – 1 ) ( k – 1 ) ⁄ M in Equation 5-3. In
Table lookup mode, the block computes and stores the sine and cosine

5-237
IFFT

values before the simulation starts. In Trigonometric fcn mode, the block
computes the sine and cosine values during the simulation.
Optimize table for
Optimization of the table of sine and cosine values for Speed or Memory.
Active only when Twiddle factor computation is set to Table lookup.
Input is in bit-reversed order
Set when the input is in bit-reversed order, and clear when the input is in
linear order. The block yields invalid outputs if you do not set this
parameter correctly.
Input is conjugate symmetric
Set when the block input is conjugate symmetric and you want real-valued
outputs. The block output is invalid if you set this parameter when the
input is not conjugate symmetric.
Skip normalization by transform length, N
When set, rather than computing the IDFT, the block computes a scaled
version of the IDFT given by Equation 5-4.

Supported Single-precision floating point Table lookup mode only

Data Types Double-precision floating point All modes

See Also FFT DSP Blockset

IDCT DSP Blockset
Pad DSP Blockset
Zero Pad DSP Blockset
bitrevorder Signal Processing Toolbox
fft Signal Processing Toolbox
ifft Signal Processing Toolbox

5-238
 Inherit Complexity

Purpose 5Inherit Complexity

Change the complexity of the input to match that of a reference signal.

Library Signal Management / Signal Attributes

Description The Inherit Complexity block alters the input data at the Data port to match
the complexity of the reference input at the Ref port. If the Data input is real,
and the Ref input is complex, the block appends a zero-valued imaginary
component, 0i, to each element of the Data input.
Data Ref Output
0 5+ i 0+0i
1 3-2i 1+0i
Simulation time

2 0+ i 2+0i
3 2-5i 3+0i
4 2-5i 4+0i
...

...

...
If the Data input is complex, and the Ref input is real, the block outputs the
real component of the Data input.
Data Ref Output
i 5 0
1-2i 5 1
Simulation time

2+ i 3 2
3-5i -2 3
4-5i -2 4
...

...

...

If both the Data input and Ref input are real, or if both the Data input and Ref
input are complex, the block propagates the Data input with no change.

5-239
Inherit Complexity

Dialog Box

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Check Signal Attributes DSP Blockset

Complex to Magnitude-Angle Simulink
Complex to Real-Imag Simulink
Magnitude-Angle to Complex Simulink
Real-Imag to Complex Simulink

5-240
 Integer Delay

Purpose 5Integer Delay

Delay an input by an integer number of sample periods.

Library Signal Operations

Description The Integer Delay block delays a discrete-time input by the number of sample
intervals specified in the Delay parameter. Noninteger delay values are
rounded to the nearest integer, and negative delays are clipped at 0.

Sample-Based Operation
When the input is a sample-based M-by-N matrix, the block treats each of the
M∗N matrix elements as an independent channel. The Delay parameter, v, can
be an M-by-N matrix of positive integers that specifies the number of sample
intervals to delay each channel of the input, or a scalar integer by which to
equally delay all channels.
For example, if the input is M-by-1 and v is the matrix
[v(1) v(2) ... v(M)]', the first channel is delayed by v(1) sample intervals,
the second channel is delayed by v(2) sample intervals, and so on. Note that
when a channel is delayed for ∆ sample-time units, the output sample at time
t is the input sample at time t – ∆ . If t – ∆ is negative, then the output is the
corresponding value specified by the Initial conditions parameter.
A 1-D vector of length M is treated as an M-by-1 matrix, and the output is 1-D.
The Initial conditions parameter specifies the output of the block during the
initial delay in each channel. The initial delay for a particular channel is the
time elapsed from the start of the simulation until the first input in that
channel is propagated to the output. Both fixed and time-varying initial
conditions can be specified in a variety of ways to suit the dimensions of the
input.

Fixed Initial Conditions. A fixed initial condition in sample-based mode can be

specified as one of the following:

• Scalar value to be repeated at each sample time of the initial delay (for every
channel). For a 2-by-2 input with the parameter settings below,

5-241
Integer Delay

the block generates the following sequence of matrices at the start of the
simulation,

1 2 1 3 2 4 3
–1 –1 u 11 – 1 u 11 u 12 u 11 u 12 u 11 u 12
, , , , ,…
1 2 1
–1 –1 –1 –1 –1 –1 u 21 – 1 u 21 u 22
k
where u ij is the i,jth element of the kth matrix in the input sequence.
• Array of size M-by-N-by-d. In this case, you can set different fixed initial
conditions for each element of a sample-based input. This setting is
explained further in the Array bullet in “Time-Varying Initial Conditions”
below.

Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions. A time-varying initial condition in sample-based

mode can be specified in one of the following ways:
• Vector of length d, where d is the maximum value specified for any channel
in the Delay parameter. The vector can be a L-by-d, 1-by-d, or 1-by-1-by-d.
The d elements of the vector are output in sequence, one at each sample time
of the initial delay.
For a scalar input and the parameters shown below,

the block outputs the sequence -1, -1, -1, 0, 1,... at the start of the
simulation.
• Array of dimension M-by-N-by-d, where d is the value specified for the Delay
parameter (the maximum value if the Delay is a vector) and M and N are the
number of rows and columns, respectively, in the input matrix. The d pages

5-242
 Integer Delay

of the array are output in sequence, one at each sample time of the initial
delay. For a 2-by-3 input, and the parameters below,

the block outputs the matrix sequence

1 2 3, 2 4 6, 3 6 9
4 5 6 1 3 5 0 4 8

at the start of the simulation. Note that setting Initial conditions to an

array with the same matrix for each entry implements constant initial
conditions; a different constant initial condition for each input matrix
element (channel).

Initial conditions cannot be specified by full matrices.

Frame-Based Operation
When the input is a frame-based M-by-N matrix, the block treats each of the N
columns as an independent channel, and delays each channel as specified by
the Delay parameter.
For frame-based inputs, the Delay parameter can be a scalar integer by which
to equally delay all channels. It can also be a 1-by-N row vector, each element
of which serves as the delay for the corresponding channel of the N-channel
input. Likewise, it can also be an M-by-1 column vector, each element of which
serves as the delay for one of the corresponding M samples for each channel.
The Delay parameter can be an M-by-N matrix of positive integers as well; in
this case, each element of each channel is delayed by the corresponding
element in the delay matrix. For instance, if the fifth element of the third
column of the delay matrix was 3, then the fifth element of the third channel of
the input matrix is always delayed by three sample-time units.
When a channel is delayed for ∆ sample-time units, the output sample at time
t is the input sample at time t – ∆ . If t – ∆ is negative, then the output is the
corresponding value specified in the Initial conditions parameter.

5-243
Integer Delay

The Initial conditions parameter specifies the output during the initial delay.
Both fixed and time-varying initial conditions can be specified. The initial
delay for a particular channel is the time elapsed from the start of the
simulation until the first input in that channel is propagated to the output.

Fixed Initial Conditions. The settings shown below specify fixed initial conditions.
The value entered in the Initial conditions parameter is repeated at the
output for each sample time of the initial delay. A fixed initial condition in
frame-based mode can be one of the following:

• Scalar value to be repeated for all channels of the output at each sample time
of the initial delay. For a general M-by-N input with the parameter settings
below,

the first five samples in each of the N channels are zero. Note that if the
frame size is larger than the delay, all of these zeros are all included in the
first output from the block.

• Array of size 1-by-N-by-D. In this case, you can also specify different fixed
initial conditions for each channel. See the Array bullet in “Time-Varying
Initial Conditions” below for details.
Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions. The following settings specify time-varying initial

conditions. For time-varying initial conditions, the values specified in the
Initial conditions parameter are output in sequence during the initial delay.
A time-varying initial condition in frame-based mode can be specified in the
following ways:
• Vector of length D, where each of the N channels have the same initial
conditions sequence specified in the vector. D is defined as follows:

- When an element of the delay entry is less than the frame size,
D = d + 1
where d is the maximum delay.

5-244
 Integer Delay

- When the all elements of the delay entry are greater than the input frame
size,
D = d + input frame size - 1
Only the first d entries of the initial condition vector will be used; the rest of
the values are ignored, but you must include them nonetheless. For a
two-channel ramp input [1:100; 1:100]' with a frame size of 4 and the
parameter settings below,

the block outputs the following sequence of frames at the start of the
simulation.

–4 –1 3 –5 7 4
–5 –2
, 4 1 , 8 5 ,…
1 –3 5 2 9 6
2 –4 6 3 10 7

Note that since one of the delays, 2, is less than the frame size of the input,
4, the length of the Initial conditions vector is the sum of the maximum
delay and 1 (5+1), which is 6. The first five entries of the initial conditions
vector are used by the channel with the maximum delay, and the rest of the
entries are ignored. Since the first channel is delayed for less than the
maximum delay (2 sample time units), it only makes use of two of the initial
condition entries.

• Array of size 1-by-N-by-D, where D is defined in the Vector bullet above in

“Time-Varying Initial Conditions” on page 5-244. In this case, the kth entry
of each 1-by-N entry in the array corresponds to an initial condition for the
kth channel of the input matrix. Thus, a 1-by-N-by-D initial conditions input
allows you to specify different initial conditions for each channel. For
instance, for a two-channel ramp input [1:100; 1:100]' with a frame size
of 4 and the parameter settings below,

5-245
Integer Delay

the block outputs the following sequence of frames at the start of the
simulation.

–1 –2 – 9 – 10 4 4
–3 –4
, 1 1 , 5 5 ,…
–5 –6 2 2 6 6
–7 –8 3 3 7 7

Note that the channels have distinct time varying initial conditions; the
initial conditions for channel 1 correspond to the first entry of each length-2
row vector in the initial conditions array, and the initial conditions for
channel 2 correspond to the second entry of each row vector in the initial
conditions array. Only the first five entries in the initial conditions array are
used; the rest are ignored.
The 1-by-N-by-D array entry can also specify different fixed initial conditions
for every channel; in this case, every 1-by-N entry in the array would be
identical, so that the initial conditions for each column are fixed over time.
Initial conditions cannot be specified by full matrices.

Examples The dspafxr demo illustrates an audio reverberation system built around the
Integer Delay block.

5-246
 Integer Delay

Input Output

ch1
ch2
ch3

ch1
ch2
ch3
[1 1 1] First input [0 1 0] First output
(sample-based)
[2 2 2] [0 2 0]
[3 3 3] [1 3 0]
[4 4 4] [2 4 0]
Simulation time

[5 5 5] [3 5 0]
[6 6 6] [4 6 1]
[7 7 7] [5 7 2]
[8 8 8] [6 8 3]
[9 9 9] [7 9 4]
Delay: [2 0 5]
...

...
Initial conditions: 0

Dialog Box

Delay
The number of sample periods to delay the input signal.
Initial conditions
The value of the block’s output during the initial delay.

5-247
Integer Delay

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Unit Delay Simulink

Variable Fractional Delay DSP Blockset
Variable Integer Delay DSP Blockset

5-248
 Kalman Adaptive Filter

Purpose 5Kalman Adaptive Filter

Compute filter estimates for an input using the Kalman adaptive filter
algorithm.

Library Filtering / Adaptive Filters

Description The Kalman Adaptive Filter block computes the optimal linear minimum
mean-square estimate (MMSE) of the FIR filter coefficients using a one-step
predictor algorithm. This Kalman filter algorithm is based on the following
physical realization of a dynamical system.

The Kalman filter assumes that there are no deterministic changes to the filter
taps over time (i.e., the transition matrix is identity), and that the only
observable output from the system is the filter output with additive noise. The
corresponding Kalman filter is expressed in matrix form as

K ( n – 1 )u ( n )
g ( n ) = --------------------------------------------------------------------
H
u ( n )K ( n – 1 )u ( n ) + Q M
H
y ( n ) = u ( n )ŵ ( n )
e(n) = d(n) – y(n)
ŵ ( n + 1 ) = ŵ ( n ) + e ( n )g ( n )
H
K ( n ) = K ( n – 1 ) – g ( n )u ( n )K ( n – 1 ) + Q P

5-249
Kalman Adaptive Filter

The variables are as follows.

Variable Description

n The current algorithm iteration

u(n) The buffered input samples at step n

K(n) The correlation matrix of the state estimation error

g(n) The vector of Kalman gains at step n

ŵ ( n ) The vector of filter-tap estimates at step n

y(n) The filtered output at step n

e(n) The estimation error at step n

d(n) The desired response at step n

QM The correlation matrix of the measurement noise

QP The correlation matrix of the process noise

The correlation matrices, QM and QP, are specified in the parameter dialog box
by scalar variance terms to be placed along the matrix diagonals, thus ensuring
that these matrices are symmetric. The filter algorithm based on this
constraint is also known as the random-walk Kalman filter.
The implementation of the algorithm in the block is optimized by exploiting the
symmetry of the input covariance matrix K(n). This decreases the total number
of computations by a factor of two.
The block icon has port labels corresponding to the inputs and outputs of the
Kalman algorithm. Note that inputs to the In and Err ports must be
sample-based scalars. The signal at the Out port is a scalar, while the signal at
the Taps port is a sample-based vector.

5-250
 Kalman Adaptive Filter

Block Ports Corresponding Variables

In u, the scalar input, which is internally buffered into the

vector u(n)
Out y(n), the filtered scalar output
Err e(n), the scalar estimation error
Taps ŵ ( n ) , the vector of filter-tap estimates

An optional Adapt input port is added when the Adapt input check box is
selected in the dialog box. When this port is enabled, the block continuously
adapts the filter coefficients while the Adapt input is nonzero. A zero-valued
input to the Adapt port causes the block to stop adapting, and to hold the filter
coefficients at their current values until the next nonzero Adapt input.
The FIR filter length parameter specifies the length of the filter that the
Kalman algorithm estimates. The Measurement noise variance and the
Process noise variance parameters specify the correlation matrices of the
measurement and process noise, respectively. The Measurement noise
variance must be a scalar, while the Process noise variance can be a vector
of values to be placed along the diagonal, or a scalar to be repeated for the
diagonal elements.
The Initial value of filter taps specifies the initial value ŵ ( 0 ) as a vector, or
as a scalar to be repeated for all vector elements. The Initial error correlation
matrix specifies the initial value K(0), and can be a diagonal matrix, a vector
of values to be placed along the diagonal, or a scalar to be repeated for the
diagonal elements.

5-251
Kalman Adaptive Filter

Dialog Box

FIR filter length

The length of the FIR filter.
Measurement noise variance
The value to appear along the diagonal of the measurement noise
correlation matrix. Tunable.
Process noise variance
The value to appear along the diagonal of the process noise correlation
matrix. Tunable.
Initial value of filter taps
The initial FIR filter coefficients.
Initial error correlation matrix
The initial value of the error correlation matrix.
Adapt input
Enables the Adapt port.

References Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall,
1996.

5-252
 Kalman Adaptive Filter

Supported Double-precision floating point

Data Types

See Also LMS Adaptive Filter DSP Blockset

RLS Adaptive Filter DSP Blockset

See “Adaptive Filters” on page 4-3 for related information.

5-253
LDL Factorization

Purpose 5LDL Factorization

Factor a square Hermitian positive definite matrix into lower, upper, and
diagonal components.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The LDL Factorization block uniquely factors the square Hermitian positive
definite input matrix S as
*
S = LDL
where L is a lower triangular square matrix with unity diagonal elements, D is
a diagonal matrix, and L* is the Hermitian (complex conjugate) transpose of L.
Only the diagonal and lower triangle of the input matrix are used, and any
imaginary component of the diagonal entries is disregarded.
The block’s output is a composite matrix with lower triangle elements lij
from L, diagonal elements dij from D, and upper triangle elements uij from L*.
It is always sample-based. The output format is shown below for a 5-by-5
matrix.

d 11 u 12 u 13 u 14 u 15
l 21 d 22 u 23 u 24 u 25
*
l 31 l 32 d 33 u 34 u 35 u ij = l ji
l 41 l 42 l 43 d 44 u 45
l 51 l 52 l 53 l 54 d 55

LDL factorization requires half the computation of Gaussian elimination

(LU decomposition), and is always stable. It is more efficient that Cholesky
factorization because it avoids computing the square roots of the diagonal
elements.
The algorithm requires that the input be square and Hermitian positive
definite. When the input is not positive definite, the block reacts with the
behavior specified by the Non-positive definite input parameter.

5-254
 LDL Factorization

The following options are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid factorization. A partial factorization will be present in the
upper left corner of the ouput.
• Warning – Display a warning message in the MATLAB command window,
and continue the simulation. The output is not a valid factorization. A partial
factorization will be present in the upper left corner of the ouput.
• Error – Display an error dialog box and terminate the simulation.

Example LDL decomposition of a 3-by-3 Hermitian positive definite matrix:

9 –1 2 9.00 – 0.11 0.22

–1 8 –5 – 0.11 7.89 – 0.61
2 –5 7 0.22 – 0.61 3.66

1 0 0 9.00 0 0 1 – 0.11 0.22

L = – 0.11 1 0 D = 0 7.89 0 L' = 0 1 – 0.61
0.22 – 0.61 1 0 0 3.66 0 0 1

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

5-255
LDL Factorization

Supported Double-precision floating point

Data Types

See Also Cholesky Factorization DSP Blockset

LDL Inverse DSP Blockset
LDL Solver DSP Blockset
LU Factorization DSP Blockset
QR Factorization DSP Blockset

See “Factoring Matrices” on page 4-17 for related information.

5-256
 LDL Inverse

Purpose 5LDL Inverse

Compute the inverse of a Hermitian positive definite matrix using LDL
factorization.

Library Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description The LDL Inverse block computes the inverse of the Hermitian positive definite
input matrix S by performing an LDL factorization.

–1 * –1
S = ( LDL )
L is a lower triangular square matrix with unity diagonal elements, D is a
diagonal matrix, and L* is the Hermitian (complex conjugate) transpose of L.
Only the diagonal and lower triangle of the input matrix are used, and any
imaginary component of the diagonal entries is disregarded. The output is
always sample-based.
LDL factorization requires half the computation of Gaussian elimination
(LU decomposition), and is always stable. It is more efficient than Cholesky
factorization because it avoids computing the square roots of the diagonal
elements.
The algorithm requires that the input be Hermitian positive definite. When the
input is not positive definite, the block reacts with the behavior specified by the
Non-positive definite input parameter. The following options are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid inverse.
• Warning – Display a warning message in the MATLAB command window,
and continue the simulation. The output is not a valid inverse.
• Error – Display an error dialog box and terminate the simulation.

Dialog Box

5-257
LDL Inverse

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Cholesky Inverse DSP Blockset

LDL Factorization DSP Blockset
LDL Solver DSP Blockset
LU Inverse DSP Blockset
Pseudoinverse DSP Blockset
inv MATLAB

See “Inverting Matrices” on page 4-19 for related information.

5-258
 LDL Solver

Purpose 5LDL Solver

Solve the equation SX=B for X when S is a square Hermitian positive definite
matrix.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The LDL Solver block solves the linear system SX=B by applying LDL
factorization to the matrix at the S port, which must be square (M-by-M) and
Hermitian positive definite. Only the diagonal and lower triangle of the matrix
are used, and any imaginary component of the diagonal entries is disregarded.
The input to the B port is the right-hand side M-by-N matrix, B. The output is
the unique solution of the equations, M-by-N matrix X, and is always
sample-based.
A length-M 1-D vector input for right-hand side B is treated as an M-by-1
matrix.
When the input is not positive definite, the block reacts with the behavior
specified by the Non-positive definite input parameter. The following options
are available:

• Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid solution.
• Warning – Proceed with the computation and display a warning message in
the MATLAB command window. The output is not a valid solution.
• Error – Display an error dialog box and terminate the simulation.

Algorithm The LDL algorithm uniquely factors the Hermitian positive definite input
matrix S as
*
S = LDL
where L is a lower triangular square matrix with unity diagonal elements, D is
a diagonal matrix, and L* is the Hermitian (complex conjugate) transpose of L.
The equation
*
LDL X = B
is solved for X by the following steps:

5-259
LDL Solver

1 Substitute
*
Y = DL X
2 Substitute
*
Z = L X
3 Solve one diagonal and two triangular systems.

LY = B

DZ = Y

*
L X = Z

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Solver DSP Blockset
LDL Factorization DSP Blockset
LDL Inverse DSP Blockset
Levinson-Durbin DSP Blockset
LU Solver DSP Blockset
QR Solver DSP Blockset

See “Solving Linear Systems” on page 4-16 for related information.

5-260
 Least Squares Polynomial Fit

Purpose 5Least Squares Polynomial Fit

Compute the coefficients of the polynomial that best fits the input data in a
least-squares sense.

Library Math Functions / Polynomial Functions

Description The Least Squares Polynomial Fit block computes the coefficients of the nth
order polynomial that best fits the input data in the least-squares sense, where
n is specified by the Polynomial order parameter. A distinct set of n+1
coefficients is computed for each column of the M-by-N input, u.
For a given input column, the block computes the set of coefficients,
c1, c2, …, cn+1, that minimizes the quantity

M
2
∑ ( ui – ûi )
i=1

where ui is the ith element in the input column, and

n n–1
û i = f ( x i ) = c 1 x i + c 2 x i + L + cn + 1

The values of the independent variable, x1, x2, …, xM, are specified as a
length-M vector by the Control points parameter. The same M control points
are used for all N polynomial fits, and can be equally or unequally spaced. The
equivalent MATLAB code is shown below.
c = polyfit(x,u,n) % Equivalent MATLAB code

Inputs can be frame-based or sample-based. For convenience, a length-M 1-D

vector input is treated as an M-by-1 matrix.
Each column of the (n+1)-by-N output matrix, c, represents a set of n+1
coefficients describing the best-fit polynomial for the corresponding column of
the input. The coefficients in each column are arranged in order of descending
exponents, c1, c2, …, cn+1. The output is always sample-based.

Example In the model below, the Polynomial Evaluation block uses the second-order
polynomial
2
y = –2 u + 3

5-261
Least Squares Polynomial Fit

to generate four values of dependent variable y from four values of independent

variable u, received at the top port. The polynomial coefficients are supplied in
the vector [-2 0 3] at the bottom port. Note that the coefficient of the
first-order term is zero.

The Control points parameter of the Least Squares Polynomial Fit block is
configured with the same four values of independent variable u that are used
as input to the Polynomial Evaluation block, [1 2 3 4]. The Least Squares
Polynomial Fit block uses these values together with the input values of
dependent variable y to reconstruct the original polynomial coefficients.

Dialog Box

Control points
The values of the independent variable to which the data in each input
column correspond. For an M-by-N input, this parameter must be a
length-M vector. Tunable.
Polynomial order
The order, n, of the polynomial to be used in constructing the best fit. The
number of coefficients is n+1. Tunable.

5-262
 Least Squares Polynomial Fit

Supported Double-precision floating point

Data Types

See Also Detrend DSP Blockset

Polynomial Evaluation DSP Blockset
Polynomial Stability Test DSP Blockset
polyfit MATLAB

5-263
Levinson-Durbin

Purpose 5Levinson-Durbin
Solve a linear system of equations using Levinson-Durbin recursion.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The Levinson-Durbin block solves the nth-order system of linear equations

Ra = b
for the particular case where R is a Hermitian, positive-definite, Toeplitz
matrix and b is identical to the first column of R shifted by one element and
with the opposite sign.

r(1) r* ( 2 ) L r* ( n ) a(2) –r ( 2 )
r ( 2 ) r ( 1 ) L r* ( n – 1 ) a(3) –r ( 3 )
=
M M O M M M
r(n) r(n – 1) L r(1) a ( n + 1 ) – r ( n + 1)

The input to the block, r = [r(1) r(2) ... r(n+1)], can be a 1-D or 2-D
vector (row or column). It contains lags 0 through n of an autocorrelation
sequence, which appear in the matrix R.
The block can output the polynomial coefficients, A, the reflection
coefficients, K, and the prediction error power, P, in various combinations. The
Output(s) parameter allows you to enable the A and K outputs by selecting one
of the following settings:

• A – Port A outputs A=[1 a(2) a(3) ... a(n+1)], the solution to the
Levinson-Durbin equation. A has the same dimension as the input. The
elements of the output can also be viewed as the coefficients of an nth-order
autoregressive (AR) process (see below).
• K – Port K outputs K=[k(1) k(2) ... k(n)], which contains n reflection
coefficients, and has the same dimension as the input, less one element.
(A scalar input causes an error when K is selected.) Reflection coefficients
are useful for realizing a lattice representation of the AR process described
below.
• A and K – The block outputs both representations at their respective ports.
(A scalar input causes an error when A and K is selected.)

Both A and K are always 1-D vectors.

5-264
 Levinson-Durbin

The prediction error power, P, (a scalar), is output when the Output

prediction error power (P) check box is selected. P represents the power of
the output of an FIR filter with taps A and input autocorrelation described by
r, where A represents a prediction error filter and r is the input to the block.
(In this case, A is a whitening filter).
When If the value of lag 0 is zero, A=[1 zeros], K=[zeros], P=0 is selected
(default), an input whose r(1) element is zero generates a zero-valued output.
When this check box is not selected, an input with r(1) = 0 generates NaNs in
the output. In general, an input with r(1) = 0 is invalid because it does not
construct a positive-definite matrix R; however, it is common for blocks to
receive zero-valued inputs at the start of a simulation. The check box allows
you to avoid propagating NaNs during this period.

Applications
One application of the Levinson-Durbin formulation above is in the
Yule-Walker AR problem, which concerns modeling an unknown system as an
autoregressive process. Such a process would be modeled as the output of an
all-pole IIR filter with white Gaussian noise input. In the Yule-Walker
problem, the use of the signal’s autocorrelation sequence to obtain an optimal
estimate leads to an Ra = b equation of the type shown above, which is most
efficiently solved by Levinson-Durbin recursion. In this case, the input to the
block represents the autocorrelation sequence, with r(1) being the zero-lag
value. The output at the block’s A port then contains the coefficients of the
autoregressive process that optimally models the system. The coefficients are
ordered in descending powers of z, and the AR process is minimum phase. The
prediction error, G, defines the gain for the unknown system, where G = P .

G G
H ( z ) = ------------ = --------------------------------------------------------------------------------
A(z) –1
1 + a ( 2 )z + … + a ( n + 1 )z
–n

The output at the block’s K port contains the corresponding reflection

coefficients, [k(1) k(2) ... k(n)], for the lattice realization of this IIR filter.
The Yule-Walker AR Estimator block implements this autocorrelation-based
method for AR model estimation, while the Yule-Walker Method block extends
the method to spectral estimation.
Another common application of the Levinson-Durbin algorithm is in linear
predictive coding, which is concerned with finding the coefficients of a moving

5-265
Levinson-Durbin

average (MA) process (or FIR filter) that predicts the next value of a signal
from the current signal sample and a finite number of past samples. In this
case, the input to the block represents the signal’s autocorrelation sequence,
with r(1) being the zero-lag value, and the output at the block’s A port contains
the coefficients of the predictive MA process (in descending powers of z).
–1 –n
H ( z ) = A ( z ) = 1 + a ( 2 )z + … + a ( n + 1 )z
These coefficients solve the optimization problem below.
N 2
min
{ ai } E xn – ∑ ai xn – i
i=1

Again, the output at the block’s K port contains the corresponding reflection
coefficients, [k(1) k(2) ... k(n)], for the lattice realization of this FIR
filter. The Autocorrelation LPC block in the Linear Prediction library
implements this autocorrelation-based prediction method.

Algorithm The algorithm requires O(n2) operations, and is thus much more efficient for
large n than standard Gaussian elimination, which requires O(n3) operations.

Dialog Box

Output(s)
The solution representation of Ra = b to output: model coefficients (A),
reflection coefficients (K), or both (A and K). For scalar inputs, this
parameter must be set to A.

5-266
 Levinson-Durbin

Output prediction error power (P)

When selected, the block outputs the prediction error at port P.
If the value of lag 0 is zero, A=[1 zeros], K=[zeros], P=0
When selected, the block outputs a zero-vector for inputs having r(1) = 0.
When unselected, the block outputs NaNs for these inputs.

References Golub, G. H., and C. F. Van Loan. Sect. 4.7 in Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.
Ljung, L. System Identification: Theory for the User. Englewood Cliffs, NJ:
Prentice Hall, 1987. Pgs. 278-280.
Kay, Steven M., Modern Spectral Estimation: Theory and Application.
Englewood Cliffs, NJ: Prentice Hall, 1988.

Supported Double-precision floating point

Data Types

See Also Cholesky Solver DSP Blockset

LDL Solver DSP Blockset
Autocorrelation LPC DSP Blockset
LU Solver DSP Blockset
QR Solver DSP Blockset
Yule-Walker AR Estimator DSP Blockset
Yule-Walker Method DSP Blockset
levinson Signal Processing Toolbox

See “Solving Linear Systems” on page 4-16 for related information.

5-267
LMS Adaptive Filter

Purpose 5LMS Adaptive Filter

Compute filter estimates for an input using the LMS adaptive filter algorithm.

Library Filtering / Adaptive Filters

Description The LMS Adaptive Filter block implements an adaptive FIR filter using the
stochastic gradient algorithm known as the normalized Least Mean-Square
(LMS) algorithm.
H
y ( n ) = ŵ ( n – 1 )u ( n )
e(n) = d(n) – y(n)
u(n)
ŵ ( n ) = ŵ ( n – 1 ) + --------------------------------------- µe∗ ( n )
H
a + u ( n )u ( n )
The variables are as follows.

Variable Description

n The current algorithm iteration

u(n) The buffered input samples at step n

ŵ ( n ) The vector of filter-tap estimates at step n

y(n) The filtered output at step n

e(n) The estimation error at step n

d(n) The desired response at step n

µ The adaptation step size

To overcome potential numerical instability in the tap-weight update, a small

positive constant (a = 1e-10) has been added in the denominator.
To turn off normalization, deselect the Use normalization check box in the
parameter dialog box. The block then computes the filter-tap estimate as

ŵ ( n ) = ŵ ( n – 1 ) + u ( n )µe∗ ( n )
The block icon has port labels corresponding to the inputs and outputs of the
LMS algorithm. Note that inputs to the In and Err ports must be sample-based

5-268
 LMS Adaptive Filter

scalars. The signal at the Out port is a scalar, while the signal at the Taps port
is a sample-based vector.

Block Ports Corresponding Variables

In u, the scalar input, which is internally buffered into the

vector u(n)
Out y(n), the filtered scalar output
Err e(n), the scalar estimation error
Taps ŵ ( n ) , the vector of filter-tap estimates

An optional Adapt input port is added when the Adapt input check box is
selected in the dialog box. When this port is enabled, the block continuously
adapts the filter coefficients while the Adapt input is nonzero. A zero-valued
input to the Adapt port causes the block to stop adapting, and to hold the filter
coefficients at their current values until the next nonzero Adapt input.
The FIR filter length parameter specifies the length of the filter that the LMS
algorithm estimates. The Step size parameter corresponds to µ in the
equations. Typically, for convergence in the mean square, 0<µ<2. The Initial
value of filter taps specifies the initial value ŵ ( 0 ) as a vector, or as a scalar
to be repeated for all vector elements. The Leakage factor specifies the value
of the leakage factor, 1 – µα , in the leaky LMS algorithm below. This
parameter must be between 0 and 1.

u(n)
ŵ ( n + 1 ) = ( 1 – µα )ω̂ ( n ) + -----------------------------µe∗ ( n )
H
u ( n )u ( n )

Examples The lmsdemo demo illustrates a noise cancellation system built around the
LMS Adaptive Filter block.

5-269
LMS Adaptive Filter

Dialog Box

FIR filter length

The length of the FIR filter.
Step-size
The step size, usually in the range (0, 2). Tunable.
Initial value of filter taps
The initial FIR filter coefficients.
Leakage factor
The leakage factor, in the range [0, 1]. Tunable.
Use normalization
Select or deselect normalization.
Adapt input
Enables the Adapt port.

References Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall,
1996.

Supported Double-precision floating point

Data Types

5-270
 LMS Adaptive Filter

See Also Kalman Adaptive Filter DSP Blockset

RLS Adaptive Filter DSP Blockset

See “Adaptive Filters” on page 4-3 for related information.

5-271
LU Factorization

Purpose 5LU Factorization

Factor a square matrix into lower and upper triangular components.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The LU Factorization block factors a row permutation of the square input
matrix A as

A p = LU

where L is a lower-triangular square matrix with unity diagonal elements, and

U is an upper-triangular square matrix. The row-pivoted matrix Ap contains
the rows of A permuted as indicated by the permutation index vector P.
Ap = A(P,:) % Equivalent MATLAB code

The output at the LU port is a composite matrix with lower subtriangle

elements from L and upper triangle elements from U, and is always
sample-based.

Example The row-pivoted matrix Ap and permutation index vector P computed by the
block are shown below for 3-by-3 input matrix A.

–1 8 –5 9 –1 2
A = 9 –1 2 P = (2 1 3) A = –1 8 –5
p
2 –5 7 2 –5 7

The LU output is a composite matrix whose lower subtriangle forms L and

whose upper triangle forms U.

9.00 – 1.00 2.00

– 0.11 7.89 – 4.78
–1 8 –5 0.22 – 0.61 3.66
9 –1 2
2 –5 7
(2 1 3)

1 0 0 9.00 – 1.00 2.00

L = – 0.11 1 0 U = 0 7.89 – 4.78
0.22 – 0.61 1 0 0 3.66

5-272
 LU Factorization

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Factorization DSP Blockset
LDL Factorization DSP Blockset
LU Inverse DSP Blockset
LU Solver DSP Blockset
Permute Matrix DSP Blockset
QR Factorization DSP Blockset
lu MATLAB

See “Factoring Matrices” on page 4-17 for related information.

5-273
LU Inverse

Purpose 5LU Inverse

Compute the inverse of a square matrix using LU factorization.

Library Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description The LU Inverse block computes the inverse of the square input matrix A by
factoring and inverting row-pivoted variant Ap.
–1 –1
A p = ( LU )

L is a lower-triangular square matrix with unity diagonal elements, and U is

an upper-triangular square matrix. The block’s output is A-1, and is always
sample-based.

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Cholesky Inverse DSP Blockset

LDL Inverse DSP Blockset
LU Factorization DSP Blockset
LU Solver DSP Blockset
inv MATLAB

See “Inverting Matrices” on page 4-19 for related information.

5-274
 LU Solver

Purpose 5LU Solver

Solve the equation AX=B for X when A is a square matrix.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The LU Solver block solves the linear system AX=B by applying
LU factorization to the M-by-M matrix at the A port. The input to the B port is
the right-hand side M-by-N matrix, B. The output is the unique solution of the
equations, M-by-N matrix X, and is always sample-based.
A length-M 1-D vector input for right-hand side B is treated as an M-by-1
matrix.

Algorithm The LU algorithm factors a row-permuted variant (Ap) of the square input
matrix A as

A p = LU

where L is a lower-triangular square matrix with unity diagonal elements, and

U is an upper-triangular square matrix.
The matrix factors are substituted for Ap in

Ap X = Bp

where Bp is the row-permuted variant of B, and the resulting equation

LUX = B p

is solved for X by making the substitution Y = UX, and solving two triangular
systems.

LY = B p

UX = Y

Dialog Box

5-275
LU Solver

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Solver DSP Blockset
LDL Solver DSP Blockset
Levinson-Durbin DSP Blockset
LU Factorization DSP Blockset
LU Inverse DSP Blockset
QR Solver DSP Blockset

See “Solving Linear Systems” on page 4-16 for related information.

5-276
 Magnitude FFT

Purpose 5Magnitude FFT

Compute a nonparametric estimate of the spectrum using the periodogram
method.

Library Estimation / Power Spectrum Estimation

Description The Magnitude FFT block computes a nonparametric estimate of the spectrum
using the periodogram method. When the Output parameter is set to
Magnitude squared, the block output for an input u is equivalent to
y = abs(fft(u,nfft)).^2 % Equivalent MATLAB code

When the Output parameter is set to Magnitude, the block output for an
input u is equivalent to
y = abs(fft(u,nfft)) % Equivalent MATLAB code

Both an M-by-N frame-based matrix input and an M-by-N sample-based

matrix input are treated as M sequential time samples from N independent
channels. The block computes a separate estimate for each of the N
independent channels and generates an Nfft-by-N matrix output. When
Inherit FFT length from input dimensions is selected, Nfft is specified by the
frame size of the input, which must be a power of 2. When Inherit FFT length
from input dimensions is not selected, Nfft is specified as a power of 2 by the
FFT length parameter, and the block zero pads or truncates the input to Nfft
before computing the FFT.
Each column of the output matrix contains the estimate of the corresponding
input column’s power spectral density at Nfft equally spaced frequency points
in the range [0,Fs), where Fs is the signal’s sample frequency. The output is
always sample-based.

Example The dspsacomp demo compares the periodogram method with several other
spectral estimation methods.

5-277
Magnitude FFT

Dialog Box

Output
Determines whether the block computes the magnitude FFT (Magnitude)
or magnitude-squared FFT (Magnitude squared) of the input. Tunable.
Inherit FFT length from input dimensions
When selected, uses the input frame size as the number of data points, Nfft,
on which to perform the FFT.
FFT size
The number of data points on which to perform the FFT, Nfft. If Nfft exceeds
the input frame size, the frame is zero-padded as needed. This parameter
is enabled when Inherit FFT length from input dimensions is not
selected.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

5-278
 Magnitude FFT

See Also Burg Method DSP Blockset

Short-Time FFT DSP Blockset
Spectrum Scope DSP Blockset
Yule-Walker Method DSP Blockset
pwelch Signal Processing Toolbox

See “Power Spectrum Estimation” on page 4-15 for related information.

5-279
Matrix 1-Norm

Purpose 5Matrix 1-Norm

Compute the 1-norm of a matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix 1-Norm block computes the 1-norm, or maximum column-sum, of
an M-by-N input matrix, A.

M
y = A 1 = max
1≤j≤N
∑ a ij
i=1

This is equivalent to
y = max(sum(abs(A))) % Equivalent MATLAB code

a 11 a 12 a 13
a 21 a 22 a 23 A 1 = max ( A 1, A 2, A 3 )
a 31 a 32 a 33

a 13 + a 23 + a 33 = A 3

a 12 + a 22 + a 32 = A 2

a 11 + a 21 + a 31 = A 1

A length-M 1-D vector input is treated as an M-by-1 matrix. The output, y, is

always a scalar.

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

5-280
 Matrix 1-Norm

Supported Double-precision floating point

Data Types

See Also Normalization DSP Blockset

Reciprocal Condition DSP Blockset
norm MATLAB

5-281
Matrix Multiply

Purpose 5Matrix Multiply

Multiply input matrices.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix Multiply block multiplies n input matrices, A, B, C, ..., Un, in the
forward direction, where n is specified by the Number of input ports
parameter and Un is the input at the nth port.
Y = ((((A*B)*C)*D) ... Un) % Equivalent MATLAB code

All inputs must have sizes compatible for matrix multiplication; that is,
size(A,2) = size(B,1), size(B,2) = size(C,1), and so on. Inputs can be real,
complex, sample-based, or frame-based in any combination, but all inputs
must have the same precision, single or double. A length-M 1-D vector input at
any port is treated as an M-by-1 matrix.
The size of sample-based output Y is [size(A,1) size(Un,2)]. That is, Y is
MA-by-NUn.

Algorithm The Matrix Multiply block is optimized to use at most two temporary variables
for storage of intermediate results.

Dialog Box

Number of input ports

The number of inputs to the block.

Supported Single-precision floating point

Data Types Double-precision floating point

5-282
 Matrix Multiply

See Also Dot Product Simulink

Matrix Product DSP Blockset
Matrix Scaling DSP Blockset
Product Simulink

5-283
Matrix Product

Purpose 5Matrix Product

Multiply the elements of a matrix along rows or columns.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix Product block multiplies the elements of an M-by-N input matrix u
along either the rows or columns.
When the Multiply along parameter is set to Rows, the block multiplies across
the elements of each row and outputs the resulting M-by-1 matrix. A length-N
1-D vector input is treated as a 1-by-N matrix.

u 11 u 12 u 13 y1 ( u 11 u 12 u 13 )
u 21 u 22 u 23 y 2 = ( u 21 u 22 u 23 )
u 31 u 32 u 33 y3 ( u 31 u 32 u 33 )

This is equivalent to
y = prod(u,2) % Equivalent MATLAB code

When the Multiply along parameter is set to Columns, the block multiplies
down the elements of each column and outputs the resulting 1-by-N matrix. A
length-M 1-D vector input is treated as a M-by-1 matrix.

u 11 u 12 u 13
u 21 u 22 u 23
u 31 u 32 u 33

y1 y2 y3 = ( u 11 u 21 u 31 ) ( u 12 u 22 u 32 ) ( u 13 u 23 u 33 )

This is equivalent to
y = prod(u) % Equivalent MATLAB code

The output has the same frame status as the input.

5-284
 Matrix Product

Dialog Box

Multiply along
The dimension of the matrix along which to multiply, row or column.

Supported Double-precision floating point

Data Types

See Also Matrix Multiply DSP Blockset

Matrix Square DSP Blockset
Matrix Sum DSP Blockset
prod MATLAB

5-285
Matrix Scaling

Purpose 5Matrix Scaling

Scale the rows or columns of a matrix by a specified vector.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix Scaling block scales the rows or columns of the M-by-N input
matrix A by the values in input vector D.
When the Mode parameter is set to Scale Rows (D*A), input D can be a 1-D or
2-D vector of length M, and the block multiplies each element of D across the
corresponding row of matrix A.

d1 × a 11 a 12 a 13 d 1 a 11 d 1 a 12 d 1 a 13
d2 × a 21 a 22 a 23 d 2 a 21 d 2 a 22 d 2 a 23
d3 × a 31 a 32 a 33 d 3 a 31 d 3 a 32 d 3 a 33

This is equivalent to premultiplying A by a diagonal matrix with diagonal D.

y = diag(D)*A % Equivalent MATLAB code

When the Mode parameter is set to Scale Columns (A*D), input D can be a 1-D
or 2-D vector of length N, and the block multiplies each element of D across the
corresponding column of matrix A.

d1 d2 d3
× × × d 1 a 11 d 2 a 12 d 3 a 13
a 11 a 12 a 13 d 1 a 21 d 2 a 22 d 3 a 23
a 21 a 22 a 23 d 1 a 31 d 2 a 32 d 3 a 33
a 31 a 32 a 33

This is equivalent to postmultiplying A by a diagonal matrix with diagonal D.

y = A*diag(D) % Equivalent MATLAB code

The output is the same size as the input matrix, A. If both inputs are
sample-based, the output is sample-based; otherwise, the output is
frame-based.

5-286
 Matrix Scaling

Dialog Box

Mode
The mode of operation, row scaling or column scaling. Tunable.

Supported Single-precision floating point

Data Types Double-precision floating point

See Also Matrix Multiply DSP Blockset

Matrix Product DSP Blockset
Matrix Sum DSP Blockset

5-287
Matrix Square

Purpose 5Matrix Square

Compute the square of the input matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix Square block computes the square of an M-by-N input matrix, u, by
premultiplying with the Hermitian transpose.
y = u' * u % Equivalent MATLAB code

A length-M 1-D vector input is treated as an M-by-1 matrix. For both

sample-based and frame-based inputs, output y is sample-based with
dimension N-by-N.

Applications
The Matrix Square block is useful in a variety of applications:

• General matrix squares – The Matrix Square block computes the output
matrix, y, without explicitly forming u'. It is therefore more efficient than
other methods for computing the matrix square.
• Sum of squares – When the input is a column vector (N=1), the block’s
operation is equivalent to a multiply-accumulate (MAC) process, or inner
product. The output is the sum of the squares of the input, and is always a
real scalar.
• Correlation matrix – When the input is a row vector (M=1), the output, y, is
the symmetric autocorrelation matrix, or outer product.

Dialog Box

Supported Double-precision floating point

Data Types

5-288
 Matrix Square

See Also Matrix Multiply DSP Blockset

Matrix Product DSP Blockset
Matrix Sum DSP Blockset
Transpose DSP Blockset

5-289
Matrix Sum

Purpose 5Matrix Sum

Sum the elements of a matrix along rows or columns.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Matrix Sum block sums the elements of an M-by-N input matrix u along
either the rows or columns.
When the Sum along parameter is set to Rows, the block sums across the
elements of each row and outputs the resulting M-by-1 matrix. A length-N
1-D vector input is treated as a 1-by-N matrix.

u 11 u 12 u 13 y1 u 11 + u 12 + u 13
u 21 u 22 u 23 y 2 = u 21 + u 22 + u 23
u 31 u 32 u 33 y3 u 31 + u 32 + u 33

This is equivalent to
y = sum(u,2) % Equivalent MATLAB code

When the Sum along parameter is set to Columns, the block sums down the
elements of each column and outputs the resulting 1-by-N matrix. A length-M
1-D vector input is treated as a M-by-1 matrix.

u 11 u 12 u 13
u 21 u 22 u 23
u 31 u 32 u 33

3 3 3
y1 y2 y3 = ∑ ui1 ∑ ui2 ∑ ui3
i=1 i=1 i=1

This is equivalent to
y = sum(u) % Equivalent MATLAB code

The output has the same frame status as the input.

5-290
 Matrix Sum

Dialog Box

Sum along
The dimension of the matrix to sum along, row or column.

Supported Single-precision floating point

Data Types Double-precision floating point

See Also Matrix Product DSP Blockset

Matrix Multiply DSP Blockset
sum MATLAB

5-291
Matrix Viewer

Purpose 5Matrix Viewer

Display a matrix as a color image.

Library DSP Sinks

Description The Matrix Viewer block displays an M-by-N matrix input by mapping the
matrix element values to a specified range of colors. The display is updated as
each new input is received. (A length-M 1-D vector input is treated as an
M-by-1 matrix.)

Image Properties
Click on the Image properties check box to expose the image property
parameters, which control the colormap and display.
The mapping of matrix element values to colors is specified by the Colormap
matrix, Minimum input, and Maximum input parameters. For a colormap
with L colors, the colormap matrix has dimension L-by-3, with one row for each
color and one column for each element of the RGB triple that defines the color.
Examples of RGB triples are
[ 1 0 0 ] (red)
[ 0 0 1 ] (blue)
[0.8 0.8 0.8] (light gray)

See ColorSpec in the MATLAB documentation for complete information about

defining RGB triples.
MATLAB provides a number of functions for generating predefined colormaps,
such as hot, cool, bone, and autumn. Each of these functions accepts the
colormap size as an argument, and can be used in the Colormap matrix
parameter. For example, if you specify gray(128) for the Colormap matrix
parameter, the matrix is displayed in 128 shades of gray. The color in the first
row of the colormap matrix is used to represent the value specified by the
Minimum input parameter, and the color in the last row is used to represent
the value specified by the Maximum input parameter. Values between the
minimum and maximum are quantized and mapped to the intermediate rows
of the colormap matrix.
The documentation for MATLAB’s colormap function provides complete
information about specifying colormap matrices, and includes a complete list of
the available colormap functions.

5-292
 Matrix Viewer

Axis Properties
Click on the Axis properties check box to expose the axis property parameters,
which control labeling and positioning.
The Axis origin parameter determines where the first element of the input
matrix, U(1,1), is displayed. When Upper left corner is specified, the matrix
is displayed in matrix orientation, with U(1,1) in the upper-left corner.

U 11 U 12 U 13 U 14
U 21 U 22 U 23 U 24
U 31 U 32 U 33 U 34
U 41 U 42 U 43 U 44

When Lower left corner is specified, the matrix is flipped vertically to image
orientation, with U(1,1) in the lower-left corner.

U 41 U 42 U 43 U 44
U 31 U 32 U 33 U 34
U 21 U 22 U 23 U 24
U 11 U 12 U 13 U 14

Axis zoom, when selected, causes the image display to completely fill the figure
window. Menus and axis titles are not displayed. This option can also be
selected from the right-click pop-up menu in the figure window.
When Axis zoom is deselected, the axis labels and titles are displayed in a gray
border surrounding the image axes, and the window’s menus (including Axes)
and toolbar are visible. The Plot Editor tools allow you to annotate and
customize the image display. Select Help Plot Editor from the figure’s Help
menu for more information about using these tools. For information on printing
or saving the image, or on the other options found in the generic figure menus
(File, Edit, Window, Help), see the MATLAB documentation.

Figure Window
The image title (in the figure title bar) is the same as the block title. The axis
tick marks reflect the size of the input matrix; the x-axis is numbered from

5-293
Matrix Viewer

1 to N (number of columns), and the y-axis is numbered from 1 to M (number

of rows).
In addition to the standard MATLAB figure window menus (File, Edit,
Window, Help), the Matrix Viewer window has an Axes menu containing the
following items:

• Refresh erases all data on the scope display, except for the most recent
image.
• Autoscale recomputes the Minimum input and Maximum input parameter
values to best fit the range of values observed in a series of 10 consecutive
inputs. The numerical limits selected by the autoscale feature are shown in
the Minimum input and Maximum input parameters, where you can make
further adjustments to them manually.
• Axis zoom, when selected, causes the image to completely fill the containing
figure window. Menus and axis titles are not displayed. When Axis zoom is
deselected, the axis labels and titles are displayed in a gray border
surrounding the scope axes, and the window’s menus (including Axes) and
toolbar are visible. This option can also be set in the Axis properties panel
of the parameter dialog box.
• Colorbar, when selected, displays a bar with the specified colormap to the
right of the image axes.
• Save Position automatically updates the Figure position parameter in the
Axis properties field to reflect the figure window’s current position and size
on the screen. To make the scope window open at a particular location on the
screen when the simulation runs, simply drag the window to the desired
location, resize it as needed, and select Save Position. Note that the
parameter dialog box must be closed when you select Save Position in order
for the Figure position parameter to be updated.

Many of these options can also be accessed by right-clicking with the mouse
anywhere on the displayed image. The right-click menu is very helpful when
the scope is in zoomed mode and the Axes menu is not visible.

Examples See the demo dspstfft.mdl for an example of using the Matrix Viewer block
to create a moving spectrogram (time-frequency plot) of a speech signal by
updating just one column of the input matrix at each sample time.

5-294
 Matrix Viewer

Dialog Box

Image properties
Select to expose the image property parameters. Tunable.
Colormap matrix
A 3-column matrix defining the colormap as a set of RGB triples, or a call
to a colormap-generating function such as hot or spring. See the
ColorSpec property for complete information about defining RGB triples,
and the colormap function for a list of colormap-generating functions.
Tunable.
Minimum input value
The input value to be mapped to the color defined in the first row of the
colormap matrix. Select Autoscale from the right-click pop-up menu to set
this parameter to the minimum value observed in a series of 10 consecutive
matrix inputs. Tunable.

5-295
Matrix Viewer

Maximum input value

The input value to be mapped to the color defined in the last row of the
colormap matrix. Select Autoscale from the right-click pop-up menu to set
this parameter to the maximum value observed in a series of 10
consecutive matrix inputs. Tunable.
Display colorbar
Select to display a bar with the selected colormap to the right of the image
axes. Tunable.
Axis properties
Select to expose the axis property parameters. Tunable.
Axis origin
The position within the axes where the first element of the input matrix,
U(1,1), is plotted; bottom left or top left. Tunable.

X-axis title
The text to be displayed below the x-axis. Tunable.
Y-axis title
The text to be displayed to the left of the y-axis. Tunable.
Colorbar title
The text to be displayed to the right of the color bar, if Display colorbar is
currently selected. Tunable.
Figure position
A 4-element vector of the form [left bottom width height] specifying
the position of the figure window, where (0,0) is the lower-left corner of
the display. Tunable.
Axis zoom
Resizes the image to fill the figure window. Tunable.

5-296
 Matrix Viewer

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Spectrum Scope DSP Blockset

Vector Scope DSP Blockset
colormap MATLAB
ColorSpec MATLAB
image MATLAB

See “Viewing Signals” on page 3-80 for related information.

5-297
Maximum

Purpose 5Maximum
Find the maximum values in an input or sequence of inputs.

Library Statistics

Description The Maximum block identifies the value and position of the largest element in
each column of the input, or tracks the maximum values in a sequence of inputs
over a period of time. The Mode parameter specifies the block’s mode of
operation and can be set to Value, Index, Value and Index, or Running.

Value Mode
When Mode is set to Value, the block computes the maximum value in each
column of the M-by-N input matrix u independently at each sample time.
val = max(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, val, is a 1-by-N vector containing the
maximum value of each column in u. For complex inputs, the block selects the
value in each column that has the maximum magnitude, max(abs(u)), as
shown below.
Complex
abs(u) Output (val)

4 + 2i 4.47
–3–i 3.16
4 + 4i 5.66 4 + 4i
–1 + 4 i 4.12
–4–i 4.12

The frame status of the output is the same as that of the input.

Index Mode
When Mode is set to Index, the block computes the maximum value in each
column of the M-by-N input matrix u,
[val,idx] = max(u) % Equivalent MATLAB code

5-298
 Maximum

and outputs the sample-based 1-by-N index vector, idx. Each value in idx is an
integer in the range [1 M] indexing the maximum value in the corresponding
column of u.
As in Value mode, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
If a maximum value occurs more than once in a particular column of u, the
computed index corresponds to the first occurrence. For example, if the input
is the column vector [3 2 1 2 3]', the computed index of the maximum value
is 1 rather than 5.

Value and Index Mode

When Mode is set to Value and Index, the block outputs both the vector of
minima, val, and the vector of indices, idx.

Running Mode
When Mode is set to Running, the block tracks the maximum value of each
channel in a time-sequence of M-by-N inputs. For sample-based inputs, the
output is a sample-based M-by-N matrix with each element yij containing the
maximum value observed in element uij for all inputs since the last reset. For
frame-based inputs, the output is a frame-based M-by-N matrix with each
element yij containing the maximum value observed in the jth column of all
inputs since the last reset, up to and including element uij of the current input.
The block resets the running maximum whenever a reset event is detected at
the optional Rst port. The reset event is specified by the Reset port menu, and
can be one of the following:

• Rising edge triggers a reset operation when the Rst input rises from a
negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers a reset operation when the Rst input falls from a
positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers a reset operation when either a rising or falling edge
(as described above) occurs.
• Non-zero sample triggers a reset operation at each sample time that the Rst
input is not zero.

5-299
Maximum

For sample-based inputs, a reset event causes the running maximum for each
channel to be initialized to the value in the corresponding channel of the
current input. For frame-based inputs, a reset event causes the running
maximum for each channel to be initialized to the earliest value in each
channel of the current input. The Rst port can be disabled by selecting None
from the Reset port menu.
As in the other modes, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.

Example The Maximum block in the model below calculates the running maximum of a
frame-based 3-by-2 (two-channel) matrix input, u. The running maximum is
reset at t=2 by an impulse to the block’s Rst port.

The Maximum block has the following settings:

• Mode = Running
• Reset port = Non-zero signal

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

5-300
 Maximum

The block’s operation is shown in the figure below.

In Rst Output

ch1 ch2 ch1 ch2

61 61
First
13 t=0 0 First output 63
input 39 69

–7 2 69
2 4 t=1 0 69
5 1 69

8 6 86
Simulation time

0 2 t=2 1 86 Reset
–1 5 86

–3 0 8 6
2 4 t=3 0 8 6
1 17 8 17

The statsdem demo illustrates the operation of several blocks from the
Statistics library.

Dialog Box

Mode
The block’s mode of operation: Output the maximum value of each input
(Value), the index of the maximum value (Index), both the value and the

5-301
Maximum

index (Value and index), or track the maximum value of the input
sequence over time (Running).
Reset port
Specifies the reset event detected at the Rst input port when Running is
selected as the Mode parameter. The reset operation can be set to occur
when a rising and/or falling edge is detected at the Rst port, (Rising edge,
Falling edge, Either Edge), or when a non-zero sample is detected at the
Rst port (Non-zero sample). The Rst port can be disabled by selecting
None.

Supported Double-precision floating point

Data Types

See Also Mean DSP Blockset

Minimum DSP Blockset
MinMax Simulink
max MATLAB

5-302
 Mean

Purpose 5Mean
Find the mean value of an input or sequence of inputs.

Library Statistics

Description The Mean block computes the mean of each column in the input, or tracks the
mean values in a sequence of inputs over a period of time. The Running mean
parameter selects between basic operation and running operation.

Basic Operation
When the Running mean check box is not selected, the block computes the
mean of each column of M-by-N input matrix u independently at each sample
time.
y = mean(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, y, is a 1-by-N vector containing the mean
value for each column in u. The mean of a complex input is computed
independently for the real and imaginary components, as shown below.
Complex
input (u)

4 + 2i Output (y)
–3 – i
4 + 4i 0 + 1.6i
–1 + 4 i
–4–i

The frame status of the output is the same as that of the input.

Running Operation
When the Running mean check box is selected, the block tracks the mean
value of each channel in a time-sequence of M-by-N inputs. For sample-based
inputs, the output is a sample-based M-by-N matrix with each element yij
containing the mean value of element uij over all inputs since the last reset. For
frame-based inputs, the output is a frame-based M-by-N matrix with each

5-303
Mean

element yij containing the mean value of the jth column over all inputs since
the last reset, up to and including element uij of the current input.
If the Reset port parameter is set to Non-zero sample, the optional Rst port
is enabled and the block resets the running mean when the scalar input at the
Rst port is nonzero. (The Rst port can be disabled by setting the Reset port
parameter to None.) For sample-based inputs, the running mean for each
channel is initialized to the value in the corresponding channel of the current
input. For frame-based inputs, the running mean for each channel is initialized
to the earliest value in each channel of the current input.
As in basic operation, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.

Example The Mean block in the model below calculates the running mean of a
frame-based 3-by-2 (two-channel) matrix input, u. The running mean is reset
at t=2 by an impulse to the block’s Rst port.

The Mean block has the following settings:

• Running mean =
• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'

5-304
 Mean

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

The block’s operation is shown in the figure below.

In Rst Output

ch1 ch2 ch1 ch2

61 6.00 1.00
First First output
13 t=0 0 3.50 2.00
input 39 3.33 4.33

–7 2 0.75 3.75
2 4 t=1 0 1.00 3.80
5 1 1.67 3.33

8 6 8.00 6.00
Simulation time

0 2 t=2 1 Reset 4.00 4.00

–1 5 2.33 4.33

–3 0 1.00 3.25
2 4 t=3 0 1.20 3.40
1 17 1.17 5.67

The statsdem demo illustrates the operation of several blocks from the
Statistics library.

Dialog Box

5-305
Mean

Running mean
Enables running operation when selected.
Reset port
Enables the Rst input port when set to Non-zero sample, and disables the
Rst input port when set to None.

Supported Double-precision floating point

Data Types

See Also Maximum DSP Blockset

Median DSP Blockset
Minimum DSP Blockset
Standard Deviation DSP Blockset
mean MATLAB

5-306
 Median

Purpose 5Median
Find the median value of an input.

Library Statistics

Description The Median block computes the median value of each column in an M-by-N
input matrix.
y = median(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, y, is a sample-based 1-by-N vector containing
the median value for each column in u.
When M is odd, the block sorts the column elements by value, and outputs the
central row of the sorted matrix.
s = sort(u);
y = s((M+1)/2,:)

When M is even, the block sorts the column elements by value, and outputs the
average of the two central rows in the sorted matrix.
s = sort(u);
y = mean([s(M/2,:);s(M/2+1,:)])

Complex inputs are sorted by magnitude, and the real and imaginary
components are averaged independently (for even M).

Dialog Box

Supported Double-precision floating point

Data Types

5-307
Median

See Also Maximum DSP Blockset

Mean DSP Blockset
Minimum DSP Blockset
Sort DSP Blockset
Standard Deviation DSP Blockset
Variance DSP Blockset
median MATLAB

5-308
 Minimum

Purpose 5Minimum
Find the minimum values in an input or sequence of inputs.

Library Statistics

Description The Minimum block identifies the value and position of the smallest element
in each column of the input, or tracks the minimum values in a sequence of
inputs over a period of time. The Mode parameter specifies the block’s mode of
operation, and can be set to Value, Index, Value and Index, or Running.

Value Mode
When Mode is set to Value, the block computes the minimum value in each
column of the M-by-N input matrix u independently at each sample time.
val = min(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, val, is a 1-by-N vector containing the
minimum value of each column in u. For complex inputs, the block selects the
value in each column that has the minimum magnitude, min(abs(u)), as
shown below.
Complex
Input (u) abs(u) Output (val)

4 + 2i 4.47
–3–i 3.16
4 + 4i 5.65 –3–i
– 1 + 4i 4.12
–4–i 4.12

The frame status of the output is the same as that of the input.

Index Mode
When Mode is set to Index, the block computes the minimum value in each
column of the M-by-N input matrix u,
[val,idx] = min(u) % Equivalent MATLAB code

5-309
Minimum

and outputs the sample-based 1-by-N index vector, idx. Each value in idx is an
integer in the range [1 M] indexing the minimum value in the corresponding
column of u.
As in Value mode, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
If a minimum value occurs more than once in a particular column of u, the
computed index corresponds to the first occurrence. For example, if the input
is the column vector [-1 2 3 2 -1]', the computed index of the minimum
value is 1 rather than 5.

Value and Index Mode

When Mode is set to Value and Index, the block outputs both the vector of
minima, val, and the vector of indices, idx.

Running Mode
When Mode is set to Running, the block tracks the minimum value of each
channel in a time-sequence of M-by-N inputs. For sample-based inputs, the
output is a sample-based M-by-N matrix with each element yij containing the
minimum value observed in element uij for all inputs since the last reset. For
frame-based inputs, the output is a frame-based M-by-N matrix with each
element yij containing the minimum value observed in the jth column of all
inputs since the last reset, up to and including element uij of the current input.
If the Reset port parameter is set to Non-zero sample, the optional Rst port
is enabled and the block resets the running minimum when the scalar input at
the Rst port is nonzero. (The Rst port can be disabled by setting the Reset port
parameter to None.) For sample-based inputs, the running minimum for each
channel is initialized to the value in the corresponding channel of the current
input. For frame-based inputs, the running minimum for each channel is
initialized to the earliest value in each channel of the current input.
As in the other modes, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.

Example The Minimum block in the model below calculates the running minimum of a
frame-based 3-by-2 (two-channel) matrix input. The running minimum is reset
at t=2 by an impulse to the block’s Rst port.

5-310
 Minimum

The Minimum block has the following settings:

• Mode = Running
• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 2 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

The block’s operation is shown in the figure below.

5-311
Minimum

In Rst Output

ch1 ch2 ch1 ch2

61 61
First
13 t=0 0 First output 11
input 39 11

–7 2 –7 1
2 4 t=1 0 –7 1
5 2 –7 1

8 6 8 6
Simulation time

0 2 t=2 1 0 2 Reset
–1 5 –1 2

–3 0 –3 0
2 4 t=3 0 –3 0
1 17 –3 0

Dialog Box

Mode
The block’s mode of operation: Output the minimum value of each input
(Value), the index of the minimum value (Index), both the value and the
index (Value and Index), or track the minimum values in the input
sequence over time (Running).
Reset port
Enables the Rst input port when set to Non-zero sample, and disables the
Rst input port when set to None.

5-312
 Minimum

Supported Double-precision floating point

Data Types

See Also Maximum DSP Blockset

Mean DSP Blockset
MinMax Simulink
Histogram DSP Blockset
min MATLAB

5-313
Modified Covariance AR Estimator

Purpose 5Modified Covariance AR Estimator

Compute an estimate of AR model parameters using the modified covariance
method.

Library Estimation / Parametric Estimation

Description The Modified Covariance AR Estimator block uses the modified covariance
method to fit an autoregressive (AR) model to the input data. This method
minimizes the forward and backward prediction errors in the least-squares
sense. The input is a frame of consecutive time samples, which is assumed to
be the output of an AR system driven by white noise. The block computes the
normalized estimate of the AR system parameters, A(z), independently for each
successive input.

G G
H ( z ) = ------------ = -------------------------------------------------------------------------------
A(z) –1
1 + a ( 2 )z + … + a ( p + 1 )z
–p

The order, p, of the all-pole model is specified by the Order parameter.

The top output, A, contains the normalized estimate of the AR model
coefficients in descending powers of z,
[1 a(2) ... a(p+1)]

The scalar gain, G, is provided at the bottom output (G).

Dialog Box

Estimation order
The order of the AR model, p.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.

5-314
 Modified Covariance AR Estimator

Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood

Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

See Also Burg AR Estimator DSP Blockset

Covariance AR Estimator DSP Blockset
Modified Covariance Method DSP Blockset
Yule-Walker AR Estimator DSP Blockset
armcov Signal Processing Toolbox

5-315
Modified Covariance Method

Purpose 5Modified Covariance Method

Compute a parametric spectral estimate using the modified covariance
method.

Library Estimation / Power Spectrum Estimation

Description The Modified Covariance Method block estimates the power spectral density
(PSD) of the input using the modified covariance method. This method fits an
autoregressive (AR) model to the signal by minimizing the forward and
backward prediction errors in the least-squares sense. The order of the all-pole
model is the value specified by the Estimation order parameter, and the
spectrum is computed from the FFT of the estimated AR model parameters.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal. The block’s output (a column vector) is the estimate of
the signal’s power spectral density at Nfft equally spaced frequency points in
the range [0,Fs), where Fs is the signal’s sample frequency.
When Inherit FFT length from input dimensions is selected, Nfft is specified
by the frame size of the input, which must be a power of 2. When Inherit FFT
length from input dimensions is not selected, Nfft is specified as a power of 2
by the FFT length parameter, and the block zero pads or truncates the input
to Nfft before computing the FFT. The output is always sample-based.
See the Burg Method block reference for a comparison of the Burg Method,
Covariance Method, Modified Covariance Method, and Yule-Walker Method
blocks.

Examples The dspsacomp demo compares the modified covariance method with several
other spectral estimation methods.

5-316
 Modified Covariance Method

Dialog Box

Estimation order
The order of the AR model.
Inherit FFT length from input dimensions
When selected, uses the input frame size as the number of data points, Nfft,
on which to perform the FFT. Tunable.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft
exceeds the input frame size, the frame is zero-padded as needed. This
parameter is enabled when Inherit FFT length from input dimensions is
not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

See Also Burg Method DSP Blockset

Covariance Method DSP Blockset
Modified Covariance AR Estimator DSP Blockset
Short-Time FFT DSP Blockset
Yule-Walker Method DSP Blockset
pmcov Signal Processing Toolbox

5-317
Modified Covariance Method

See “Power Spectrum Estimation” on page 4-15 for related information.

5-318
 Multiphase Clock

Purpose 5Multiphase Clock

Generate multiple binary clock signals.

Library Signal Management / Switches and Counters

Description The Multiphase Clock block generates a sample-based 1-by-N vector of clock
signals, where the integer N is specified by the Number of phases parameter.
Each of the N phases has the same frequency, f, specified in hertz by the Clock
frequency parameter.

The clock signal indexed by the Starting phase parameter is the first to
become active, at t=0. The other signals in the output vector become active in
turn, each one lagging the preceding signal’s activation by 1/(N∗f) seconds, the
phase interval. The period of the sample-based output is therefore 1/(N∗f)
seconds.
The active level can be either high (1) or low (0), as specified by the Active level
(polarity) parameter. The duration of the active level, D, is set by the Number
of phase intervals over which the clock is active. This value, which can be
an integer value between 1 and N-1, specifies the number of phase intervals
that each signal should remain in the active state after becoming active. The
active duty cycle of the signal is D/N.

Example Configure the Multiphase Clock block in the model below to generate a 100 Hz
five-phase output in which the third signal is first to become active. Use a high
active level with a duration of one interval.

The corresponding settings are as follows:

• Clock frequency = 100

• Number of phases = 5
• Starting phase = 3
• Number of phase intervals over which the clock is active = 1
• Active level (polarity) = High (1)

5-319
Multiphase Clock

The Scope window below shows the Multiphase Clock block’s output for these
settings. Note that the first active level appears at t=0 on y(3), the second
active level appears at t=0.002 on y(4), the third active level appears at
t=0.004 on y(5), the fourth active level appears at t=0.006 on y(1), and the
fifth active level appears at t=0.008 on y(2). Each signal becomes active
1/(5∗100) seconds after the previous signal.

Signal 1

Signal 2

Signal 3

Signal 4

Signal 5

To experiment further, try changing the Number of phase intervals over

which clock is active setting to 3 so that the active-level duration is three
phase intervals (60% duty cycle).

5-320
 Multiphase Clock

Dialog Box

Clock frequency
The frequency of all output clock signals.
Number of phases
The number of different phases, N, in the output vector.
Starting phase
The vector index of the output signal to first become active. Tunable.
Number of phase intervals over which clock is active
The duration of the active level for every output signal. Tunable.
Active level
The active level, high (1) or low (0). Tunable.

Supported Double-precision floating point

Data Types

See Also Clock Simulink

Counter DSP Blockset
Pulse Generator Simulink
Event-Count Comparator DSP Blockset

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-321
Multiport Selector

Purpose 5Multiport Selector

Distribute arbitrary subsets of input rows or columns to multiple output ports.

Library Signal Management / Indexing

Description The Multi-port Selector block extracts multiple subsets of rows or columns
from M-by-N input matrix u, and propagates each new submatrix to a distinct
output port. A length-M 1-D vector input is treated as an M-by-1 matrix.
The Indices to output parameter is a cell array whose kth cell contains a
one-dimensional indexing expression specifying the subset of input rows or
columns to be propagated to the kth output port. The total number of cells in
the array determines the number of output ports on the block.
When the Select parameter is set to Rows, the specified one-dimensional
indices are used to select matrix rows, and all elements on the chosen rows are
included. When the Select parameter is set to Columns, the specified
one-dimensional indices are used to select matrix columns, and all elements on
the chosen columns are included. A given input row or column can appear any
number of times in any of the outputs, or not at all.
The Indices to output parameter is tunable, so you can change the values of
the indices at any time during the simulation; however, the number of cells in
the array (i.e., the number of output ports) and the size of each submatrix in
the output must remain the same while the simulation is running.
When an index references a nonexistent row or column of the input, the block
reacts with the behavior specified by the Invalid index parameter. The
following options are available:

• Clip index – Clip the index to the nearest valid value, and do not issue an
alert.
Example: For a 64-by-4 input with Select = Rows, an index of 72 is clipped
to 64; with Select = Columns, an index of 72 is clipped to 4. In both cases, an
index of -2 is clipped to 1.
• Clip and warn – Display a warning message in the MATLAB command
window, and clip as above.
• Generate error – Display an error dialog box and terminate the simulation.

5-322
 Multiport Selector

Example Consider the following Indices to output cell array:

{4,[1:2 5],[7;8],10:-1:6}

This is a four-cell array, which requires the block to generate four independent
outputs (each at a distinct port). The table below shows the dimensions of these
outputs when Select = Rows and the input dimension is M-by-N.

Cell Expression Description Output size

1 4 Row 4 of input 1-by-N

2 [1:2 5] Rows 1, 2, and 5 of input 3-by-N

3 [7;8] Rows 7 and 8 of input 2-by-N

4 10:-1:6 Rows 10, 9, 8, 7, and 6 of input 5-by-N

Dialog Box

Select
The dimension of the input to select, Rows or Columns.
Indices to output
A cell array specifying the row- or column-subsets to propagate to each of
the output ports. The number of cells in the array determines the number
of output ports on the block. This parameter is tunable, but the size of the
cell array (i.e., the number of output ports) and the size of each submatrix
in the output must remain the same while the simulation is running.

5-323
Multiport Selector

Invalid index
Response to an invalid index value. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Permute Matrix DSP Blockset

Selector Simulink
Submatrix DSP Blockset
Variable Selector DSP Blockset

5-324
 N-Sample Enable

Purpose 5N-Sample Enable

Output ones or zeros for a specified number of sample times.

Library DSP Sources,

Signal Management / Switches and Counters

Description The N-Sample Enable block outputs the inactive value (0 or 1, whichever is not
selected in the Active level parameter) during the first N sample times, where
N is the Trigger count value. Beginning with output sample N+1, the block
outputs the active value (1 or 0, whichever is selected in the Active level
parameter) until a reset event occurs or the simulation terminates.
The Reset input check box enables the Rst input port. At any time during the
count, a trigger event at the input port resets the counter to its initial state.
The triggering event is specified by the Trigger type pop-up menu, and can be
one of the following:

• Rising edge triggers the reset when the trigger input rises from a negative
value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers the reset when the trigger input falls from a positive
value to zero or a negative value, or from zero to a negative value.
• Either edge triggers the reset when either a rising or falling edge (as
described above) occurs.

The output is always sample-based.

Dialog Box

5-325
N-Sample Enable

Trigger count
The number of samples for which the block outputs the active value.
Tunable.
Active level
The value to output after the first N sample times, 0 or 1. Tunable.
Reset input
Enables the Rst input port.
Trigger type
The type of event that triggers a reset when the Rst port is enabled.
Tunable.
Sample time
The sample period, Ts, for the block’s counter. The block switches from the
active value to the inactive value at t=Ts∗(N+1).

Supported Double-precision floating point

Data Types

See Also Counter DSP Blockset

N-Sample Switch DSP Blockset

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-326
 N-Sample Switch

Purpose 5N-Sample Switch

Switch between two inputs after a specified number of sample periods.

Library Signal Management / Switches and Counters

Description The N-Sample Switch block outputs the signal connected to the top input port
during the first N sample times after the simulation begins or the block is reset,
where N is specified by the Switch count value. Beginning with output sample
N+1, the block outputs the signal connected to the bottom input until the next
reset event or the end of the simulation.
The sample period of the output is specified by the Sample time parameter
(i.e., the output sample period is not inherited from the sample period of either
input). The block applies a zero-order hold at the input ports, so the value the
block reads from a given port between input sample times is the value of the
most recent input to that port.
Both inputs must have the same dimension, except in the following two cases:

• When one input is a scalar, the block expands the scalar input to match the
size of the other input.
• When one input is a 1-D vector and the other input is a row or column vector
with the same number of elements, the block reshapes the 1-D vector to
match the dimension of the other input.

The inputs must either both be frame-based or both be sample-based.

The Reset input check box enables the Rst input port. At any time during the
count, a trigger event at the Rst port resets the counter to zero. The triggering
event is specified by the Trigger type pop-up menu, and can be one of the
following:

• Rising edge triggers the reset when the trigger input rises from a negative
value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers the reset when the trigger input falls from a positive
value to zero or a negative value, or from zero to a negative value.
• Either edge triggers the reset when either a rising or falling edge (as
described above) occurs.

5-327
N-Sample Switch

Dialog Box

Switch count
The number of sample periods, N, for which the output is connected to the
top input before switching to the bottom input. Tunable.
Reset input
Enables the Rst input port when selected.
Trigger type
The type of event at the Rst port that resets the block’s counter. This
parameter is enabled when Reset input is selected. Tunable.
Sample time
The sample period, Ts, for the block’s counter. The block switches inputs at
t=Ts∗(N+1).

Supported Double-precision floating point

Data Types

See Also Counter DSP Blockset

N-Sample Enable DSP Blockset

5-328
 Normalization

Purpose 5Normalization
Normalize an input by its 2-norm or squared 2-norm.

Library Math Functions / Math Operations

Description The Normalization block independently normalizes each column of the M-by-N
matrix input, u.

2-Norm
When the Norm parameter specifies 2-norm, the block normalizes the jth
input column as follows.

u ij
y ij = ---------------------
u j+b

where b is specified by the Normalization bias parameter, and u j is the

2-norm (or Euclidean norm) of the jth input column.

2 2 2
u j = u1 + u2 + L + uM

Equivalently,
y = u ./ (norm(u) + b) % Equivalent MATLAB code

The normalization bias, b, is typically chosen to be a small positive constant

(e.g., 1e-10) that prevents potential division by zero.

Squared 2-Norm
When the Norm parameter specifies Squared 2-norm, the block normalizes
the jth input column as follows.

u ij
y ij = ----------------------
2
u j +b

where
2 2 2 2
u j = u1 + u2 + L + uM

Equivalently,
y = u ./ (norm(u).^2 + b) % Equivalent MATLAB code

5-329
Normalization

The output has the same dimension and frame status as the input. For
convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors, and the output retains
the dimensions of the input.

Dialog Box

Norm
The type of normalization to apply, 2-norm or Squared 2-norm. Tunable.
Normalization bias
The value b to be added in the denominator to avoid division by zero.
Tunable.

Supported Double-precision floating point

Data Types

See Also Matrix Scaling DSP Blockset

Reciprocal Condition DSP Blockset
norm MATLAB

5-330
 Overlap-Add FFT Filter

Purpose 5Overlap-Add FFT Filter

Implement the overlap-add method of frequency-domain filtering.

Library Filtering / Filter Designs

Description The Overlap-Add FFT Filter block uses an FFT to implement the overlap-add
method, a technique that combines successive frequency-domain filtered
sections of an input sequence.
Valid inputs to this block are 1-D vectors, sample-based vectors, frame-based
vectors, and frame-based full matrices. All outputs are unbuffered into
sample-based row vectors. The length of the output vector is equal to the
number of channels in the input vector. An M-by-1 sample-based input has M
channels, so it would result in a length-M sample-based output vector. An
M-by-1 frame-based input has only one channel, so would result in a 1-by-1
(scalar) output.
The block’s data output rate is M times faster than its data input rate, where
M is the input frame-size. Thus, the block’s data input and output rates are the
same when the inputs are 1-D vectors, sample-based vectors, or frame-based
row vectors. For frame-based column and frame-based full-matrix inputs, the
block’s data output rate is M times greater than the block’s data input rate.
1-D vectors are treated as length-N sample-based vectors, and result in
sample-based length-N row vectors.
The block breaks the scalar input sequence u, of length nu, into length-L
nonoverlapping data sections,

u . . .
L 2L 3L ceil(nu/L)*L

which it linearly convolves with the filter’s FIR coefficients,

–1 –n
H ( z ) = B ( z ) = b1 + b2 z + … + bn + 1 z

The numerator coefficients for H(z) are specified as a vector by the FIR
coefficients parameter. The coefficient vector, b = [b(1) b(2) ... b(n+1)],
can be generated by one of the filter design functions in the Signal Processing
Toolbox, such as fir1. All filter states are internally initialized to zero.

5-331
Overlap-Add FFT Filter

If either the filter coefficients or the inputs to the block are complex, the
Output parameter should be set to Complex. Otherwise, the default Output
setting, Real, instructs the block to take only the real part of the solution.
The block’s overlap-add operation is equivalent to
y = ifft(fft(u(i:i+L-1),nfft) .* fft(b,nfft))

where nfft is specified by the FFT size parameter as a power-of-two value

greater (typically much greater) than n+1. Values for FFT size that are not
powers of two are rounded upwards to the nearest power-of-two value to obtain
nfft.

The block overlaps successive output sections by n points and sums them.

L L+n

2L 2L+n

3L 3L+n
. . .

The first L samples of each summation are output in sequence. The block
chooses the parameter L based on the filter order and the FFT size.
L = nfft - n

Latency
In single-tasking operation, the Overlap-Add FFT Filter block has a latency of
nfft-n+1 samples. The first nfft-n+1 consecutive outputs from the block are
zero; the first filtered input value appears at the output as sample nfft-n+2.
In multitasking operation, the Overlap-Add FFT Filter block has a latency of
2*(nfft-n+1) samples. The first 2*(nfft-n+1) consecutive outputs from the
block are zero; the first filtered input value appears at the output as sample
2*(nfft-n)+3.

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

5-332
 Overlap-Add FFT Filter

Dialog Box

FFT size
The size of the FFT, which should be a power-of-two value greater than the
length of the specified FIR filter.
FIR coefficients
The filter numerator coefficients.
Output
The complexity of the output; Real or Complex. If the input signal or the
filter coefficients are complex, this should be set to Complex.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

See Also Direct-Form II Transpose Filter DSP Blockset

Overlap-Save FFT Filter DSP Blockset

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-333
Overlap-Save FFT Filter

Purpose 5Overlap-Save FFT Filter

Implement the overlap-save method of frequency-domain filtering.

Library Filtering / Filter Designs

Description The Overlap-Save FFT Filter block uses an FFT to implement the overlap-save
method, a technique that combines successive frequency-domain filtered
sections of an input sequence.
Valid inputs to this block are 1-D vectors, sample-based vectors, frame-based
vectors, and frame-based full matrices. All outputs are unbuffered into
sample-based row vectors. The length of the output vector is equal to the
number of channels in the input vector. An M-by-1 sample-based input has M
channels, so it would result in a length-M sample-based output vector. An
M-by-1 frame-based input has only one channel, so would result in a 1-by-1
(scalar) output.
The block’s data output rate is M times faster than its data input rate, where
M is the input frame-size. Thus, the block’s data input and output rates are the
same when the inputs are 1-D vectors, sample-based vectors, or frame-based
row vectors. For frame-based column and frame-based full-matrix inputs, the
block’s data output rate is M times greater than the block’s data input rate.
1-D vectors are treated as length-N sample-based vectors, and result in
sample-based length-N row vectors.
Overlapping sections of input u are circularly convolved with the FIR filter
coefficients
–1 –n
H ( z ) = B ( z ) = b1 + b2 z + … + bn + 1 z

The numerator coefficients for H(z) are specified as a vector by the FIR
coefficients parameter. The coefficient vector, b = [b(1) b(2) ... b(n+1)],
can be generated by one of the filter design functions in the Signal Processing
Toolbox, such as fir1. All filter states are internally initialized to zero.
If either the filter coefficients or the inputs to the block are complex, the
Output parameter should be set to Complex. Otherwise, the default Output
setting, Real, instructs the block to take only the real part of the solution.

5-334
 Overlap-Save FFT Filter

The circular convolution of each section is computed by multiplying the FFTs

of the input section and filter coefficients, and computing the inverse FFT of
the product.
y = ifft(fft(u(i:i+(L-1)),nfft) .* fft(b,nfft))

where nfft is specified by the FFT size parameter as a power-of-two value

greater (typically much greater) than n+1. Values for FFT size that are not
powers of two are rounded upwards to the nearest power-of-two value to obtain
nfft.

The first n points of the circular convolution are invalid and are discarded. The
Overlap-Save FFT Filter block outputs the remaining nfft-n points, which are
equivalent to the linear convolution.

Latency
In single-tasking operation, the Overlap-Save FFT Filter block has a latency of
nfft-n+1 samples. The first nfft-n+1 consecutive outputs from the block are
zero; the first filtered input value appears at the output as sample nfft-n+2.
In multitasking operation, the Overlap-Save FFT Filter block has a latency of
2*(nfft-n+1) samples. The first 2*(nfft-n+1) consecutive outputs from the
block are zero; the first filtered input value appears at the output as sample
2*(nfft-n)+3.

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

5-335
Overlap-Save FFT Filter

FFT size
The size of the FFT, which should be a power-of-two value greater than the
length of the specified FIR filter.
FIR coefficients
The filter numerator coefficients.
Output
The complexity of the output; Real or Complex. If the input signal or the
filter coefficients are complex, this should be set to Complex.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

See Also Direct-Form II Transpose Filter DSP Blockset

Overlap-Add FFT Filter DSP Blockset

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-336
 Pad

Purpose 5Pad
Alter the input size by padding or truncating rows and/or columns.

Library Signal Operations

Description The Pad block changes the size of the input matrix from Mi-by-Ni to Mo-by-No
by padding or truncating along the rows, the columns, or both dimensions. The
dimensions of the output, Mo and No, are specified by the Number of output
rows and Number of output columns parameters, respectively. The value
with which to pad the input is set by the Value parameter.
The behavior of the Pad block and Zero Pad block are identical, with the
exception that the Pad block can pad the input matrix with values other than
zero. See the Zero Pad block reference for more information on the behavior of
the Pad block.

Dialog Box

Value
The scalar value with which to pad the input matrix. Tunable.
Pad along
The direction along which to pad or truncate. Columns specifies that the
row dimension should be changed to Mo. Rows specifies that the column
dimension should be changed to No. Columns and rows specifies that both
column and row dimensions should be changed. None disables padding and
truncation and passes the input through to the output unchanged.

5-337
Pad

Number of output rows

The desired number of rows in the output, Mo. This parameter is enabled
when Columns or Columns and rows is selected in the Pad along menu.
Number of output columns
The desired number of columns in the output, No. This parameter is
enabled when Rows or Columns and rows is selected in the Pad along
menu.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Matrix Concatenation Simulink

Repeat DSP Blockset
Submatrix DSP Blockset
Upsample DSP Blockset
Variable Selector DSP Blockset
Zero Pad DSP Blockset

5-338
 Permute Matrix

Purpose 5Permute Matrix

Reorder the rows or columns of a matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Permute Matrix block reorders the rows or columns of M-by-N input
matrix A as specified by indexing input P.
When the Permute parameter is set to Rows, the block uses the rows of A to
create a new matrix with the same column dimension. Input P is a length-L
vector whose elements determine where each row from A should be placed in
the L-by-N output matrix.
% Equivalent MATLAB code
y = [A(P(1),:) ; A(P(2),:) ; A(P(3),:) ; ... ; A(P(end),:)]

For row permutation, a length-M 1-D vector input at the A port is treated as a
M-by-1 matrix.
When the Permute parameter is set to Columns, the block uses the columns
of A to create a new matrix with the same row dimension. Input P is a length-L
vector whose elements determine where each column from A should be placed
in the M-by-L output matrix.
% Equivalent MATLAB code
y = [A(:,P(1)) A(:,P(2)) A(:,P(3)) ... A(:,P(end))]

For column permutation, a length-N 1-D vector input at the A port is treated as
a 1-by-N matrix.
When an index value in input P references a nonexistent row or column of
matrix A, the block reacts with the behavior specified by the Invalid
permutation index parameter. The following options are available:

• Clip index – Clip the index to the nearest valid value (1 or M for row
permutation, and 1 or N for column permutation), and do not issue an alert.
Example: For a 3-by-7 input matrix, a column index of 9 is clipped to 7, and
a row index of -2 is clipped to 1.
• Clip and warn – Display a warning message in the MATLAB command
window, and clip the index as described above.
• Generate error – Display an error dialog box and terminate the simulation.

5-339
Permute Matrix

When length of the permutation vector P is not equal to the number of rows or
columns of the input matrix A, you can choose to get an error dialog box and
terminate the simulation by checking Error when length of P is not equal
to Permute dimension size.
If input A is frame-based, the output is frame-based; otherwise, the output is
sample-based.

Example In the model below, the top Permute Matrix block places the second row of the
input matrix in both the first and fifth rows of the output matrix, and places
the third row of the input matrix in the three middle rows of the output matrix.
The bottom Permute Matrix block places the second column of the input matrix
in both the first and fifth columns of the output matrix, and places the third
column of the input matrix in the three middle columns of the output matrix.

4 5 6
7 8 9
7 8 9
7 8 9
4 5 6

23332
56665
89998

As shown in the example above, rows and columns of A can appear any number
of times in the output, or not at all.

5-340
 Permute Matrix

Dialog Box

Permute
Method of constructing the output matrix; by permuting rows or columns
of the input.
Invalid permutation index
Response to an invalid index value. Tunable, except in Simulink’s external
mode.
Error when length of P is not equal to Permute dimension size
Option to display an error dialog box and terminate the simulation if the
length of the permutation vector P is not equal to the number of rows or
columns of the input matrix A.

Supported Fixed-point Only supported by input port A

Data Types Custom data types Only supported by input port A
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Submatrix DSP Blockset

Transpose DSP Blockset
Variable Selector DSP Blockset
permute MATLAB

5-341
Permute Matrix

See “Reordering Channels in a Frame-Based Multichannel Signal” on

page 3-61 for related information.

5-342
 Polynomial Evaluation

Purpose 5Polynomial Evaluation

Evaluate a polynomial expression.

Library Math Functions / Polynomial Functions

Description The Polynomial Evaluation block applies a polynomial function to the real or
complex input at the In port.
y = polyval(u) % Equivalent MATLAB code

The Polynomial Evaluation block performs these types of operation more

efficiently than the equivalent construction using Simulink Sum and Math
Function blocks.
When the Use constant coefficients check box is selected, the polynomial
expression is specified by the Constant coefficients parameter. When Use
constant coefficients is not selected, a variable polynomial expression is
specified by the input to the Coeffs port. In both cases, the polynomial is
specified as a vector of real or complex coefficients in order of descending
exponents.
The table below shows some examples of the block’s operation for various
coefficient vectors.

Coefficient Vector Equivalent Polynomial Expression

[1 2 3 4 5] 4 3 2
y = u + 2u + 3u + 4u + 5

[1 0 3 0 5] 4 2
y = u + 3u + 5

[1 2+i 3 4-3i 5i] 4 3 2

y = u + ( 2 + i )u + 3u + ( 4 – 3i )u + 5i

Each element of a vector or matrix input to the In port is processed

independently, and the output size and frame status are the same as the input.

5-343
Polynomial Evaluation

Dialog Box

Use constant coefficients

When selected, enables the Constant coefficients parameter and disables
the Coeffs input port.
Constant coefficients
The vector of polynomial coefficients to apply to the input, in order of
descending exponents. This parameter is enabled when the Use constant
coefficients check box is selected.

Supported Double-precision floating point

Data Types

See Also Least Squares Polynomial Fit DSP Blockset

Math Function Simulink
Sum Simulink
polyval MATLAB

5-344
 Polynomial Stability Test

Purpose 5Polynomial Stability Test

Determine whether all roots of the input polynomial are inside the unit circle
using the Schur-Cohn algorithm.

Library Math Functions / Polynomial Functions

Description The Polynomial Stability Test block uses the Schur-Cohn algorithm to
determine whether all roots of a polynomial are within the unit circle.
y = all(abs(roots(u)) < 1) % Equivalent MATLAB code

Each column of the M-by-N input matrix u contains M coefficients from a

distinct polynomial,
M–1 M–2
f ( x ) = u1 x + u2 x + L + uM

arranged in order of descending exponents, u1, u2, …, uM. The polynomial has
order M-1 and positive integer exponents.
Inputs can be frame-based or sample-based, and both represent the polynomial
coefficients as shown above. For convenience, a length-M 1-D vector input is
treated as an M-by-1 matrix.
The output is a 1-by-N matrix with each column containing the value 1 or 0.
The value 1 indicates that the polynomial in the corresponding column of the
input is stable; i.e., the magnitudes of all solutions to f(x) = 0 are less than 1.
The value 0 indicates that the polynomial in the corresponding column of the
input may be unstable; i.e., the magnitude of at least one solution to f(x) = 0 is
greater than or equal to 1.
The output is always sample-based.

Applications
This block is most commonly used to check the pole locations of the
denominator polynomial, A(z), of a transfer function, H(z).
–1 –( m – 1 )
B(z) b1 + b2 z + … + bm z
H ( z ) = ------------ = ---------------------------------------------------------------------------
A(z) a1 + a2 z + … + an z
–1 –( n – 1 )

The poles are the n-1 roots of the denominator polynomial, A(z). If any poles are
located outside the unit circle, the transfer function H(z) is unstable. As is

5-345
Polynomial Stability Test

typical in DSP applications, the transfer function above is specified in

descending powers of z-1 rather than z.

Dialog Box

Supported Single-precision floating point

Data Types Double-precision floating point

See Also Least Squares Polynomial Fit DSP Blockset

Polynomial Evaluation DSP Blockset
polyfit MATLAB

5-346
 Pseudoinverse

Purpose 5Pseudoinverse
Compute the Moore-Penrose pseudoinverse of a matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description The Pseudoinverse block computes the Moore-Penrose pseudoinverse of input

matrix A.
[U,S,V] = svd(A,0) % Equivalent MATLAB code

The pseudoinverse of A is the matrix A+ such that

+ + *
A = VS U

where U and V are orthogonal matrices, and S is a diagonal matrix. The

pseudoinverse has the following properties:

• AA+ = (AA+)*
• A+A = (A+A)*
• AA+A = A
• A+AA+ = A+

The output is always sample-based.

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

5-347
Pseudoinverse

See Also Cholesky Inverse DSP Blockset

LDL Inverse DSP Blockset
LU Inverse DSP Blockset
Singular Value Decomposition DSP Blockset
inv MATLAB

See “Inverting Matrices” on page 4-19 for related information.

5-348
 QR Factorization

Purpose 5QR Factorization

Factor a rectangular matrix into unitary and upper triangular components.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The QR Factorization block uses modified Gram-Schmidt iteration to factor a

column permutation of the M-by-N input matrix A as

A e = QR

where Q is an M-by-min(M,N) unitary matrix, and R is a min(M,N)-by-N

upper-triangular matrix. A length-M vector input is treated as an M-by-1
matrix, and is always sample-based.
The column-pivoted matrix Ae contains the columns of A permuted as
indicated by the contents of length-N permutation vector E.
Ae = A(:,E) % Equivalent MATLAB code

The block selects a column permutation vector E, which ensures that the
diagonal elements of matrix R are arranged in order of decreasing magnitude.

r i + 1 , j + 1 > r i, j i=j

QR factorization is an important tool for solving linear systems of equations

because of good error propagation properties and the invertability of unitary
matrices.
–1 *
Q = Q
Unlike LU and Cholesky factorizations, the matrix A does not need to be
square for QR factorization. Note, however, that QR factorization requires
twice as many operations as Gaussian elimination.

Example A sample factorization is shown below. The input to the block is matrix A,
which is permuted according to vector E to produce matrix Ae. Matrix Ae is
factored to produce the Q and R output matrices.

5-349
QR Factorization

– 0.105 – 0.986 – 0.131

0.843 – 0.159 0.514
– 0.527 – 0.057 0.848

9 –1 2 9.487 – 2.846 – 8.117

–1 8 –5 0 – 8.826 – 1.575
2 –5 7 0 0 3.105

(2 1 3)
–1 9 2
A = 8 –1 –5
e
–5 2 7

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Cholesky Factorization DSP Blockset

LU Factorization DSP Blockset
QR Solver DSP Blockset
Singular Value Decomposition DSP Blockset
qr MATLAB

See “Factoring Matrices” on page 4-17 for related information.

5-350
 QR Solver

Purpose 5QR Solver

Find a minimum-norm-residual solution to the equation AX=B.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The QR Solver block solves the linear system AX=B, which can be
overdetermined, underdetermined, or exactly determined. The system is solved
by applying QR factorization to the M-by-N matrix, A, at the A port. The input
to the B port is the right-hand-side M-by-L matrix, B. A length-M 1-D vector
input at either port is treated as an M-by-1 matrix.
The output at the x port is the N-by-L matrix, X. X is always sample based, and
is chosen to minimize the sum of the squares of the elements of B-AX. When B
is a vector, this solution minimizes the vector 2-norm of the residual (B-AX is
the residual). When B is a matrix, this solution minimizes the matrix
Frobenius norm of the residual. In this case, the columns of X are the solutions
to the L corresponding systems AXk=Bk, where Bk is the kth column of B, and
Xk is the kth column of X.
X is known as the minimum-norm-residual solution to AX=B. The
minimum-norm-residual solution is unique for overdetermined and exactly
determined linear systems, but it is not unique for underdetermined linear
systems. Thus when the QR Solver is applied to an underdetermined system,
the output X is chosen such that the number of nonzero entries in X is
minimized.

Algorithm QR factorization factors a column-permuted variant (Ae) of the M-by-N input

matrix A as

A e = QR

where Q is a M-by-min(M,N) unitary matrix, and R is a min(M,N)-by-N

upper-triangular matrix.
The factored matrix is substituted for Ae in

Ae X = Be ,

and

QRX = B e

5-351
QR Solver

is solved for X by noting that Q-1 = Q* and substituting Y = Q*Be. This requires
computing a matrix multiplication for Y and solving a triangular system for X.

RX = Y

Dialog Box

Supported Double-precision floating point

Data Types

See Also Levinson-Durbin DSP Blockset

LDL Solver DSP Blockset
LU Solver DSP Blockset
QR Factorization DSP Blockset
SVD Solver DSP Blockset

See “Solving Linear Systems” on page 4-16 for related information.

5-352
 Queue

Purpose 5Queue
Store inputs in a FIFO register.

Library Signal Management / Buffers

Description The Queue block stores a sequence of input samples in a FIFO (first in, first
out) register. The register capacity is set by the Register size parameter, and
inputs can be scalars, vectors, or matrices.
The block pushes the input at the In port onto the end of the queue when a
trigger event is received at the Push port. When a trigger event is received at
the Pop port, the block pops the first element off the queue and holds the Out
port at that value. The first input to be pushed onto the queue is always the
first to be popped off.

1
1
register size
0
0
1 1 0 0 1
empty

empty

empty

Pushing the queue 1 0 0 1 1

1 0 0 0 0
1 1 0 1 1

first in

1 1 1 0 0 1
empty

empty

1 1 0 0 1 1
0 1 0 0 0 0
0 1 1 0 1 1

1 1 1 0 0
empty

empty

empty

1 1 0 0 1
Popping the queue
0 1 0 0 0
0 1 1 0 1

1
1 first out
0
1

A trigger event at the optional Clr port (enabled by the Clear input check box)
empties the queue contents. If Clear output port on reset is selected, then a
trigger event at the Clr port empties the queue and sets the value at the Out
port to zero. This setting also applies when a disabled subsystem containing

5-353
Queue

the Queue block is reenabled; the Out port value is only reset to zero in this case
if Clear output port on reset is selected.
When two or more of the control input ports are triggered at the same time
step, the operations are executed in the following order:

1 Clr
2 Push
3 Pop

The triggering event for the Push, Pop, and Clr ports is specified by the Trigger
type pop-up menu, and can be one of the following:

• Rising edge triggers execution of the block when the trigger input rises from
a negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers execution of the block when the trigger input falls from
a positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers execution of the block when either a rising or falling
edge (as described above) occurs.

The Push onto full register parameter specifies the block’s behavior when a
trigger is received at the Push port but the register is full. The Pop empty
register parameter specifies the block’s behavior when a trigger is received at
the Pop port but the register is empty. The following options are available for
both cases:

• Ignore – Ignore the trigger event, and continue the simulation.

• Warning – Ignore the trigger event, but display a warning message in the
MATLAB command window.
• Error – Display an error dialog box and terminate the simulation.

The Push onto full register parameter additionally offers the Dynamic
reallocation option, which dynamically resizes the register to accept as many
additional inputs as memory permits. To find out how many elements are on
the queue at a given time, enable the Num output port by selecting the Output
number of register entries option.

5-354
 Queue

Examples Example 1
The table below illustrates the Queue block’s operation for a Register size of 4,
Trigger type of Either edge, and Clear output port on reset enabled.
Because the block triggers on both rising and falling edges in this example,
each transition from 1 to 0 or 0 to 1 in the Push, Pop, and Clr columns below
represents a distinct trigger event. A 1 in the Empty column indicates an empty
queue, while a 1 in the Full column indicates a full queue.

In Push Pop Clr Queue Out Empty Full Num

1 0 0 0 top bottom 0 1 0 0

2 1 0 0 top 2 bottom 0 0 0 1

3 0 0 0 top 3 2 bottom 0 0 0 2

4 1 0 0 top 4 3 2 bottom 0 0 0 3

5 0 0 0 top 5 4 3 2 bottom 0 0 1 4

6 0 1 0 top 5 4 3 bottom 2 0 0 3

7 0 0 0 top 5 4 bottom 3 0 0 2

8 0 1 0 top 5 bottom 4 0 0 1

9 0 0 0 top bottom 5 1 0 0

10 1 0 0 top 10 bottom 5 0 0 1

11 0 0 0 top 11 10 bottom 5 0 0 2

12 1 0 1 top 12 bottom 0 0 0 1

Note that at the last step shown, the Push and Clr ports are triggered
simultaneously. The Clr trigger takes precedence, and the queue is first
cleared and then pushed.

Example 2
The dspqdemo demo provides another example of Queue operation.

5-355
Queue

Dialog Box

Register size
The number of entries that the FIFO register can hold.
Trigger type
The type of event that triggers the block’s execution. Tunable.
Push onto full register
Response to a trigger received at the Push port when the register is full.
Pop empty register
Response to a trigger received at the Pop port when the register is empty.
Tunable.
Empty register output
Enable the Empty output port, which is high (1) when the queue is empty,
and low (0) otherwise.
Full register output
Enable the Full output port, which is high (1) when the queue is full, and
low (0) otherwise. The Full port remains low when Dynamic reallocation
is selected from the Push onto full register parameter.
Output number of register entries
Enable the Num output port, which tracks the number of entries currently
on the queue.

5-356
 Queue

Clear input
Enable the Clr input port, which empties the queue when the trigger
specified by the Trigger type is received.
Clear output port on reset
Reset the Out port to zero (in addition to clearing the queue) when a trigger
is received at the Clr input port. Tunable.

Supported Double-precision floating point

Data Types

See Also Buffer DSP Blockset

Delay Line DSP Blockset
Stack DSP Blockset

5-357
Random Source

Purpose 5Random Source

Generate randomly distributed values.

Library DSP Sources

Description The Random Source block generates a frame of M values drawn from a uniform
or Gaussian pseudorandom distribution, where M is specified by the Samples
per frame parameter.
This reference page contains a detailed discussion of the following Random
Source block topics:

• “Distribution Type” on page 5-358

• “Output Data Type” on page 5-359
• “Output Repeatability” on page 5-360
• “Specifying the Initial Seed” on page 5-360
• “Sample Period” on page 5-361

Distribution Type
When the Source type parameter is set to Uniform, the output samples are
drawn from a uniform distribution whose minimum and maximum values are
specified by the Minimum and Maximum parameters, respectively. All values
in this range are equally likely to be selected. A length-N vector specified for
one or both of these parameters generates an N-channel output (M-by-N
matrix) containing a unique random distribution in each channel.
For example, specify

• Minimum = [ 0 0 -3 -3]
• Maximum = [10 10 20 20]

to generate a four-channel output whose first and second columns contain

random values in the range [0, 10], and whose third and fourth columns
contain random values in the range [-3, 20]. When only one of the Minimum
and Maximum parameters is specified as a vector, the other is scalar expanded
to the same length.
When the Source type parameter is set to Gaussian, the output samples are
drawn from the normal distribution defined by the Mean and Variance
parameters. A length-N vector specified for one or both of the Mean and

5-358
 Random Source

Variance parameters generates an N-channel output (M-by-N frame matrix)

containing a distinct random distribution in each column. When only one of
these parameters is specified as a vector, the other is scalar expanded to the
same length.

Output Data Type

The block’s output can be either real or complex, as selected by the Real and
Complex options in the Output complexity parameter. (These settings
control all channels of the output, so real and complex data cannot be combined
in the same output.) For complex output with a Uniform distribution, the real
and imaginary components in each channel are both drawn from the same
uniform random distribution, defined by the Minimum and Maximum
parameters for that channel.
For complex output with a Gaussian distribution, the real and imaginary
components in each channel are drawn from normal distributions with
different means. In this case, the Mean parameter for each channel should
specify a complex value; the real component of the Mean parameter specifies
the mean of the real components in the channel, while the imaginary
component specifies the mean of the imaginary components in the channel. If
either the real or imaginary component is omitted from the Mean parameter,
a default value of 0 is used for the mean of that component.
For example, a Mean parameter setting of [5+2i 0.5 3i] generates a
three-channel output with the following means.

Channel 1 mean real = 5 imaginary = 2

Channel 2 mean real = 0.5 imaginary = 0

Channel 3 mean real = 0 imaginary = 3

For complex output, the Variance parameter, σ2, specifies the total variance
for each output channel. This is the sum of the variances of the real and
imaginary components in that channel.
2 2 2
σ = σ Re + σ Im

5-359
Random Source

The specified variance is equally divided between the real and imaginary
components, so that

2
2 σ
σ Re = ------
2
2
2 σ
σ Im = ------
2

Output Repeatability
The Repeatability parameter determines whether or not the block outputs the
same signal each time you run the simulation. You can set the parameter to one
of the following options:

• Repeatable — The block outputs the same signal each time you run the
simulation. The first time you run the simulation, the block randomly selects
an initial seed. The block reuses these same initial seeds every time you
rerun the simulation.
• Specify seed — The block outputs the same signal each time you run the
simulation. Every time you run the simulation, the block uses the initial
seed(s) specified by the Initial seed parameter. Also see the next section,
“Specifying the Initial Seed”.
• Not repeatable — The block does not output the same signal each time you
run the simulation. Every time you run the simulation, the block randomly
selects an initial seed.

Specifying the Initial Seed

When you set the Repeatability parameter to Specify seed, you must set the
Initial seed parameter. The Initial seed parameter specifies the initial seed
for the pseudorandom number generator. The generator produces an identical
sequence of pseudorandom numbers each time it is executed with a particular
initial seed.
For real outputs (Output complexity parameter set to Real), a length-N seed
vector can be specified to set a distinct initial generator seed for each individual
channel. When a scalar seed is specified for a multichannel output, the block
uses the specified seed for the first channel, and increments the seed by 2 for
each additional channel. For example, specifying an Initial seed value of 10 for

5-360
 Random Source

a five-channel output is equivalent to specifying an Initial seed vector

of [10 12 14 16 18].
For complex outputs (Output complexity parameter set to Complex), a
length-N seed vector can be specified to set a distinct initial generator seed to
be used for the real components of each individual channel. The block
increments these values by 1 to determine the initial seeds used for the
imaginary components of the corresponding channels.
When a scalar seed is specified for a multichannel complex output, the block
uses the specified seed for the real components of the first channel, and
increments the seed by 2 for the real components of each additional channel.
The block increments the specified seed by 1 for the imaginary components of
the first channel, and increments the first channel’s imaginary seed by 2 for
the imaginary components of each additional channel. For example, specifying
an Initial seed value of 10 for a five-channel complex output is equivalent to
specifying an Initial seed vector of [10 12 14 16 18]. These values are used
to seed the real-component generator for each channel; the vector
[11 13 15 17 19] is used to seed the imaginary-component generator for each
channel.

Sample Period
The Sample time parameter value, Ts, specifies the random sequence sample
period when the Sample mode parameter is set to Discrete. In this mode, the
block generates the number of samples specified by the Samples per frame
parameter value, M, and outputs this frame with a period of M∗Ts. For M=1,
the output is sample-based; otherwise, the output is frame-based.
When Sample mode is set to Continuous, the block is configured for
continuous-time operation, and the Sample time and Samples per frame
parameters are disabled. Note that many blocks in the DSP Blockset do not
accept continuous-time inputs.

5-361
Random Source

Dialog Box

Source type
The distribution from which to draw the random values, Uniform or
Gaussian.

Minimum
The minimum value in the uniform distribution. This parameter is only
enabled when Uniform is selected from the Source type parameter.
Tunable.

5-362
 Random Source

Maximum
The maximum value in the uniform distribution. This parameter is only
enabled when Uniform is selected from the Source type parameter.
Tunable.
Mean
The mean of the Gaussian (normal) distribution. This parameter is only
enabled when Gaussian is selected from the Source type parameter.
Tunable.
Variance
The variance of the Gaussian (normal) distribution. This parameter is only
enabled when Gaussian is selected from the Source type parameter.
Tunable.
Repeatability
The repeatability of the block output: Not repeatable, Repeatable, or
Specify seed. In the Repeatable and Specify seed settings, the block
outputs the same signal every time you run the simulation. For details, see
“Output Repeatability” on page 5-360.
Initial seed
The initial seed(s) to use for the random number generator when you set
the Repeatability parameter to Specify seed. For details, see “Specifying
the Initial Seed” on page 5-360.
Inherit output port attributes
When selected, allows the block to inherit the sample mode, sample period,
and complexity of a downstream block. (The Sample mode, Sample time,
Samples per frame, and Output complexity parameters are disabled.)
The output is a length-M sample-based 1-D vector, where length M is
inherited from the downstream block. If the Minimum, Maximum, Mean,
or Variance parameter specifies N channels, the 1-D vector output
contains M/N samples from each channel. An error occurs in this case if M
is not an integer multiple of N.
Sample mode
The sample mode, Continuous or Discrete. This parameter is enabled
when the Inherit output port attributes check box is deselected.

5-363
Random Source

Sample time
The sample period, Ts, of the random output sequence. The output frame
period is M∗Ts. This parameter is enabled when the Inherit output port
attributes check box is deselected.

Samples per frame

The number of samples, M, in each output frame. This parameter is
enabled when the Inherit output port attributes check box is deselected.
Output complexity
The data type of the output, Real or Complex. This parameter is enabled
when the Inherit output port attributes check box is deselected.

Supported Double-precision floating point

Data Types

See Also Discrete Impulse DSP Blockset

DSP Constant DSP Blockset
Maximum DSP Blockset
Minimum DSP Blockset
Random Number Simulink
Signal From Workspace DSP Blockset
Signal Generator Simulink
Standard Deviation DSP Blockset
Variance DSP Blockset
rand MATLAB
randn MATLAB

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-364
 Real Cepstrum

Purpose 5Real Cepstrum

Compute the real cepstrum of an input.

Library Transforms

Description The Real Cepstrum block computes the real cepstrum of each channel in the
real-valued M-by-N input matrix, u. For both sample-based and frame-based
inputs, the block assumes that each input column is a frame containing M
consecutive samples from an independent channel. The block does not accept
complex-valued inputs.
The output is a real Mo-by-N matrix, where Mo is specified by the FFT length
parameter. Each output column contains the length-Mo real cepstrum of the
corresponding input column.
y = real(ifft(log(abs(fft(u,Mo))))) % Equivalent MATLAB code

or, more compactly,

y = rceps(u,Mo)

When the Inherit FFT length from input port dimensions check box is
selected, the output frame size matches the input frame size (Mo=M). In this
case, a sample-based length-M row vector input is processed as a single channel
(i.e., as an M-by-1 column vector), and the output is a length-M row vector. A
1-D vector input is always processed as a single channel, and the output is a
1-D vector.
The output is always sample-based, and the output port rate is the same as the
input port rate.

Dialog Box

5-365
Real Cepstrum

Inherit FFT length from input port dimensions

When selected, matches the output frame size to the input frame size.
FFT length
The number of frequency points at which to compute the FFT, which is also
the output frame size, Mo. This parameter is available when Inherit FFT
length from input port dimensions is not selected.

Supported Double-precision floating point

Data Types

See Also Complex Cepstrum DSP Blockset

DCT DSP Blockset
FFT DSP Blockset
rceps Signal Processing Toolbox

5-366
 Reciprocal Condition

Purpose 5Reciprocal Condition

Compute the reciprocal condition of a square matrix in the 1-norm.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Reciprocal Condition block computes the reciprocal of the condition
number for a square input matrix A.
y = rcond(A) % Equivalent MATLAB code

or

1 1
y = --- = -------------------------------
κ –1
A 1 A 1
where κ is the condition number (κ ≥ 1), and y is the scalar sample-based output
(0 ≤ y < 1).
The matrix 1-norm, A 1 , is the maximum column-sum in the M-by-M
matrix A.

M
A 1 = max
1≤j≤M
∑ a ij
i=1

For a 3-by-3 matrix:

a 11 a 12 a 13
a 21 a 22 a 23 A 1 = max ( A 1, A 2, A 3 )
a 31 a 32 a 33

a 13 + a 23 + a 33 = A 3

a 12 + a 22 + a 32 = A 2

a 11 + a 21 + a 31 = A 1

5-367
Reciprocal Condition

Dialog Box

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Matrix 1-Norm DSP Blockset

Normalization DSP Blockset
rcond MATLAB

5-368
 Repeat

Purpose 5Repeat
Resample an input at a higher rate by repeating values.

Library Signal Operations

Description The Repeat block upsamples each channel of the Mi-by-N input to a rate
L times higher than the input sample rate by repeating each consecutive input
sample L times at the output. The integer L is specified by the Repetition
count parameter.

Sample-Based Operation
When the input is sample-based, the block treats each of the M∗N matrix
elements as an independent channel, and upsamples each channel over time.
The Frame-based mode parameter must be set to Maintain input frame size.
The output sample rate is L times higher than the input sample rate
(Tso = Tsi/L), and the input and output sizes are identical.

Frame-Based Operation
When the input is frame-based, the block treats each of the N input columns as
a frame containing Mi sequential time samples from an independent channel.
The block upsamples each channel independently by repeating each row of the
input matrix L times at the output. The Frame-based mode parameter
determines how the block adjusts the rate at the output to accommodate the
repeated rows. There are two available options:
• Maintain input frame size
The block generates the output at the faster (upsampled) rate by using a
proportionally shorter frame period at the output port than at the input port.
For L repetitions of the input, the output frame period is L times shorter
than the input frame period (Tfo = Tfi/L), but the input and output frame
sizes are equal.

The model below shows a single-channel input with a frame period of

1 second being upsampled through 4-times repetition to a frame period of
0.25 seconds. The input and output frame sizes are identical.

5-369
Repeat

• Maintain input frame rate

The block generates the output at the faster (upsampled) rate by using a
proportionally larger frame size than the input. For L repetitions of the
input, the output frame size is L times larger than the input frame size
(Mo = Mi∗L), but the input and output frame rates are equal.
The model below shows a single-channel input of frame size 16 being
upsampled through 4-times repetition to a frame size of 64. The input and
output frame rates are identical.

Latency

Zero Latency. The Repeat block has zero tasking latency for all single-rate
operations. The block is single-rate for the particular combinations of sampling
mode and parameter settings shown in the table below.

Sampling Mode Parameter Settings

Sample-based Repetition count parameter, L, is 1.

Repetition count parameter, L, is 1, or

Frame-based Frame-based mode parameter is Maintain input
frame rate.

5-370
 Repeat

The block also has zero latency for all multirate operations in Simulink’s
single-tasking mode.
Zero tasking latency means that the block repeats the first input (received
at t=0) for the first L output samples, the second input for the next L output
samples, and so on. The Initial condition parameter value is not used.

Nonzero Latency. The Repeat block has tasking latency only for multirate
operation in Simulink’s multitasking mode:

• In sample-based mode, the initial condition for each channel is repeated for
the first L output samples. The channel’s first input appears as output
sample L+1. The Initial condition value can be an Mi-by-N matrix
containing one value for each channel, or a scalar to be applied to all signal
channels.
• In frame-based mode, the first row of the initial condition matrix is repeated
for the first L output samples, the second row of the initial condition matrix
is repeated for the next L output samples, and so on. The first row of the first
input matrix appears in the output as sample MiL+1. The Initial condition
value can be an Mi-by-N matrix, or a scalar to be repeated across all elements
of the Mi-by-N matrix. See the example below for an illustration of this case.

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Example Construct the frame-based model shown below.

Adjust the block parameters as follows.

• Configure the Signal From Workspace block to generate a two-channel

signal with frame size of 4 and sample period of 0.25. This represents an

5-371
Repeat

output frame period of 1 (0.25∗4). The first channel should contain the
positive ramp signal 1, 2, ..., 100, and the second channel should contain the
negative ramp signal -1, -2, ..., -100.
- Signal = [(1:100)' (-1:-1:-100)']
- Sample time = 0.25
- Samples per frame = 4
• Configure the Repeat block to upsample the two-channel input by increasing
the output frame rate by a factor of 2 relative to the input frame rate. Set an
initial condition matrix of

11 – 11
12 – 12
13 – 13
14 – 14

- Repetition count = 2
- Initial condition = [11 -11;12 -12;13 -13;14 -14]
- Frame-based mode = Maintain input frame size
• Configure the Probe blocks by deselecting the Probe width and Probe
complex signal check boxes (if desired).

This model is multirate because there are at least two distinct sample rates, as
shown by the two Probe blocks. To run this model in Simulink’s multitasking
mode, select Fixed-step and discrete from the Type controls in the Solver
panel of the Simulation Parameters dialog box, and select MultiTasking from
the Mode parameter. Also set the Stop time to 30.
Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout =

11 -11
11 -11
12 -12
12 -12
13 -13
13 -13
14 -14

5-372
 Repeat

14 -14
1 -1
1 -1
2 -2
2 -2
3 -3
3 -3
4 -4
4 -4
5 -5
5 -5

Since we ran this frame-based multirate model in multitasking mode, the block
repeats each row of the initial condition matrix for L output samples, where
L is the Repetition count of 2. The first row of the first input matrix appears
in the output as sample 9 (i.e., sample MiL+1, where Mi is the input frame
size).

Dialog Box

Repetition count
The integer number of times, L, that the input value is repeated at the
output. This is the factor by which the output frame size or sample rate is
increased. Tunable.
Initial conditions
The value with which the block is initialized for cases of nonzero latency; a
scalar or matrix. Tunable.

5-373
Repeat

Frame-based mode
For frame-based operation, the method by which to implement the
repetition (upsampling): Maintain input frame size (i.e., increase the
frame rate), or Maintain input frame rate (i.e., increase the frame size).
The Frame-based mode parameter must be set to Maintain input frame
size for sample-base inputs. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also FIR Interpolation DSP Blockset

Upsample DSP Blockset
Zero Pad DSP Blockset

5-374
 RLS Adaptive Filter

Purpose 5RLS Adaptive Filter

Compute filter estimates for an input using the RLS adaptive filter algorithm.

Library Filtering / Adaptive Filters

Description The RLS Adaptive Filter block recursively computes the least squares estimate
(RLS) of the FIR filter coefficients.
The corresponding RLS filter is expressed in matrix form as

–1
λ P ( n – 1 )u ( n )
k ( n ) = -----------------------------------------------------------------------
–1 H
1 + λ u ( n )P ( n – 1 )u ( n )
H
y ( n ) = ŵ ( n – 1 )u ( n )
e(n) = d(n) – y(n)
ŵ ( n ) = ŵ ( n – 1 ) + k ( n )e∗ ( n )
–1 –1 H
P ( n ) = λ P ( n – 1 ) – λ k ( n )u ( n ) P ( n – 1 )

where λ-1 denotes the reciprocal of the exponential weighting factor. The
variables are as follows.

Variable Description

n The current algorithm iteration

u(n) The buffered input samples at step n

P(n) The inverse correlation matrix at step n

k(n) The gain vector at step n

ŵ ( n ) The vector of filter-tap estimates at step n

y(n) The filtered output at step n

e(n) The estimation error at step n

d(n) The desired response at step n

λ The exponential memory weighting factor

5-375
RLS Adaptive Filter

The block icon has port labels corresponding to the inputs and outputs of the
RLS algorithm. Note that inputs to the In and Err ports must be sample-based
scalars. The signal at the Out port is a scalar, while the signal at the Taps port
is a sample-based vector.

Block Ports Corresponding Variables

In u, the scalar input, which is internally buffered into the

vector u(n)
Out y(n), the filtered scalar output
Err e(n), the scalar estimation error
Taps ŵ ( n ) , the vector of filter-tap estimates

An optional Adapt input port is added when the Adapt input check box is
selected in the dialog box. When this port is enabled, the block continuously
adapts the filter coefficients while the Adapt input is nonzero. A zero-valued
input to the Adapt port causes the block to stop adapting, and to hold the filter
coefficients at their current values until the next nonzero Adapt input.
The implementation of the algorithm in the block is optimized by exploiting the
symmetry of the inverse correlation matrix P(n). This decreases the total
number of computations by a factor of two.
The FIR filter length parameter specifies the length of the filter that the RLS
algorithm estimates. The Memory weighting factor corresponds to λ in the
equations, and specifies how quickly the filter “forgets” past sample
information. Setting λ=1 specifies an infinite memory; typically, 0.95 ≤ λ ≤ 1.
The Initial value of filter taps specifies the initial value ŵ ( 0 ) as a vector, or
as a scalar to be repeated for all vector elements. The initial value of P(n) is

1
I ------
2
σ̂
2
where σ̂ is specified by the Initial input variance estimate parameter.

Example The rlsdemo demo illustrates a noise cancellation system built around the RLS
Adaptive Filter block.

5-376
 RLS Adaptive Filter

Dialog Box

FIR filter length

The length of the FIR filter.
Memory weighting factor
The exponential weighting factor, in the range [0,1]. A value of 1 specifies
an infinite memory. Tunable.
Initial value of filter taps
The initial FIR filter coefficients.
Initial input variance estimate
The initial value of 1/P(n).
Adapt input
Enables the Adapt port.

References Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall,
1996.

Supported Double-precision floating point

Data Types

See Also Kalman Adaptive Filter DSP Blockset

LMS Adaptive Filter DSP Blockset

5-377
RLS Adaptive Filter

See “Adaptive Filters” on page 4-3 for related information.

5-378
 RMS

Purpose 5RMS
Compute the root-mean-square (RMS) value of an input or sequence of inputs.

Library Statistics

Description The RMS block computes the RMS value of each column in the input, or tracks
the RMS value of a sequence of inputs over a period of time. The Running RMS
parameter selects between basic operation and running operation.

Basic Operation
When the Running RMS check box is not selected, the block computes the
RMS value of each column in M-by-N input matrix u independently at each
sample time.
y = sqrt(sum(u.^2)/size(u,1)) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, y, is a 1-by-N vector containing the RMS value
for each column in u. The RMS value of the jth column is

∑ uij2
i=1
yj = ------------------
M
The frame status of the output is the same as that of the input.

Running Operation
When the Running RMS check box is selected, the block tracks the RMS value
of each channel in a time-sequence of M-by-N inputs. For sample-based inputs,
the output is a sample-based M-by-N matrix with each element yij containing
the RMS value of element uij over all inputs since the last reset. For
frame-based inputs, the output is a frame-based M-by-N matrix with each
element yij containing the RMS value of the jth column over all inputs since the
last reset, up to and including element uij of the current input.
If the Reset port parameter is set to Non-zero sample, the optional Rst port
is enabled and the block resets the running RMS when the scalar input at the
Rst port is nonzero. (The Rst port can be disabled by setting the Reset port

5-379
RMS

parameter to None.) For sample-based inputs, the running RMS for each
channel is initialized to the value in the corresponding channel of the current
input. For frame-based inputs, the running RMS for each channel is initialized
to the earliest value in each channel of the current input.
As in basic operation, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.

Example The RMS block in the model below calculates the running RMS of a
frame-based 3-by-2 (two-channel) matrix input, u. The running RMS is reset at
t=2 by an impulse to the block’s Rst port.

The RMS block has the following settings:

• Running RMS =
• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

The block’s operation is shown in the figure below.

5-380
 RMS

In Rst Output

ch1 ch2 ch1 ch2

61 6.00 1.00
First First output
13 t=0 0 4.30 2.24
input 39 3.92 5.51

–7 2 4.87 4.87
2 4 t=1 0 4.45 4.71
5 1 4.55 4.32

8 6 8.00 6.00
Simulation time

0 2 t=2 1 Reset 5.66 4.47

–1 5 4.65 4.65

–3 0 4.30 4.03
2 4 t=3 0 3.95 4.02
1 17 3.63 7.85

Dialog Box

Running RMS
Enables running operation when selected.
Reset port
Enables the Rst input port when set to Non-zero sample, and disables the
Rst input port when set to None.

Supported Double-precision floating point

Data Types

5-381
RMS

See Also Mean DSP Blockset

Variance DSP Blockset

5-382
 Sample and Hold

Purpose 5Sample and Hold

Sample and hold an input signal.

Library Signal Operations

Description The Sample and Hold block acquires the input at the signal port whenever it
receives a trigger event at the trigger port (marked by ). The block then holds
the output at the acquired input value until the next triggering event occurs. If
the acquired input is frame-based, the output is frame-based; otherwise, the
output is sample-based.
The trigger input must be a sample-based scalar with sample rate equal to the
input frame rate at the signal port. The trigger event is specified by the
Trigger type pop-up menu, and can be one of the following:

• Rising edge triggers the block to acquire the signal input when the trigger
input rises from zero to a positive value.
• Falling edge triggers the block to acquire the signal input when the trigger
input falls from zero to a negative value.
• Either edge triggers the block to acquire the signal input when the trigger
input either rises from zero to a positive value or falls from zero to a negative
value.

The block’s output prior to the first trigger event is specified by the Initial
condition parameter. If the acquired input is an M-by-N matrix, the Initial
condition can be an M-by-N matrix, or a scalar to be repeated across all
elements of the matrix. If the input is a length-M 1-D vector, the Initial
condition can be a length-M row or column vector, or a scalar to be repeated
across all elements of the vector.

Dialog Box

Trigger type
The type of event that triggers the block to acquire the input signal.

5-383
Sample and Hold

Initial condition
The block’s output prior to the first trigger event.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Downsample DSP Blockset

N-Sample Switch DSP Blockset

5-384
 Short-Time FFT

Purpose 5Short-Time FFT

Compute a nonparametric estimate of the spectrum using the short-time, fast
Fourier transform (ST-FFT) method.

Library Estimation / Power Spectrum Estimation

Description The Short-Time FFT block computes a nonparametric estimate of the

spectrum. The block averages the squared magnitude of the FFT computed
over windowed sections of the input, and normalizes the spectral average by
the square of the sum of the window samples.
Both an M-by-N frame-based matrix input and an M-by-N sample-based
matrix input are treated as M sequential time samples from N independent
channels. The block computes a separate estimate for each of the N
independent channels and generates an Nfft-by-N matrix output. When
Inherit FFT length from input dimensions is selected, Nfft is specified by the
frame size of the input, which must be a power of 2. When Inherit FFT length
from input dimensions is not selected, Nfft is specified as a power of 2 by the
FFT length parameter, and the block zero pads or truncates the input to Nfft
before computing the FFT.
Each column of the output matrix contains the estimate of the corresponding
input column’s power spectral density at Nfft equally spaced frequency points
in the range [0,Fs), where Fs is the signal’s sample frequency. The output is
always sample-based.
The Number of spectral averages specifies the number of spectra to average.
Setting this parameter to 1 effectively disables averaging.
The Window type, Stopband ripple, Beta, and Window sampling
parameters all apply to the specification of the window function; see the
reference page for the Window Function block for more details on these four
parameters.

Example The dspstfft demo provides an illustration of using the Short-Time FFT and
Matrix Viewer blocks to create a spectrogram. The dspsacomp demo compares
the ST-FFT with several other spectral estimation methods.

5-385
Short-Time FFT

Dialog Box

Window type
The type of window to apply. (See the Window Function block reference.)
Tunable.
Stopband attenuation in dB
The level (dB) of stopband attenuation, Rs, for the Chebyshev window.
Disabled for other Window type selections. Tunable.
Beta
The β parameter for the Kaiser window. Disabled for other Window type
selections. Increasing Beta widens the mainlobe and decreases the
amplitude of the window sidelobes in the window’s frequency magnitude
response. Tunable.
Window sampling
The window sampling, symmetric or periodic. Tunable.
Inherit FFT length from input dimensions
When selected, uses the input frame size as the number of data points, Nfft,
on which to perform the FFT.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft
exceeds the input frame size, the frame is zero-padded as needed. This

5-386
 Short-Time FFT

parameter is enabled when Inherit FFT length from input dimensions is

not selected.
Number of spectral averages
The number of spectra to average; setting this parameter to 1 effectively
disables averaging.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

See Also Burg Method DSP Blockset

Magnitude FFT DSP Blockset
Window Function DSP Blockset
Spectrum Scope DSP Blockset
Yule-Walker Method DSP Blockset
pwelch Signal Processing Toolbox

See “Power Spectrum Estimation” on page 4-15 for related information.

5-387
Signal From Workspace

Purpose 5Signal From Workspace

Import a signal from the MATLAB workspace.

Library DSP Sources

Description The Signal From Workspace block imports a signal from the MATLAB
workspace into the Simulink model. The Signal parameter specifies the name
of a MATLAB workspace variable containing the signal to import, or any valid
MATLAB expression defining a matrix or 3-D array.
When the Signal parameter specifies an M-by-N matrix (M≠1), each of the N
columns is treated as a distinct channel. The frame size is specified by the
Samples per frame parameter, Mo, and the output is an Mo-by-N matrix
containing Mo consecutive samples from each signal channel. The output
sample period is specified by the Sample time parameter, Ts, and the output
frame period is Mo∗Ts. For Mo=1, the output is sample-based; otherwise the
output is frame-based. For convenience, an imported row vector (M=1) is
treated as a single channel, so the output dimension is Mo-by-1.
When the Signal parameter specifies an M-by-N-by-P array, each of the
P pages (an M-by-N matrix) is output in sequence with period Ts. The Samples
per frame parameter must be set to 1, and the output is always sample-based.

Initial and Final Conditions

Unlike Simulink’s From Workspace block, the Signal From Workspace block
holds the output value constant between successive output frames (i.e., no
linear interpolation takes place). Additionally, the initial signal values are
always produced immediately at t=0.
When the block has output all of the available signal samples, it can start again
at the beginning of the signal, or simply repeat the final value or generate zeros
until the end of the simulation. (The block does not extrapolate the imported
signal beyond the last sample.) The Form output after final data value by
parameter controls this behavior:

• If Setting To Zero is specified, the block generates zero-valued outputs for

the duration of the simulation after generating the last frame of the signal.
• If Holding Final Value is specified, the block repeats the final sample for the
duration of the simulation after generating the last frame of the signal.

5-388
 Signal From Workspace

• If Cyclic Repetition is specified, the block repeats the signal from the
beginning after generating the last frame. If there are not enough samples
at the end of the signal to fill the final frame, the block zero-pads the final
frame as necessary to ensure that the output for each cycle is identical
(e.g., the ith frame of one cycle contains the same samples as the ith frame
of any other cycle).

Examples Example 1
In the first model below, the Signal From Workspace imports a two-channel
signal from the workspace matrix A. The Sample time is set to 1 and the
Samples per frame is set to 4, so the output is frame-based with a frame size
of 4 and a frame period of 4 seconds. The Form output after final data value
by parameter specifies Setting To Zero, so all outputs after the third frame (at
t=8) are zero.

MATLAB Workspace Matrix output, frame period = M o∗T s

Ch 1 Ch 2
1 1
2 1
ch1
ch2

ch1
ch2

ch1
ch2

ch1
ch2
3 0
4 0 0 0 9 1 5 1 1 1
A = 5 1 0 0 10 1 6 1 2 1
6 1 0 0 0 0 7 0 3 0
7 0 0 0 0 0 8 0 4 0
8 0
t=12 t=8 t=4 t=0
9 1 (Ts=1, Mo=4)
10 1
first matrix output

Example 2
In the second model below, the Signal From Workspace block imports a
sample-based matrix signal from the 3-D workspace array A. Again, the Form
output after final data value by parameter specifies Setting To Zero, so all
outputs after the third (at t=2) are zero.

5-389
Signal From Workspace

MATLAB Workspace Matrix output, frame period = T s

A ( :, :, 1 ) = 1 1
11

A ( :, :, 2 ) = 2 2 00 33 22 11
22 00 33 22 11

t=3 t=2 t=1 t=0

A ( :, :, 3 ) = 3 3
33 (Ts=1, Mo=1)
first matrix output

The Samples per frame parameter is set to 1 for 3-D input.

Dialog Box

Signal
The name of the MATLAB workspace variable from which to import the
signal, or a valid MATLAB expression specifying the signal.
Sample time
The sample period, Ts, of the output. The output frame period is Mo∗Ts.
Samples per frame
The number of samples, Mo, to buffer into each output frame. This value
must be 1 if a 3-D array is specified in the Signal parameter.

5-390
 Signal From Workspace

Form output after final data value by

Specifies the output after all of the specified signal samples have been
generated. The block can output zeros for the duration of the simulation
(Setting to zero), repeat the final data sample (Holding Final Value) or
repeat the entire signal from the beginning (Cyclic Repetition). Tunable.

Supported (MATLAB commands for casting values to certain data types are provided in
Data Types parentheses.)
Boolean (boolean)
8-, 16-, and 32-bit signed integer (int8, int16, int32)
8-, 16-, and 32-bit unsigned integer (uint8, uint16, uint32)
Single-precision floating point (single)
Double-precision floating point (double)

See Also From Wave Device DSP Blockset

From Wave File DSP Blockset
Signal From Workspace DSP Blockset
To Workspace Simulink
Triggered Signal From Workspace DSP Blockset

See the sections below for related information:

• “Discrete-Time Signals” on page 3-3

• “Multichannel Signals” on page 3-11
• “Benefits of Frame-Based Processing” on page 3-14
• “Creating Signals Using the Signal From Workspace Block” on page 3-38
“Importing Signals” on page 3-62

5-391
Signal To Workspace

Purpose 5Signal To Workspace

Write simulation data to an array in MATLAB’s main workspace.

Library DSP Sinks

Description The Signal To Workspace block writes data from your simulation into an array
in MATLAB’s main workspace. The output array can be 2-D or 3-D, depending
on whether the data is 1-D, sample-based, or frame-based. The Signal To
Workspace block and Simulink’s To Workspace block can output the same
arrays if their parameters are set appropriately.
For more information on the Signal To Workspace block, see the following
sections of this reference page:

• “Parameter Descriptions” on page 5-392

• “Output Dimension Summary” on page 5-393
• “Matching the Outputs of Signal To Workspace and To Workspace Blocks” on
page 5-394
• “Examples” on page 5-394

Parameter Descriptions
The Variable name parameter is the name of the array in the MATLAB
workspace into which the block logs the simulation data. The array is created
in the workspace only after the simulation stops running. If you enter the name
of an existing workspace variable, the block overwrites the variable with an
array of simulation data after the simulation stops running.
When the block input is sample-based or 1-D, the Limit data points to last
parameter indicates how many samples of data to save. If the block input is
frame-based, this parameter indicates how many frames of data to save. If the
simulation generates more than the specified maximum number of samples or
frames, the simulation saves only the most recently generated data. To capture
all data, set Limit data points to last to inf.
The Decimation parameter is the decimation factor. It can be set to any
positive integer d, and allows you to write data at every dth sample. The
default decimation, 1, writes data at every time step.

5-392
 Signal To Workspace

The Frames parameter sets the dimension of the output array to 2-D or 3-D for
frame-based inputs. The block ignores this parameter for 1-D and
sample-based inputs. The Frames parameter has the following two settings:

• Log frames separately (3-D array): Given an M-by-N frame-based input

signal, the block outputs an M-by-N-by-K array, where K is the number of
frames logged by the end of the simulation. (K is bounded above by the Limit
data points to last parameter.) Each input frame is an element of the 3-D
array. (See “Example 2: Frame-Based Inputs” on page 5-395.)
• Concatenate frames (2-D array): Given an M-by-N frame-based input
signal with frame size f, the block outputs a (K∗f)-by-N matrix, where K∗f is
the number of samples acquired by the end of the simulation. Each input
frame is vertically concatenated to the previous frame to produce the 2-D
array output. (See “Example 2: Frame-Based Inputs” on page 5-395.)

Signal to Workspace always logs sample-based input data as 3-D arrays,

regardless of the Frame parameter setting. Given an M-by-N sample-based
signal, the block outputs an M-by-N-by-L array, where L is the number of
samples logged by the end of the simulation (L is bounded above by the Limit
data points to last parameter). Each sample-based matrix is an element of the
3-D array. (See “Example 1: Sample-Based Inputs” on page 5-394.)
For 1-D vector inputs, the block outputs a 2-D matrix regardless of the setting
of Frame. For a length-N 1-D vector input, the block outputs an L-by-N matrix.
Each input vector is a row of the output matrix, vertically concatenated to the
previous vector.

Output Dimension Summary

The following table summarizes the output array dimensions for various block
inputs. In the table, f is the frame size of the input, K is the number of frames
acquired by the end of the simulation, and L is the number of samples acquired
by the end of the simulation (K and L are bounded above by the Limit data
points to last parameter).

Input Signal Type Signal To Workspace Output Dimension

Sample-based M-by-N matrix M-by-N-by-L array

Length-N 1-D vector L-by-N matrix

5-393
Signal To Workspace

Input Signal Type Signal To Workspace Output Dimension

Frame-based M-by-N matrix; M-by-N-by-K array

Frame set to Log frames
separately (3-D array)

Frame-based M-by-N matrix; (K∗f)-by-N matrix

Frame set to Concatenate K∗f is the number of samples acquired by the end of the
frames (2-D array) simulation.

Matching the Outputs of Signal To Workspace and To Workspace Blocks

The To Workspace block in Simulink’s Sinks Library and the Signal To
Workspace block can output the same array if they are given the same inputs.
To match the blocks’ outputs, set their parameters as follows.

Block Parameters Signal To Workspace To Workspace

Limit data points to last x (any positive integer or x

inf)

Decimation y (any positive integer, not y

inf)

Sample Time No such parameter -1

Save format No such parameter Array

Frames Concatenate frames No such parameter

(2-D array)

Examples Example 1: Sample-Based Inputs. In the following Example 1 model, the input to
the Signal To Workspace block is a 2-by-2 sample-based matrix signal with a
sample time of 1 (generated by a Signal From Workspace block). The Signal To
Workspace block logs 11 samples by the end of the simulation, and creates a
2-by-2-by-11 array, A, in the MATLAB workspace.

5-394
 Signal To Workspace

2-by-2 sample-based input MATLAB Workspace

A ( :, :, 1 ) = 1 1
–1 0

A ( :, :, 2 ) = 2 1
11 1 ... 3 1 2 1 1 1 –2 0
– 11 0 –3 0 –2 0 –1 0
A ( :, :, 3 ) = 3 1
t=10 . . . t=2 t=1 t=0 –3 0

…
Last Sample First Sample
Sample 11 Sample 1 11 1
A ( :, :, 11 ) =
– 11 0

The Example 1 block settings are as follows.

Signal To Workspace Block Parameters
Variable name yout
Limit data points to last inf
Decimation 1
Frames ignored since block input is not frame-based

Simulation Parameters Dialog Parameters

Start time 0
Stop time 10

Signal From Workspace Parameters (provides Signal To Workspace input)

Signal input1 (defined below)
Sample time 1
Samples per frame 1
Form output after final Setting to zero
data value by

input1 = cat(3, [1 1; -1 0], [2 1; -2 0],...,[11 1; -11 0])

Example 2: Frame-Based Inputs. In the following Example 2 model, the input to the
Signal To Workspace block is a 2-by-4 frame-based matrix signal with a frame
period of 1 (generated by a Signal From Workspace block). The block logs 11

5-395
Signal To Workspace

frames (two samples per frame) by the end of the simulation. The frames are
concatenated to create a 22-by-4 matrix, A, in the MATLAB workspace.
The block settings for the following Example 2 model are similar to the
Example 1 block settings, except Frames is set to Concatenate frames (2-D
array) and the Signal From Workspace parameter, Signal, is set to input2,
where
input2 = [1 -1 1 0; 2 -2 1 0; 3 -3 1 0;...; 22 -22 1 0]

2-by-4 frame-based input MATLAB Workspace

1 –1 1 0
2 –2 1 0
21 – 21 1 0 ... 3 –3 1 0 1 –1 1 0 3 –3 1 0
22 – 22 1 0 4 –4 1 0 2 –2 1 0 A = 4 –4 1 0
... M M M M
t=10 t=1 t=0
21 – 21 1 0
22 – 22 1 0
Last Frame First Frame
Frame 11 Frame 1
Concatenate Frames

In the 2-D output, there is no indication of where one frame ends and another
begins. By setting Frames to Log frames separately (3-D array) in the
Example 2 model, you can easily see each frame in the MATLAB workspace, as
illustrated in the following model. Each of the 11 frames is logged separately to
create a 2-by-4-by-11 array, A, in the MATLAB workspace.

MATLAB Workspace
2-by-4 frame-based input

A ( :, :, 1 ) = 1 – 1 1 0
2 –2 1 0

A ( :, :, 2 ) = 3 – 3 1 0
21 – 21 1 0 ... 3 –3 1 0 1 –1 1 0 4 –4 1 0
22 – 22 1 0 4 –4 1 0 2 –2 1 0
t=10 ... t=1 t=0 A ( :, :, 3 ) = 5 – 5 1 0
6 –6 1 0
…

Last Frame First Frame

Frame 11 Frame 1
A ( :, :, 11 ) = 21 – 21 1 0
Log frames separately 22 – 22 1 0

5-396
 Signal To Workspace

Dialog Box

Variable name
The name of the array that holds the input data. Tunable.
Limit data points to last
The maximum number of input samples (for sample-based inputs) or input
frames (for frame-based inputs) to be saved. Tunable.
Decimation
The decimation factor, d. Data is written at every dth sample. Tunable.
Frames
The output dimensionality for frame-based inputs. Frames can be set to
Concatenate frames (2-D array) or Log frames separately (3-D array).
This parameter is ignored when inputs are not frame-based. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Triggered To Workspace DSP Blockset

To Workspace Simulink

5-397
Sine Wave

Purpose 5Sine Wave

Generate a continuous or discrete sine wave.

Library DSP Sources

Description The Sine Wave block generates a multichannel real or complex sinusoidal
signal, with independent amplitude, frequency, and phase in each output
channel. A real sinusoidal signal is generated when the Output complexity
parameter is set to Real, and is defined by an expression of the type

y = A sin ( 2πft + φ )
where A is specified by the Amplitude parameter, f is specified in hertz by the
Frequency parameter, and φ is specified in radians by the Phase parameter.
A complex exponential signal is generated when the Output complexity
parameter is set to Complex, and is defined by an expression of the type
j ( 2πft + φ )
y = Ae = A { cos ( 2πft + φ ) + j sin ( 2πft + φ ) }
Each parameter value (A, f, φ) for real and complex sinusoids can be a scalar or
length-N vector, where N is the desired number of channels in the output. If at
least one parameter is specified as a length-N vector, scalar values specified for
the other parameters are scalar expanded to length N (i.e., they are applied to
every channel).
For example, specify

• Amplitude = [1 2 3]
• Frequency = [1000 500 250]
• Phase = [0 0 pi/2]

with Output complexity set to Real to generate a three-channel output

containing the real sinusoids below.

5-398
 Sine Wave


 sin ( 2000πt ) ( channel 1 )



y =  2 sin ( 1000πt ) ( channel 2 )


 3 sin  500πt + --π- ( channel 3 )
  2


In all discrete modes (see below), the block buffers the sampled sinusoids into
frames of size M, where M is specified by the Samples per frame parameter.
The output is a frame-based M-by-N matrix with frame period M∗Ts, where Ts
is specified by the Sample time parameter. For M=1, the output is
sample-based.
The Sample mode parameter specifies the block’s sampling property, which
can be Continuous or Discrete, described below:
• Continuous
In continuous mode, the sinusoid in the ith channel, yi, is computed as a
continuous function,
y i = A i sin ( 2πf i t + φ i ) ( real )

or
j ( 2πf i t + φ i )
yi = Ai e ( complex )

and the block’s output is continuous. In this mode, the block’s operation is the
same as that of a Simulink Sine Wave block with Sample time set to 0. This
mode offers high accuracy, but requires trigonometric function evaluations
at each simulation step, which is computationally expensive. Additionally,
because this method tracks absolute simulation time, a discontinuity will
eventually occur when the time value reaches its maximum limit.
Note also that many blocks in the DSP Blockset do not accept
continuous-time inputs.

5-399
Sine Wave

• Discrete
In discrete mode, the block’s discrete-time output can be generated by
directly evaluating the trigonometric function, by table look-up, or by a
differential method. The three options are explained below.

Discrete Computational Methods

When Discrete is selected from the Sample mode parameter, the secondary
Computation method parameter provides three options for generating the
discrete sinusoid:
• Trigonometric Fcn
• Table Lookup
• Differential

Trigonometric Fcn. The trigonometric function method computes the sinusoid in

the ith channel, yi, by sampling the continuous function

y i = A i sin ( 2πf i t + φ i ) ( real )

or
j ( 2πf i t + φ i )
yi = Ai e ( complex )

with a period of Ts, where Ts is specified by the Sample time parameter. This
mode of operation shares the same benefits and liabilities as the Continuous
sample mode described above.
If the period of every sinusoid in the output is evenly divisible by the sample
period, meaning that 1/(fiTs) = ki is an integer for every output yi, then the
sinusoidal output in the ith channel is a repeating sequence with a period of
ki samples. At each sample time, the block evaluates the sine function at the
appropriate time value within the first cycle of the sinusoid. By constraining
trigonometric evaluations to the first cycle of each sinusoid, the block avoids
the imprecision of computing the sine of very large numbers, and eliminates
the possibility of discontinuity during extended operations (when an absolute
time variable might overflow). This method therefore avoids the memory
demands of the table look-up method at the expense of many more
floating-point operations.

5-400
 Sine Wave

Table Lookup. The table look-up method precomputes the unique samples of
every output sinusoid at the start of the simulation, and recalls the samples
from memory as needed. Because a table of finite length can only be
constructed if all output sequences repeat, the method requires that the period
of every sinusoid in the output be evenly divisible by the sample period. That
is, 1/(fiTs) = ki must be an integer value for every channel i = 1, 2, ..., N. When
the Optimize table for parameter is set to Speed, the table constructed for
each channel contains ki elements. When the Optimize table for parameter is
set to Memory, the table constructed for each channel contains ki/4 elements.
For long output sequences, the table look-up method requires far fewer
floating-point operations than any of the other methods, but may demand
considerably more memory, especially for high sample rates (long tables). This
is the recommended method for models that are intended to emulate or
generate code for DSP hardware, and that therefore need to be optimized for
execution speed.

Differential. The differential method uses an incremental (differential)

algorithm rather than one based on absolute time. The algorithm computes the
output samples based on the output values computed at the previous sample
time (and precomputed update terms) by making use of the following
identities.

sin ( t + T s ) = sin ( t ) cos ( T s ) + cos ( t ) sin ( T s )

cos ( t + T s ) = cos ( t ) cos ( T s ) – sin ( t ) sin ( T s )

The update equations for the sinusoid in the ith channel, yi, can therefore be
written in matrix form (for real output) as

sin { 2πf i ( t + T s ) + φ i } cos ( 2πf i T s ) sin ( 2πf i T s ) sin ( 2πf i t + φ i )

=
cos { 2πf i ( t + T s ) + φ i } – sin ( 2πf i T s ) cos ( 2πf i T s ) cos ( 2πf i t + φ i )

where Ts is specified by the Sample time parameter. Since Ts is constant, the

right-hand matrix is a constant and can be computed once at the start of the
simulation. The value of Aisin[2πfi(t+Ts)+φi] is then computed from the values
of sin(2πfit+φi) and cos(2πfit+φi) by a simple matrix multiplication at each time
step.

5-401
Sine Wave

This mode offers reduced computational load, but is subject to drift over time
due to cumulative quantization error. Because the method is not contingent on
an absolute time value, there is no danger of discontinuity during extended
operations (when an absolute time variable might overflow).

Examples The dspsinecomp demo provides a comparison of all the available sine
generation methods.

Dialog Box

Amplitude
A length-N vector containing the amplitudes of the sine waves in each of N
output channels, or a scalar to be applied to all N channels. The vector

5-402
 Sine Wave

length must be the same as that specified for the Frequency and Phase
parameters. Tunable; the amplitude values can be altered while a
simulation is running, but the vector length must remain the same.
Frequency
A length-N vector containing the frequencies, in rad/s, of the sine waves in
each of N output channels, or a scalar to be applied to all N channels. The
vector length must be the same as that specified for the Amplitude and
Phase parameters. Tunable; the frequency values can be altered while a
simulation is running, but the vector length must remain the same. Not
tunable in Simulink’s external mode when using the differential method.
Phase
A length-N vector containing the phase offsets, in radians, of the sine
waves in each of N output channels, or a scalar to be applied to all N
channels. The vector length must be the same as that specified for the
Amplitude and Frequency parameters. Tunable; the phase values can be
altered while a simulation is running, but the vector length must remain
the same. Not tunable in Simulink’s external mode when using the
differential method.
Sample mode
The block’s sampling behavior, Continuous or Discrete.
Output complexity
The type of waveform to generate: Real specifies a real sine wave,
Complex specifies a complex exponential. Tunable.

Computation method
The method by which discrete-time sinusoids are generated:
Trigonometric fcn, Table lookup, or Differential. This parameter is
disabled when Continuous is selected from the Sample mode parameter.
For details, see “Discrete Computational Methods” on page 5-400.
Optimize table for
Optimizes the table of sine values for Speed or Memory (this parameter is
enabled only when the Computation method parameter is set to Table
lookup). When optimized for speed, the table contains k elements, and
when optimized for memory, the table contains k/4 elements, where k is the
number of input samples in one full period of the sine wave.

5-403
Sine Wave

Sample time
The period with which the sine wave is sampled, Ts. The block’s output
frame period is M∗Ts, where M is specified by the Samples per frame
parameter. This parameter is disabled when Continuous is selected from
the Sample mode parameter.
Samples per frame
The number of consecutive samples from each sinusoid to buffer into the
output frame, M. This parameter is disabled when Continuous is selected
from the Sample mode parameter.
State when re-enabled
The behavior of the block when a disabled subsystem containing it is
reenabled. The block can either reset itself to its starting state (Restart at
time zero), or resume generating the sinusoid based on the current
simulation time (Catch up to simulation time). This parameter is
disabled when Continuous is selected from the Sample mode parameter.

Supported Double-precision floating point

Data Types

See Also Chirp DSP Blockset

Complex Exponential DSP Blockset
Signal From Workspace DSP Blockset
Signal Generator Simulink
Sine Wave Simulink
sin MATLAB

See “Creating Signals Using Signal Generator Blocks” on page 3-36 for related
information.

5-404
 Singular Value Decomposition

Purpose 5Singular Value Decomposition

Factor a matrix using singular value decomposition.

Library Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description The Singular Value Decomposition block factors the M-by-N input matrix A
such that

A = U∗ diag ( S ) ⋅ V T
where U is an M-by-P matrix, V is an N-by-P matrix, S is a length-P vector, and
P is defined as min(M,N).
When M = N, U and V are both M-by-M unitary matrices. When M > N, V is an
N-by-N unitary matrix, and U is an M-by-N matrix whose columns are the first
N columns of a unitary matrix. When N > M, U is an M-by-M unitary matrix,
and V is an M-by-N matrix whose columns are the first N columns of a unitary
matrix. In all cases, S is a 1-D vector of positive singular values having length
P. The output is always sample-based.
Length-N row inputs are treated as length-N columns.
[U,S,V] = svd(A,0) % Equivalent MATLAB code for M > N

Note that the first (maximum) element of output S is equal to the 2-norm of the
matrix A.
You can enable the U and V output ports by selecting the Output the singular
vectors parameter.

Dialog Box

Compute singular vectors

Enables the U and V output ports when selected.

5-405
Singular Value Decomposition

References Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed.
Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Double-precision floating point

Data Types

See Also Autocorrelation LPC DSP Blockset

Cholesky Factorization DSP Blockset
LDL Factorization DSP Blockset
LU Inverse DSP Blockset
Pseudoinverse DSP Blockset
QR Factorization DSP Blockset
SVD Solver DSP Blockset
svd MATLAB

See “Factoring Matrices” on page 4-17 for related information.

5-406
 Sort

Purpose 5Sort
Sort the elements in the input by value.

Library Statistics

Description The Sort block sorts the elements in each column of the input using a Quicksort
algorithm. The Mode parameter specifies the block’s mode of operation, and
can be set to Value, Index, or Value and Index.

Value Mode
When Mode is set to Value, the block sorts the elements in each column of the
M-by-N input matrix u in order of ascending or descending value, as specified
by the Sort order parameter.
val = sort(u) % Equivalent MATLAB code (ascending)
val = flipud(sort(u)) % Equivalent MATLAB code (descending)

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.
The output at each sample time, val, is a M-by-N matrix containing the sorted
columns of u. Complex inputs are sorted by magnitude, and the output has the
same frame status as the input.

Index Mode
When Mode is set to Index, the block sorts the elements in each column of the
M-by-N input matrix u,
[val,idx] = sort(u) % Equivalent MATLAB code (ascending)
[val,idx] = flipud(sort(u))% Equivalent MATLAB code (descending)

and outputs the sample-based M-by-N index matrix, idx. The jth column of idx
is an index vector that permutes the jth column of u to the desired sorting
order:
val(:,j) = u(idx(:,j),j)

As in Value mode, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors.

5-407
Sort

Value and Index Mode

When Mode is set to Value and Index, the block outputs both the sorted
matrix, val, and the index matrix, idx.

Dialog Box

Mode
The block’s mode of operation: Output the sorted matrix (Value), the index
matrix (Index), or both (Value and Index).
Sort order
The order in which to sort the input values, Descending or Ascending.
Tunable, except in Simulink’s external mode.

Supported Double-precision floating point

Data Types

See Also Histogram DSP Blockset

Median DSP Blockset
sort MATLAB

5-408
 Spectrum Scope

Purpose 5Spectrum Scope

Compute and display the short-time FFT of each input signal.

Library DSP Sinks

Description The Spectrum Scope block computes and displays the magnitude-squared FFT
of the input. The input be a 1-D vector or a 2-D matrix of any frame status.
When the input is a 1-by-N sample-based vector or M-by-N sample-based
matrix, you must select the Buffer input check box. Each of the N vector
elements (or M∗N matrix elements) is then treated as an independent channel,
and the block buffers and displays the data in each channel independently.
When the input is frame-based, you can leave the input as is, or rebuffer data
by checking the Buffer input check box and specifying the new buffer size. In
the latter case, you can also specify an optional Buffer overlap.
Buffering 1-D vector inputs is recommended. In this case, the inputs are
buffered into frames (the length of which are specified in the Buffer size
parameter), where each 1-D input vector becomes a row in the buffered
outcome. If a 1-D vector input is left unbuffered, you will get a warning because
the block is computing the FFT of a scalar; though the scope window appears,
it is unlikely you will be able to see the plot, and a warning is also displayed on
the scope itself. It is not recommended that you leave 1-D inputs unbuffered.
The number of input samples that the block buffers before computing and
displaying the magnitude FFT is specified by the Buffer size parameter, Mo.
The Buffer overlap parameter, L, specifies the number of samples from the
previous buffer to include in the current buffer. The number of new input
samples the block acquires before computing and displaying the magnitude
FFT is the difference between the Buffer size and Buffer overlap, Mo-L.
The display update period is (Mo-L)∗Ts, where Ts is the input sample period,
and is equal to the input sample period when the Buffer overlap is Mo-1. For
negative Buffer overlap values, the block simply discards the appropriate
number of input samples after the buffer fills, and updates the scope display at
a slower rate than the zero-overlap case.
When the FFT length check box is deselected and the input is buffered, the
block uses the buffer size as the FFT size. If the check box is deselected and the
input is not buffered, the block uses the input size as the FFT size. When the
check box is selected, the FFT length parameter, Nfft, is enabled, and specifies

5-409
Spectrum Scope

the number of samples on which to perform the FFT. The block zero pads or
truncates every channel’s buffer to Nfft before computing the FFT.
The number of spectra to average is set by the Number of spectral averages
parameter. Setting this parameter to 1 effectively disables averaging; See
Short-Time FFT for more information.
In order to correctly scale the frequency axis (i.e., to determine the frequencies
against which the transformed input data should be plotted), the block needs
to know the actual sample period of the time-domain input. This is specified by
the Sample time of original time series parameter, Ts.
When the Inherit sample time from input check box is selected, the block
computes the frequency data from the sample period of the input to the block.
This is valid when the following conditions hold:

• The input to the block is the original signal, with no samples added or deleted
(by insertion of zeros, for example).
• The sample period of the time-domain signal in the simulation is equal to the
period with which the physical signal was originally sampled.
One example when these conditions do not hold, is such as when the input to
the block is not the original signal, but a zero-padded or otherwise rate-altered
version. In such cases, you should specify the appropriate value for the Sample
time of original time-series parameter.

The Frequency units parameter specifies whether the frequency axis values
should be in units of Hertz or rad/s, and the Frequency range parameter
specifies the range of frequencies over which the magnitudes in the input
should be plotted. The available options are [0..Fs/2], [-Fs/2..Fs/2], and [0..Fs],
where Fs is the time-domain signal’s actual sample frequency. If the
Frequency units parameter specifies Hertz, the spacing between frequency
points is 1/(NfftTs). For Frequency units of rad/sec, the spacing between
frequency points is 2π/(NfftTs).
Note that all of the FFT-based blocks in the DSP Blockset, including those in
the Power Spectrum Estimation library, compute the FFT at frequencies in the
range [0,Fs). The Frequency range parameter controls only the displayed
range of the signal.

5-410
 Spectrum Scope

For information about the scope window, as well as the Display properties,
Axis properties, and Line properties panels in the dialog box, see the
reference page for the Vector Scope block.

Dialog Box

Scope properties
Select to expose Scope properties panel. Tunable.
Buffer input
Select to expose Buffer input panel. Tunable.
Buffer size
The number of signal samples to include in each buffer. Tunable.
Buffer overlap
The number of samples by which consecutive buffers overlap. Tunable.
Specify FFT length
Select to expose Specify FFT length panel. Tunable.

5-411
Spectrum Scope

FFT length
The number of samples on which to perform the FFT. If the FFT length
differs from the buffer size, the data is zero-padded or truncated as needed.
Tunable.
Number of spectral averages
The the number of spectra to average. Setting this parameter to 1 effectively
disables averaging. See Short-Time FFT for more information. Tunable.
Display properties
Select to expose the Display properties panel. See Vector Scope for more
information. Tunable.
Axis properties
Select to expose the Axis properties panel. See Vector Scope for more
information. Tunable.
Line properties
Select to expose the Line properties panel. See Vector Scope for more
information. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also FFT DSP Blockset

Vector Scope DSP Blockset

See “Viewing Signals” on page 3-80 for related information.

5-412
 Stack

Purpose 5Stack
Store inputs into a LIFO register.

Library Signal Management / Buffers

Description The Stack block stores a sequence of input samples in a LIFO (last in, first out)
register. The register capacity is set by the Stack depth parameter, and inputs
can be scalars, vectors, or matrices.
The block pushes the input at the In port onto the top of the stack when a
trigger event is received at the Push port. When a trigger event is received at
the Pop port, the block pops the top element off the stack and holds the Out port
at that value. The last input to be pushed onto the stack is always the first to
be popped off.
Pushing the stack Popping the stack

1100 1100
last in first out

1111 1100 1111

1001 1111 1001

0000 1001 0000

0101 0000 0101

stack depth
1101 0101 1101

empty 1101 empty

empty empty oldest empty

input
empty empty empty

A trigger event at the optional Clr port (enabled by the Clear input check box)
empties the stack contents. If Clear output port on reset is selected, then a
trigger event at the Clr port empties the stack and sets the value at the Out
port to zero. This setting also applies when a disabled subsystem containing
the Stack block is re-enabled; the Out port value is only reset to zero in this case
if Clear output port on reset is selected.

5-413
Stack

When two or more of the control input ports are triggered at the same time
step, the operations are executed in the following order:

1 Clr
2 Push
3 Pop

The triggering event for the Push, Pop, and Clr ports is specified by the Trigger
type pop-up menu, and can be one of the following:

• Rising edge triggers execution of the block when the trigger input rises from
a negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers execution of the block when the trigger input falls from
a positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers execution of the block when either a rising or falling
edge (as described above) occurs.

The Push full stack parameter specifies the block’s behavior when a trigger is
received at the Push port but the register is full. The Pop empty stack
parameter specifies the block’s behavior when a trigger is received at the Pop
port but the register is empty. The following options are available for both
cases:

• Ignore – Ignore the trigger event, and continue the simulation.

• Warning – Ignore the trigger event, but display a warning message in the
MATLAB command window.
• Error – Display an error dialog box and terminate the simulation.

The Push full stack parameter additionally offers the Dynamic reallocation
option, which dynamically resizes the register to accept as many additional
inputs as memory permits. To find out how many elements are on the stack at
a given time, enable the Num output port by selecting the Output number of
stack entries option.

Examples Example 1
The table below illustrates the Stack block’s operation for a Stack depth of 4,
Trigger type of Either edge, and Clear output port on reset enabled.
Because the block triggers on both rising and falling edges in this example,
each transition from 1 to 0 or 0 to 1 in the Push, Pop, and Clr columns below

5-414
 Stack

represents a distinct trigger event. A 1 in the Empty column indicates an empty

buffer, while a 1 in the Full column indicates a full buffer.

In Push Pop Clr Stack Out Empty Full Num

1 0 0 0 top bottom 0 1 0 0

2 1 0 0 top 2 bottom 0 0 0 1

3 0 0 0 top 3 2 bottom 0 0 0 2

4 1 0 0 top 4 3 2 bottom 0 0 0 3

5 0 0 0 top 5 4 3 2 bottom 0 0 1 4

6 0 1 0 top 4 3 2 bottom 5 0 0 3

7 0 0 0 top 3 2 bottom 4 0 0 2

8 0 1 0 top 2 bottom 3 0 0 1

9 0 0 0 top bottom 2 1 0 0

10 1 0 0 top 10 bottom 2 0 0 1

11 0 0 0 top 11 10 bottom 2 0 0 2

12 1 0 1 top 12 bottom 0 0 0 1

Note that at the last step shown, the Push and Clr ports are triggered
simultaneously. The Clr trigger takes precedence, and the stack is first cleared
and then pushed.

Example 2
The dspqdemo demo provides an example of the related Queue block.

5-415
Stack

Dialog Box

Stack depth
The number of entries that the LIFO register can hold.
Trigger type
The type of event that triggers the block’s execution. Tunable.
Push full stack
Response to a trigger received at the Push port when the register is full.
Pop empty stack
Response to a trigger received at the Pop port when the register is empty.
Tunable.
Empty stack output
Enable the Empty output port, which is high (1) when the stack is empty,
and low (0) otherwise.
Full stack output
Enable the Full output port, which is high (1) when the stack is full, and
low (0) otherwise. The Full port remains low when Dynamic reallocation
is selected from the Push full stack parameter.
Output number of stack entries
Enable the Num output port, which tracks the number of entries currently
on the stack.

5-416
 Stack

Clear input
Enable the Clr input port, which empties the stack when the trigger
specified by the Trigger type is received.
Clear output port on reset
Reset the Out port to zero (in addition to clearing the stack) when a trigger
is received at the Clr input port. Tunable.

Supported Double-precision floating point

Data Types

See Also Buffer DSP Blockset

Delay Line DSP Blockset
Queue DSP Blockset

5-417
Standard Deviation

Purpose 5Standard Deviation

Find the standard deviation of an input or sequence of inputs.

Library Statistics

Description The Standard Deviation block computes the standard deviation of each column
in the input, or tracks the standard deviation of a sequence of inputs over a
period of time. The Running standard deviation parameter selects between
basic operation and running operation.

Basic Operation
When the Running standard deviation check box is not selected, the block
computes the standard deviation of each column in M-by-N input matrix u
independently at each sample time.
y = std(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors. (A scalar input
generates a zero-valued output.)
The output at each sample time, y, is a 1-by-N vector containing the standard
deviation for each column in u. For purely real or purely imaginary inputs, the
standard deviation of the jth column is the square root of the variance

∑
2
u ij – µ j

yj = σj = i=1
----------------------------------- 1≤j≤N
M–1

where µj is the mean of jth column. For complex inputs, the output is the total
standard deviation for each column in u, which is the square root of the total
variance for that column.

2 2
σj = σ j, Re + σ j, Im

Note that the total standard deviation is not equal to the sum of the real and
imaginary standard deviations. The frame status of the output is the same as
that of the input.

5-418
 Standard Deviation

Running Operation
When the Running standard deviation check box is selected, the block tracks
the standard deviation of each channel in a time-sequence of M-by-N inputs.
For sample-based inputs, the output is a sample-based M-by-N matrix with
each element yij containing the standard deviation of element uij over all inputs
since the last reset. For frame-based inputs, the output is a frame-based
M-by-N matrix with each element yij containing the standard deviation of the
jth column over all inputs since the last reset, up to and including element uij
of the current input.
If the Reset port parameter is set to Non-zero sample, the optional Rst port
is enabled and the block resets the running standard deviation when the scalar
input at the Rst port is nonzero. (The Rst port can be disabled by setting the
Reset port parameter to None.)

As in basic operation, length-M 1-D vector inputs and sample-based length-M

row vector inputs are both treated as M-by-1 column vectors.

Example The Standard Deviation block in the model below calculates the running
standard deviation of a frame-based 3-by-2 (two-channel) matrix input, u. The
running standard deviation is reset at t=2 by an impulse to the block’s Rst port.

The Standard Deviation block has the following settings:

• Running standard deviation =

• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

5-419
Standard Deviation

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

The block’s operation is shown in the figure below.

In Rst Output

ch1 ch2 ch1 ch2

61 0 0
First First output
13 t=0 0 3.54 1.41
input 39 2.52 4.16

–7 2 5.56 3.59
2 4 t=1 0 4.85 3.11
5 1 4.63 3.01

8 6 0 0
Simulation time

0 2 t=2 1 Reset 5.66 2.83

–1 5 4.93 2.08

–3 0 4.83 2.75
2 4 t=3 0 4.21 2.41
1 17 3.76 5.96

5-420
 Standard Deviation

Dialog Box

Running standard deviation

Enables running operation when selected.
Reset port
Enables the Rst input port when set to Non-zero sample, and disables the
Rst input port when set to None.

Supported Double-precision floating point

Data Types

See Also Mean DSP Blockset

RMS DSP Blockset
Variance DSP Blockset
std MATLAB

5-421
Submatrix

Purpose 5Submatrix
Select a subset of elements (submatrix) from a matrix input.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations,

Signal Management / Indexing

Description The Submatrix block extracts a contiguous submatrix from the M-by-N input
matrix u. A length-M 1-D vector input is treated as an M-by-1 matrix. The Row
span parameter provides three options for specifying the range of rows in u to
be retained in submatrix output y:
• All rows
Specifies that y contains all M rows of u.
• One row
Specifies that y contains only one row from u. The Starting row parameter
(described below) is enabled to allow selection of the desired row.
• Range of rows
Specifies that y contains one or more rows from u. The Row and Ending row
parameters (described below) are enabled to allow selection of the desired
range of rows.

The Column span parameter contains a corresponding set of three options for
specifying the range of columns in u to be retained in submatrix y: All
columns, One column, or Range of columns. The One column option enables
the Column parameter, and Range of columns options enable the Starting
column and Ending column parameters.

The output has the same frame status as the input.

Range Specification Options

When One row or Range of rows is selected from the Row span parameter,
the desired row or range of rows is specified by the Row parameter, or the
Starting row and Ending row parameters. Similarly, when One column or
Range of columns is selected from the Column span parameter, the desired
column or range of columns is specified by the Column parameter, or the
Starting column and Ending column parameters.

5-422
 Submatrix

The Row, Column, Starting row or Starting column can be specified in six
ways:
• First
For rows, this specifies that the first row of u should be used as the first row
of y. If all columns are to be included, this is equivalent to y(1,:) = u(1,:).
For columns, this specifies that the first column of u should be used as the
first column of y. If all rows are to be included, this is equivalent to
y(:,1) = u(:,1).
• Index
For rows, this specifies that the row of u, firstrow, forward-indexed by the
Row index parameter or the Starting row index parameter, should be used
as the first row of y. If all columns are to be included, this is equivalent to
y(1,:) = u(firstrow,:).
For columns, this specifies that the column of u, forward-indexed by the
Column index parameter or the Starting column index parameter,
firstcol, should be used as the first column of y. If all rows are to be
included, this is equivalent to y(:,1) = u(:,firstcol).
• Offset from last
For rows, this specifies that the row of u offset from row M by the Row offset
or Starting row offset parameter, firstrow, should be used as the first row
of y. If all columns are to be included, this is equivalent to
y(1,:) = u(M-firstrow,:).
For columns, this specifies that the column of u offset from column N by the
Column offset or Starting column offset parameter, firstcol, should be
used as the first column of y. If all rows are to be included, this is equivalent
to y(:,1) = u(:,N-firstcol).
• Last
For rows, this specifies that the last row of u should be used as the only row
of y. If all columns are to be included, this is equivalent to y = u(M,:).
For columns, this specifies that the last column of u should be used as the
only column of y. If all rows are to be included, this is equivalent to
y = u(:,N).
• Offset from middle
For rows, this specifies that the row of u offset from row M/2 by the Starting
row offset parameter, firstrow, should be used as the first row of y. If all

5-423
Submatrix

columns are to be included, this is equivalent to

y(1,:) = u(M/2-firstrow,:).
For columns, this specifies that the column of u offset from column N/2 by the
Starting column offset parameter, firstcol, should be used as the first
column of y. If all rows are to be included, this is equivalent to
y(:,1) = u(:,N/2-firstcol).
• Middle
For rows, this specifies that the middle row of u should be used as the only
row of y. If all columns are to be included, this is equivalent to y = u(M/2,:).
For columns, this specifies that the middle column of u should be used as the
only column of y. If all rows are to be included, this is equivalent to
y = u(:,N/2).

The Ending row or Ending column can similarly be specified in five ways:
• Index
For rows, this specifies that the row of u forward-indexed by the Ending row
index parameter, lastrow, should be used as the last row of y. If all columns
are to be included, this is equivalent to y(end,:) = u(lastrow,:).
For columns, this specifies that the column of u forward-indexed by the
Ending column index parameter, lastcol, should be used as the last
column of y. If all rows are to be included, this is equivalent to
y(:,end) = u(:,lastcol).
• Offset from last
For rows, this specifies that the row of u offset from row M by the Ending
row offset parameter, lastrow, should be used as the last row of y. If all
columns are to be included, this is equivalent to
y(end,:) = u(M-lastrow,:).
For columns, this specifies that the column of u offset from column N by the
Ending column offset parameter, lastcol, should be used as the last
column of y. If all rows are to be included, this is equivalent to
y(:,end) = u(:,N-lastcol).

5-424
 Submatrix

• Last
For rows, this specifies that the last row of u should be used as the last row
of y. If all columns are to be included, this is equivalent to
y(end,:) = u(M,:).
For columns, this specifies that the last column of u should be used as the
last column of y. If all rows are to be included, this is equivalent to
y(:,end) = u(:,N).
• Offset from middle
For rows, this specifies that the row of u offset from row M/2 by the Ending
row offset parameter, lastrow, should be used as the last row of y. If all
columns are to be included, this is equivalent to
y(end,:) = u(M/2-lastrow,:).
For columns, this specifies that the column of u offset from column N/2 by the
Ending column offset parameter, lastcol, should be used as the last
column of y. If all rows are to be included, this is equivalent to
y(:,end) = u(:,N/2-lastcol).
• Middle
For rows, this specifies that the middle row of u should be used as the last
row of y. If all columns are to be included, this is equivalent to
y(end,:) = u(M/2,:).
For columns, this specifies that the middle column of u should be used as the
last column of y. If all rows are to be included, this is equivalent to
y(:,end) = u(:,N/2).

Example To extract the lower-right 3-by-2 submatrix from a 5-by-7 input matrix, enter
the following set of parameters:

• Row span = Range of rows

• Starting row = Index
• Starting row index = 3
• Ending row = Last
• Column span = Range of columns
• Starting column = Offset from last
• Starting column offset = 1
• Ending column = Last

5-425
Submatrix

The figure below shows the operation for a 5-by-7 matrix with random integer
elements, randint(5,7,10).

8 6 5 3 0 1 6
2 4 7 8 3 6 3 2 7
5 0 8 8 7 2 7 4 7
4 7 6 3 0 4 7 1 5
8 4 1 8 1 1 5

There are often several possible parameter combinations that select the same
submatrix from the input. For example, instead of specifying Last for Ending
column, you could select the same submatrix by specifying:

• Ending column = Index

• Ending column index = 7

Dialog Box

The parameters displayed in the dialog box vary for different menu
combinations. Only some of the parameters listed below are visible in the
dialog box at any one time.

5-426
 Submatrix

Row span
The range of input rows to be retained in the output. Options are All rows,
One row, or Range of rows.

Row/Starting row
The input row to be used as the first row of the output. Row is enabled
when One row is selected from Row span, and Starting row when Range
of rows is selected from Row span.

Row index/Starting row index

The index of the input row to be used as the first row of the output. Row
index is enabled when Index is selected from Row, and Starting row
index when Index is selected from Starting row.

Row offset/Starting row offset

The offset of the input row to be used as the first row of the output. Row
offset is enabled when Offset from middle or Offset from last is selected
from Row, and Starting row offset is enabled when Offset from middle or
Offset from last is selected from Starting row.

Ending row
The input row to be used as the last row of the output. This parameter is
enabled when Range of rows is selected from Row span and any option
but Last is selected from Starting row.
Ending row index
The index of the input row to be used as the last row of the output. This
parameter is enabled when Index is selected from Ending row.
Ending row offset
The offset of the input row to be used as the last row of the output. This
parameter is enabled when Offset from middle or Offset from last is
selected from Ending row.
Column span
The range of input columns to be retained in the output. Options are All
columns, One column, or Range of columns.

5-427
Submatrix

Column/Starting column
The input column to be used as the first column of the output. Column is
enabled when One column is selected from Column span, and Starting
column is enabled when Range of columns is selected from Column span.

Column index/Starting column index

The index of the input column to be used as the first column of the output.
Column index is enabled when Index is selected from Column, and
Starting column index is enabled when Index is selected from Starting
column.

Column offset/Starting column offset

The offset of the input column to be used as the first column of the output.
Column offset is enabled when Offset from middle or Offset from last is
selected from Column. Starting column offset is enabled when Offset
from middle or Offset from last is selected from Starting column.

Ending column
The input column to be used as the last column of the output. This
parameter is enabled when Range of columns is selected from Column
span and any option but Last is selected from Starting column.

Ending column index

The index of the input column to be used as the last column of the output.
This parameter is enabled when Index is selected from Ending column.
Ending column offset
The offset of the input column to be used as the last column of the output.
This parameter is enabled when Offset from middle or Offset from last is
selected from Ending column.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-428
 Submatrix

See Also Reshape Simulink

Selector Simulink
Variable Selector DSP Blockset
reshape MATLAB

See “Deconstructing Signals” on page 3-54 for related information.

5-429
SVD Solver

Purpose 5SVD Solver

Solve the equation AX=B using singular value decomposition.

Library Math Functions / Matrices and Linear Algebra / Linear System Solvers

Description The SVD Solver block solves the linear system AX=B, which can be
overdetermined, underdetermined, or exactly determined. The system is solved
by applying SVD factorization to the M-by-N matrix, A, at the A port. The input
to the B port is the right hand-side M-by-L matrix, B. A length-M 1-D vector
input at either port is treated as an M-by-1 matrix.
The output at the x port is the N-by-L matrix, X. X is always sample based, and
is chosen to minimize the sum of the squares of the elements of B-AX. When B
is a vector, this solution minimizes the vector 2-norm of the residual (B-AX is
the residual). When B is a matrix, this solution minimizes the matrix
Frobenius norm of the residual. In this case, the columns of X are the solutions
to the L corresponding systems AXk=Bk, where Bk is the kth column of B, and
Xk is the kth column of X.
X is known as the minimum-norm-residual solution to AX=B. The
minimum-norm-residual solution is unique for overdetermined and exactly
determined linear systems, but it is not unique for underdetermined linear
systems. Thus when the SVD Solver is applied to an underdetermined system,
the output X is chosen such that the number of nonzero entries in X is
minimized.

Dialog Box

Supported Double-precision floating point

Data Types

5-430
 SVD Solver

See Also Autocorrelation LPC DSP Blockset

Cholesky Solver DSP Blockset
LDL Solver DSP Blockset
Levinson-Durbin DSP Blockset
LU Inverse DSP Blockset
Pseudoinverse DSP Blockset
QR Solver DSP Blockset
Singular Value Decomposition DSP Blockset

See “Solving Linear Systems” on page 4-16 for related information.

5-431
Time Scope

5Time Scope

The Time Scope block is the same as the Scope block in Simulink. To learn how
to use the Time Scope block, see the Scope block reference page in the Simulink
documentation.

Library DSP Sinks

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-432
 Time-Varying Direct-Form II Transpose Filter

Purpose 5Time-Varying Direct-Form II Transpose Filter

Apply a variable IIR filter to the input.

Library Filtering / Filter Designs

Description The Time-Varying Direct-Form II Transpose Filter block is a version of the

Direct-Form II Transpose Filter block whose filter coefficients can be updated
during the simulation. The block applies a direct-form II transposed IIR filter
to the top input (In).

x( k) ...
b( m) b(3) b(2) b(1)

Σ z-1
... Σ z-1 Σ z-1 Σ y(k)
zn-1(k) z2( k) z 1 ( k)
-a(n) -a(3) -a(2)
...

This is a canonical form that has the minimum number of delay elements. The
filter order is max(m,n)-1.
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and an M-by-N frame-based matrix input is treated as N
independent channels. In both cases, the block filters each channel
independently over time, and the output has the same size and frame status as
the input.
The block’s two lower inputs (Num and Den) specify the filter’s transfer function,
–1 –( m – 1 )
B(z) b1 + b2 z + … + bm + 1 z
H ( z ) = ------------ = -----------------------------------------------------------------------------------
A(z) –1
a1 + a2 z + … + an + 1 z
–( n – 1 )

By default the filter coefficients are normalized by a1. To prevent

normalization by a1, deselect the Support non-normalized filters check box.

Filter Type
The Filter type parameter specifies whether the filter is an all-zero (FIR or
MA) filter, all-pole (AR) filter, or pole-zero (IIR or ARMA) filter:

5-433
Time-Varying Direct-Form II Transpose Filter

• Pole-zero
The block accepts inputs for both the numerator (Num) and denominator (Den)
vectors.
Input Num is a vector of numerator coefficients,
[b(1) b(2) ... b(m)]

and input Den is a vector of denominator coefficients,

[a(1) a(2) ... a(n)]

• All-zero
The block accepts only the numerator vector (Num). The denominator of the
all-zero filter is 1.
• All-pole
The block accepts only the denominator vector (Den). The numerator of the
all-pole filter is 1.
For any of these designs, the coefficient vector inputs can change over time to
alter the filter’s response characteristics during the simulation.

Initial Conditions
In its default form, the filter initializes the internal filter states to zero, which
is equivalent to assuming past inputs and outputs are zero. The block also
accepts optional nonzero initial conditions for the filter delays. Note that the
number of filter states (delay elements) per input channel is
max(m,n)-1

The Initial conditions parameter may take one of four forms:

• Empty matrix
The empty matrix, [], causes a zero (0) initial condition to be applied to all
delay elements in each filter channel.
• Scalar
The scalar value is copied to all delay elements in each filter channel. Note
that a value of zero is equivalent to setting the Initial conditions parameter
to the empty matrix, [].

5-434
 Time-Varying Direct-Form II Transpose Filter

• Vector
The vector has a length equal to the number of delay elements in each filter
channel, max(m,n)-1, and specifies a unique initial condition for each delay
element in the filter channel. This vector of initial conditions is applied to
each filter channel.
• Matrix
The matrix specifies a unique initial condition for each delay element, and
can specify different initial conditions for each filter channel. The matrix
must have the same number of rows as the number of delay elements in the
filter, max(m,n)-1, and must have one column per filter channel.

Filter Update Rate

In frame-based operation, the Filter update rate parameter determines how
frequently the block updates the filter coefficients (i.e., how often it checks the
Num and Den inputs). There are two available options:

• One filter per sample time

The block updates the filter coefficients (from inputs Num and Den) for each
individual scalar sample in the frame-based input. This means that each
output sample could potentially be computed by a different filter (assuming
that Num and Den inputs are updated frequently enough).
• One filter per frame time
The block updates the filter coefficients (from inputs Num and Den) for each
new input frame, rather than at each sample in the frame. This means that
each output sample in a given frame is a result of an identical filtering
process.

5-435
Time-Varying Direct-Form II Transpose Filter

Dialog Box

Filter type
The type of filter to apply: Pole-Zero (IIR), All-Zero (FIR), or All-Pole
(AR). The Num and Den input ports are enabled or disabled as appropriate.

Initial conditions
The filter’s initial conditions, a scalar, vector, or matrix.
Support non-normalized filters
Normalizes the filter by a1 when selected.
Filter update rate
The frequency with which the block updates the filter coefficients; once per
sample, or once per frame.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

5-436
 Time-Varying Direct-Form II Transpose Filter

See Also Discrete Filter Simulink

Filter Realization Wizard DSP Blockset
Direct-Form II Transpose Filter DSP Blockset
Time-Varying Lattice Filter DSP Blockset
filter MATLAB

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-437
Time-Varying Lattice Filter

Purpose 5Time-Varying Lattice Filter

Apply a variable lattice filter to the input.

Library Filtering / Filter Designs

Description The Time-Varying Lattice Filter block applies a moving average (MA) or
autoregressive (AR) lattice filter to the top input (In). The filter reflection
coefficients are specified by the vector input to the MA or AR port, and can vary
with time.
An M-by-N sample-based matrix input to the In port is treated as M∗N
independent channels, and an M-by-N frame-based matrix input is treated as
N independent channels. In both cases, the block filters each channel
independently over time, and the output has the same size and frame status as
the input.

Filter Type
The Filter type parameter specifies whether the filter is an all-zero
(FIR or MA) filter or all-pole (AR) filter.
• All-zero
The block constructs an nth order MA filter using the n reflection coefficients
contained in the vector input to the MA port.
k = [k(1) k(2) ... k(n)]

• All-pole
The block constructs an nth order AR filter using the n reflection coefficients
contained in the vector input to the AR port.
k = [k(1) k(2) ... k(n)]

For both designs, the coefficient vector inputs can change over time to alter the
filter’s response characteristics during the simulation.

Initial Conditions
In its default form, the filter initializes the internal filter states to zero, which
is equivalent to assuming past inputs and outputs are zero. The block also
accepts optional nonzero initial conditions for the filter delays. Note that the
number of filter states (delay elements) per input channel is
length(k)

5-438
 Time-Varying Lattice Filter

The Initial conditions parameter may take one of four forms:

• Empty matrix
The empty matrix, [], causes a zero (0) initial condition to be applied to all
delay elements in each filter channel.
• Scalar
The scalar value is copied to all delay elements in each filter channel. Note
that a value of zero is equivalent to setting the Initial conditions parameter
to the empty matrix.
• Vector
The vector has a length equal to the number of delay elements in each filter
channel, length(k), and specifies a unique initial condition for each delay
element in the filter channel. This vector of initial conditions is applied to
each filter channel.
• Matrix
The matrix specifies a unique initial condition for each delay element, and
can specify different initial conditions for each filter channel. The matrix
must have the same number of rows as the number of delay elements in the
filter, length(k), and must have one column per filter channel.

Filter Update Rate

In frame-based operation, the Filter update rate parameter determines how
frequently the block updates the filter coefficients (i.e., how often it checks the
MA or AR input). There are two available options:

• One filter per sample time

The block updates the filter coefficients (from input MA or AR) for each
individual scalar sample in the framed input. This means that each output
sample could potentially be computed by a different filter (assuming that the
MA or AR input is updated frequently enough).
• One filter per frame time
The block updates the filter coefficients (from input MA or AR) for each new
input frame, rather than at each sample in the frame. This means that each
output sample in a given frame is a result of an identical filtering process.

5-439
Time-Varying Lattice Filter

Dialog Box

Filter type
The type of filter to apply: MA or AR. The MA or AR input port is enabled or
disabled appropriately.
Initial conditions
The filter’s initial conditions.
Filter update rate
The frequency with which the block updates the filter coefficients; once per
sample, or once per frame.

References Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing.

Englewood Cliffs, NJ: Prentice Hall, 1989.
Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood
Cliffs, NJ: Prentice-Hall, 1996.

Supported Double-precision floating point

Data Types

See Also Discrete Filter Simulink

Direct-Form II Transpose Filter DSP Blockset
Filter Realization Wizard DSP Blockset
Time-Varying Direct-Form II Transpose Filter DSP Blockset
filter MATLAB

5-440
 Time-Varying Lattice Filter

See “Designing Filters with Various Filter Structures” on page 4-6 for related
information.

5-441
Toeplitz

Purpose 5Toeplitz
Generate a matrix with Toeplitz symmetry.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Toeplitz block generates a Toeplitz matrix from inputs defining the first
column and first row. The top input (Col) is a vector containing the values to
be placed in the first column of the matrix, and the bottom input (Row) is a
vector containing the values to be placed in the first row of the matrix.
y = toeplitz(Col,Row) % Equivalent MATLAB code

The other elements of the matrix obey the relationship

y(i,j) = y(i-1,j-1)

and the output has dimension [length(Col) length(Row)]. The y(1,1)

element is inherited from the Col input. For example, the following inputs
Col = [1 2 3 4 5]
Row = [7 7 3 3 2 1 3]

produce the Toeplitz matrix

1 7 3 3 2 1 3
2 1 7 3 3 2 1
3 2 1 7 3 3 2
4 3 2 1 7 3 3
5 4 3 2 1 7 3

If both of the inputs are sample-based, the output is sample-based. Otherwise,

the output is frame-based.
When the Symmetric check box is selected, the block generates a symmetric
(Hermitian) Toeplitz matrix from a single input, u, defining both the first row
and first column of the matrix.
y = toeplitz(u) % Equivalent MATLAB code

The output has dimension [length(u) length(u)]. For example, the Toeplitz
matrix generated from the input vector [1 2 3 4] is

5-442
 Toeplitz

1 2 3 4
2 1 2 3
3 2 1 2
4 3 2 1

The output has the same frame status as the input.

Dialog Box

Symmetric
When selected, enables the single-input configuration for symmetric
Toeplitz matrix output.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Constant Diagonal Matrix DSP Blockset

toeplitz MATLAB

5-443
To Wave Device

Purpose 5To Wave Device

Send audio data to a standard audio device in real-time (Windows only).

Library DSP Sinks

Description The To Wave Device block sends audio data to a standard Windows audio
device in real-time. It is compatible with most popular Windows hardware,
including Sound Blaster cards. (Models that contain both this block and the
From Wave Device block require a duplex-capable sound card.) The data is sent
to the hardware in uncompressed PCM (pulse code modulation) format, and
should typically be sampled at one of the standard Windows audio device rates:
8000, 11025, 22050, or 44100 Hz. Some hardware may support other rates in
addition to these.
The Use default audio device parameter allows the block to detect and use the
system’s default audio hardware. This option should be selected on systems
that have a single sound device installed, or when the default sound device on
a multiple-device system is the desired target. In cases when the default sound
device is not the desired output device, deselect Use default audio device, and
enter the desired device identification number in the Audio device ID
parameter. The device ID is an integer value that the block associates with the
sound device. A 3-device system, for example, has device ID numbers of 1, 2,
and 3.
The input to the block, u, can contain audio data from a mono or stereo signal.
A mono signal is represented as either a sample-based scalar or frame-based
length-M vector, while a stereo signal is represented as a sample-based
length-2 vector or frame-based M-by-2 matrix. If the input data type is double,
single, or int16, the block conveys the signal samples to the audio device
using 16 bits. If the input data type is uint8, the block conveys the signal
samples to the audio device using 8 bits.
sound(u,Fs,bits) % Equivalent MATLAB code

Note that the block does not support uint16 or int8 data types. The 16-bit
sample width requires more memory but in general yields better fidelity. The
amplitude of the input should be in the range ±1. Values outside this range are
clipped to the nearest allowable value.

5-444
 To Wave Device

Buffering
Because the audio device generates real-time audio output, Simulink must
maintain a continuous flow of data to the device throughout the simulation.
Delays in passing data to the audio hardware can result in hardware errors or
distortion of the output. This means that the To Wave Device block must in
principle supply data to the audio hardware as quickly as the hardware reads
the data. However, the To Wave Device block often cannot match the
throughput rate of the audio hardware, especially when the simulation is
running from within Simulink rather than as generated code. (Simulink
execution speed routinely varies during the simulation as the host operating
system services other processes.) The block must therefore rely on a buffering
strategy to ensure that signal data is accessible to the hardware on demand.
At the start of the simulation, the To Wave Device block writes Td seconds
worth of signal data to the device (hardware) buffer, where Td is specified by
the Initial output delay parameter. When this initial data is loaded into the
buffer, the audio device begins processing the buffered data, and continues at
a constant rate until the buffer empties. The size of the buffer, Tb, is specified
by the Queue duration parameter. As the audio device reads data from the
front of the buffer, the To Wave Device block continues appending inputs to the
back of the buffer at the rate they are received.
The following figure shows an audio signal with 8 samples per frame. The
buffer of the sound board has a five-frame capacity, not fully used at the instant
shown. (If the signal sample rate was 8kHz, for instance, this small buffer
could hold approximately 0.005 seconds of data.)
Simulink execution rate varies Hardware execution rate is constant
board

Simulation delay
Hardware buffer with no delays
5-frame capacity

If the simulation throughput rate is higher than the hardware throughput

rate, the buffer remains at a constant level throughout the simulation. If
necessary, the To Wave Device block buffers inputs until space becomes
available in the hardware buffer (i.e., data is not thrown away). More typically,

5-445
To Wave Device

the hardware throughput rate is higher than the simulation throughput rate,
and the buffer tends to empty over the duration of the simulation.
Under normal operation, an empty buffer indicates that the simulation is
finished, and the entire length of the audio signal has been processed.
However, if the buffer size is too small in relation to the simulation throughput
rate, the buffer may also empty before the entire length of signal is processed.
This usually results in a device error or undesired device output.
When the device fails to process the entire signal length because the buffer
prematurely empties, you can choose to either increase the buffer size or the
simulation throughput rate.

• Increase the buffer size. The Queue duration parameter specifies the length
of signal, Tb (in real-time seconds), to buffer to the audio device during the
simulation. The number of frames buffered is approximately
Tb Fs
-------------
Mo

where Fs is the sample rate of the signal and Mo is the number of samples
per frame. The optimal buffer size for a given signal depends on the signal
length, the frame size, and the speed of the simulation. The maximum
number of frames that can be buffered is 1024.
• Increase the simulation throughput rate. Two useful methods for improving
simulation throughput rates are increasing the signal frame size and
compiling the simulation into native code.
- Increase frame sizes (and convert sample-based signals to frame-based
signals) throughout the model to reduce the amount of block-to-block
communication overhead. This can drastically increase throughput rates
in many cases. However, larger frame sizes generally result in greater
model latency due to initial buffering operations. (Note that increasing the
audio signal frame size does not affect the number of samples buffered to
the hardware since the Queue duration is specified in seconds.)
- Generate executable code with Real-Time Workshop. Native code runs
much faster than Simulink, and should provide rates adequate for
real-time audio processing.
Audio problems at startup can often be corrected by entering a larger value for
the Initial output delay parameter, which allows a greater portion of the

5-446
 To Wave Device

signal to be preloaded into the hardware buffer. A value of 0 for the Initial
output delay parameter specifies the smallest possible initial delay, which is
one frame.
More general ways to improve throughput rates include simplifying the model,
and running the simulation on a faster PC processor. See the Simulink
documentation and “Delay and Latency” on page 3-85 for other ideas on
improving simulation performance.

Dialog Box

Queue duration (seconds)

The length of signal (in seconds) to buffer to the hardware at the start of
the simulation.
Initial output delay (seconds)
The amount of time by which to delay the initial output to the audio device.
A value of 0 specifies the smallest possible initial delay, a single frame.
Use default audio device
Directs audio output to the system’s default audio device when selected.
Deselect to enable the Audio device ID parameter and manually enter a
device ID number.
Audio device ID
The number of the audio device to receive the audio output. In a system
with several audio devices installed, a value of 1 selects the first audio card,

5-447
To Wave Device

a value of 2 selects the second audio card, and so on. Select Use default
audio device if the system has only a single audio card installed.

Supported Double-precision floating point

Data Types

See Also From Wave Device DSP Blockset

To Wave File DSP Blockset
sound MATLAB

See “Exporting and Playing WAV Files” on page 3-79 for related information.

5-448
 To Wave File

Purpose 5To Wave File

Write audio data to file in the Microsoft Wave (.wav) format (Windows only).

Library DSP Sinks

Description The To Wave File block writes audio data to a Microsoft Wave (.wav) file in the
uncompressed PCM (pulse code modulation) format. For compatibility reasons,
the sample rate of the discrete-time input signal should typically be one of the
standard Windows audio device rates (8000, 11025, 22050, or 44100 Hz),
although the block supports arbitrary rates.
The input to the block, u, can contain audio data from a mono or stereo signal.
A mono signal is represented as either a sample-based scalar or frame-based
length-M vector, while a stereo signal is represented as a sample-based
length-2 vector or frame-based M-by-2 matrix. The amplitude of the input
should be in the range ±1. Values outside this range are clipped to the nearest
allowable value.
wavwrite(u,Fs,bits,'filename') % Equivalent MATLAB code

The Sample Width (bits) parameter specifies the number of bits used to
represent the signal samples in the file. Two settings are available:

• 8 – allocates 8 bits to each sample, allowing a resolution of 256 levels

• 16 – allocates 16 bits to each sample, allowing a resolution of 65536 levels

The 16-bit sample width setting requires more memory but yields better
fidelity for double-precision inputs.
The File name parameter can specify an absolute or relative path to the file.
You do not need to specify the.wav extension. To reduce the required number
of file accesses, the block writes L consecutive samples to the file during each
access, where L is specified by the Minimum number of samples for each
write to file parameter (L ≥ M). For L < M, the block instead writes M
consecutive samples during each access. Larger values of L result in fewer file
accesses, which reduces run-time overhead.

5-449
To Wave File

Dialog Box

File name
The path and name of the file to write. Paths can be relative or absolute.
Tunable.
Sample width (bits)
The number of bits used to represent each signal sample. Tunable.
Minimum number of samples for each write to file
The number of consecutive samples to write with each file access, L.
Tunable.

Supported Double-precision floating point

Data Types

See Also From Wave File DSP Blockset

To Wave Device DSP Blockset
To Workspace Simulink
wavwrite MATLAB

See “Exporting and Playing WAV Files” on page 3-79 for related information.

5-450
 Transpose

Purpose 5Transpose
Compute the transpose of a matrix.

Library Math Functions / Matrices and Linear Algebra / Matrix Operations

Description The Transpose block transposes the M-by-N input matrix to size N-by-M. When
the Hermitian check box is selected, the block performs the Hermitian
(complex conjugate) transpose
y = u' % Equivalent MATLAB code

u *11 u *21
u 11 u 12 u 13
u' u *12 u *22
u 21 u 22 u 23
u *13 u *23

When the Hermitian check box is not selected, the block performs the
nonconjugate transpose
y = u.' % Equivalent MATLAB code

u 11 u 21
u 11 u 12 u 13
u.' u 12 u 22
u 21 u 22 u 23
u 13 u 23

A length-M 1-D vector input is treated as an M-by-1 matrix. The output is

always sample-based.

Dialog Box

Hermitian
When selected, specifies the complex conjugate transpose. Tunable, except
in Simulink’s external mode.

5-451
Transpose

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Permute Matrix DSP Blockset

Reshape Simulink
Submatrix DSP Blockset

5-452
 Triggered Delay Line

Purpose 5Triggered Delay Line

Buffer a sequence of inputs into a frame-based output.

Library Signal Management / Buffers

Description The Triggered Delay Line block acquires a collection of Mo input samples into
a frame, where Mo is specified by the Delay line size parameter. The block
buffers a single sample from input 1 whenever it is triggered by the control
signal at input 2 ( ). The newly acquired input sample is appended to the
output frame (in the same simulation step) so that the new output overlaps the
previous output by Mo-1 samples. Between triggering events the block ignores
input 1 and holds the output at its last value.
The triggering event at input 2 is specified by the Trigger type pop-up menu,
and can be one of the following:

• Rising edge triggers execution of the block when the trigger input rises from
a negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers execution of the block when the trigger input falls from
a positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers execution of the block when either a rising or falling
edge (as described above) occurs.

The Triggered Delay Line block has zero latency, so the new input appears at
the output in the same simulation time step. The output frame period is the
same as the input sample period, Tfo=Tsi.

Sample-Based Operation
In sample-based operation, the Triggered Delay Line block buffers a sequence
of sample-based length-N vector inputs (1-D, row, or column) into a sequence
of overlapping sample-based Mo-by-N matrix outputs, where Mo is specified by
the Delay line size parameter (Mo>1). That is, each input vector becomes a row
in the sample-based output matrix. When Mo=1, the input is simply passed
through to the output, and retains the same dimension. Sample-based
full-dimension matrix inputs are not accepted.

Frame-Based Operation
In frame-based operation, the Triggered Delay Line block rebuffers a sequence
of frame-based Mi-by-N matrix inputs into an sequence of overlapping

5-453
Triggered Delay Line

frame-based Mo-by-N matrix outputs, where Mo is the output frame size

specified by the Delay line size parameter (i.e., the number of consecutive
samples from the input frame to rebuffer into the output frame). Mo can be
greater or less than the input frame size, Mi. Each of the N input channels is
rebuffered independently.

Initial Conditions
The Triggered Delay Line block’s buffer is initialized to the value specified by
the Initial condition parameter. The block always outputs this buffer at the
first simulation step (t=0). If the block’s output is a vector, the Initial
condition can be a vector of the same size, or a scalar value to be repeated
across all elements of the initial output. If the block’s output is a matrix, the
Initial condition can be a matrix of the same size, a vector (of length equal to
the number of matrix rows) to be repeated across all columns of the initial
output, or a scalar to be repeated across all elements of the initial output.

Dialog Box

Trigger type
The type of event that triggers the block’s execution. Tunable.
Delay line size
The length of the output frame (number of rows in output matrix), Mo.
Initial condition
The value of the block’s initial output, a scalar, vector, or matrix.

5-454
 Triggered Delay Line

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

Delay Line DSP Blockset
Unbuffer DSP Blockset

5-455
Triggered Signal From Workspace

Purpose 5Triggered Signal From Workspace

Import signal samples from the MATLAB workspace when triggered.

Library DSP Sources

Description The Triggered Signal From Workspace block imports signal samples from the
MATLAB workspace into the Simulink model when triggered by the control
signal at the input port ( ). The Signal parameter specifies the name of a
MATLAB workspace variable containing the signal to import, or any valid
MATLAB expression defining a matrix or 3-D array.
When the Signal parameter specifies an M-by-N matrix (M≠1), each of the N
columns is treated as a distinct channel. The frame size is specified by the
Samples per frame parameter, Mo, and the output when triggered is an
Mo-by-N matrix containing Mo consecutive samples from each signal channel.
For Mo=1, the output is sample-based; otherwise the output is frame-based.
For convenience, an imported row vector (M=1) is treated as a single channel,
so the output dimension is Mo-by-1.
When the Signal parameter specifies an M-by-N-by-P array, the block
generates a single page of the array (an M-by-N matrix) at each trigger time.
The Samples per frame parameter must be set to 1, and the output is always
sample-based.

Trigger Event
The triggering event at the input port is specified by the Trigger type pop-up
menu, and can be one of the following:

• Rising edge triggers execution of the block when the trigger input rises from
a negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers execution of the block when the trigger input falls from
a positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers execution of the block when either a rising or falling
edge (as described above) occurs.

Initial and Final Conditions

The Initial output parameter specifies the output of the block from the start
of the simulation until the first trigger event arrives. Between trigger events,
the block holds the output value constant at its most recent value (i.e., no linear

5-456
 Triggered Signal From Workspace

interpolation takes place). For single-channel signals, the Initial output

parameter value can be a vector of length Mo or a scalar to repeat across the
Mo elements of the initial output frames. For matrix outputs (Mo-by-N or
M-by-N), the Initial output parameter value can be a vector of length N to
repeat across all rows of the initial outputs, or a scalar to repeat across all
elements of the initial matrix outputs.
When the block has output all of the available signal samples, it can start again
at the beginning of the signal, or simply repeat the final value or generate zeros
until the end of the simulation. (The block does not extrapolate the imported
signal beyond the last sample.) The Form output after final data value by
parameter controls this behavior:

• If Setting To Zero is specified, the block generates zero-valued outputs for

the duration of the simulation after generating the last frame of the signal.
• If Holding Final Value is specified, the block repeats the final sample for the
duration of the simulation after generating the last frame of the signal.
• If Cyclic Repetition is specified, the block repeats the signal from the
beginning after generating the last frame. If there are not enough samples
at the end of the signal to fill the final frame, the block zero-pads the final
frame as necessary to ensure that the output for each cycle is identical
(e.g., the ith frame of one cycle contains the same samples as the ith frame
of any other cycle).

5-457
Triggered Signal From Workspace

Dialog Box

Signal
The name of the MATLAB workspace variable from which to import the
signal, or a valid MATLAB expression specifying the signal.
Trigger type
The type of event that triggers the block’s execution. Tunable, except in
Simulink’s external mode.
Initial output
The value to output until the first trigger event is received.
Samples per frame
The number of samples, Mo, to buffer into each output frame. This value
must be 1 if a 3-D array is specified in the Signal parameter.
Form output after final data value by
Specifies the output after all of the specified signal samples have been
generated. The block can output zeros for the duration of the simulation
(Setting to zero), repeat the final data sample (Holding Final Value) or
repeat the entire signal from the beginning (Cyclic Repetition).

5-458
 Triggered Signal From Workspace

Supported (MATLAB commands for casting values to certain data types are provided in
Data Types parentheses.)
Boolean (boolean)
8-, 16-, and 32-bit signed integer (int8, int16, int32)
8-, 16-, and 32-bit unsigned integer (uint8, uint16, uint32)
Single-precision floating point (single)
Double-precision floating point (double)

See Also From Wave Device DSP Blockset

From Wave File DSP Blockset
Signal To Workspace DSP Blockset
Signal From Workspace DSP Blockset
Triggered To Workspace DSP Blockset

See the sections below for related information:

• “Discrete-Time Signals” on page 3-3

• “Multichannel Signals” on page 3-11
• “Benefits of Frame-Based Processing” on page 3-14
• “Creating Signals Using the Signal From Workspace Block” on page 3-38
• “Importing Signals” on page 3-62

5-459
Triggered To Workspace

Purpose 5Triggered To Workspace

Write the input sample to the workspace when triggered.

Library DSP Sinks

Description The Triggered To Workspace block creates a matrix or array variable in the
workspace, where it stores the acquired inputs at the end of a simulation. An
existing variable with the same name is overwritten.
For an M-by-N frame-based input, the block creates an N-column workspace
matrix in which each group of M rows represents a single input frame from
each of N channels (the most recent frame occupying the last M rows). The
maximum size of this workspace variable is limited to P-by-N, where P is the
Maximum number of rows parameter. (If the simulation progresses long
enough for the block to acquire more than P samples, it stores only the most
recent P samples.) The Decimation factor, D, allows you to store only every
Dth input frame.
For an M-by-N sample-based input, the block creates a three-dimensional
array in which each M-by-N page represents a single sample from each of M∗N
channels (the most recent input matrix occupying the last page). The
maximum size of this variable is limited to M-by-N-by-P, where P is the
Maximum number of rows parameter. (If the simulation progresses long
enough for the block to acquire more than P inputs, it stores only the last P
inputs.) The Decimation factor, D, allows you to store only every Dth input
matrix.
The block acquires and buffers a single frame from input 1 whenever it is
triggered by the control signal at input 2 ( ). At all other times, the block
ignores input 1. The triggering event at input 2 is specified by the Trigger type
pop-up menu, and can be one of the following:

• Rising edge triggers execution of the block when the trigger input rises from
a negative value to zero or a positive value, or from zero to a positive value.
• Falling edge triggers execution of the block when the trigger input falls from
a positive value to zero or a negative value, or from zero to a negative value.
• Either edge triggers execution of the block when either a rising or falling
edge (as described above) occurs.

To save a record of the sample time corresponding to each sample value, check
the Time box in the Save to workspace parameters list of the Simulation

5-460
 Triggered To Workspace

Parameters dialog. You can access these parameters by selecting Parameters

from the Simulation menu, and clicking on the Workspace I/O tab.
The nontriggered version of this block is To Workspace.

Dialog Box

Trigger type
The type of event that triggers the block’s execution. Tunable.
Variable name
The name of the workspace matrix in which to store the data.
Maximum number of rows
The maximum number of rows (one row per time step) to be saved, P. The
default is 100 rows.
Decimation
The decimation factor, D. The default is 1.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-461
Triggered To Workspace

See Also Signal From Workspace DSP Blockset

To Workspace Simulink

See “Exporting Signals” on page 3-72 for related information.

5-462
 Unbuffer

Purpose 5Unbuffer
Unbuffer a frame input to a sequence of scalar outputs.

Library Signal Management / Buffers

Description The Unbuffer block unbuffers an Mi-by-N frame-based input into a 1-by-N
sample-based output. That is, inputs are unbuffered row-wise so that each
matrix row becomes an independent time-sample in the output. The rate at
which the block receives inputs is generally less than the rate at which the
block produces outputs.
“slow-time” input “fast-time” output
(frame size = 3, frame period = 3∗Tsi) (frame size = 1, sample period = T si)
7 4 1
8 5 2 9 8 7 6 5 4 3 2 1
9 6 3

The block adjusts the output rate so that the sample period is the same at both
the input and output, Tso=Tsi. Therefore, the output sample period for an input
of frame size Mi and frame period Tfi is Tfi/Mi, which represents a rate Mi times
higher than the input frame rate. In the example above, the block receives
inputs only once every three sample periods, but produces an output once every
sample period. To rebuffer frame-based inputs to a larger or smaller frame size,
use the Buffer block.
In the model below, the block unbuffers a four-channel frame-based input with
frame size 3. The Initial conditions parameter is set to zero and the tasking
mode is set to multitasking, so the first three outputs are zero vectors (see
“Latency” below).

5-463
Unbuffer

ch2 ch3
ch1 ch4 ch2 ch3
ch1 ch4
7 0 0 –7 0000 t=0
t=6 8 0 0 –8
9 0 1 –9 initial condition 0000 t=1
(multitasking delay)
Tfi = 3 0000 t=2
Frame-based input ,
4 0 0 –4 frame period = T fi 1 0 1 –1 t=3
t=3 5 0 1 –5
6 0 1 –6 2 0 1 –2 t=4
Sample-based output ,
sample period = Tfi/Mi 3 0 0 –3 t=5

1 0 1 –1 4 0 0 –4 t=6
t=0 2 0 1 –2 first matrix input Tso = Tsi = 1
3 0 0 –3 5 0 1 –5 t=7

Latency

Zero Latency. The Unbuffer block has zero tasking latency in Simulink’s
single-tasking mode. Zero tasking latency means that the first input sample
(received at t=0) appears as the first output sample.

Nonzero Latency. For multitasking operation, the Unbuffer block’s buffer is

initialized with the value specified by the Initial condition parameter, and the
block begins unbuffering this frame at the start of the simulation. Inputs to the
block are therefore delayed by one buffer length, or Mi samples.
The Initial condition parameter can be one of the following:

• A scalar to be repeated for the first Mi output samples of every channel

• A length-Mi vector containing the values of the first Mi output samples for
every channel
• An Mi-by-N matrix containing the values of the first Mi output samples in
each of N channels

5-464
 Unbuffer

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

Initial conditions
The value of the block’s initial output for cases of nonzero latency; a scalar,
vector, or matrix.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Buffer DSP Blockset

See “Unbuffering a Frame-Based Signal into a Sample-Based Signal” on

page 3-60 for related information.

5-465
Uniform Decoder

Purpose 5Uniform Decoder

Decode an integer input to a floating-point output.

Library Quantizers

Description The Uniform Decoder block performs the inverse operation of the Uniform
Encoder block, and reconstructs quantized floating-point values from encoded
integer input. The block adheres to the definition for uniform decoding
specified in ITU-T Recommendation G.701.
Inputs can be real or complex values of the following six integer data types:
uint8, uint16, uint32, int8, int16, or int32.

The block first casts the integer input values to floating-point values, and then
uniquely maps (decodes) them to one of 2B uniformly spaced floating point
values in the range [-V, (1-21-B)V], where B is specified by the Bits parameter
(as an integer between 2 and 32) and V is a floating-point value specified by the
Peak parameter. The smallest input value representable by B bits (0 for an
unsigned input data type; -2B-1 for a signed input data type) is mapped to the
value -V. The largest input value representable by B bits (2B-1 for an unsigned
input data type; 2B-1-1 for a signed input data type) is mapped to the value
(1-21-B)V. Intermediate input values are linearly mapped to the intermediate
values in the range [-V, (1-21-B)V].
To correctly decode values encoded by the Uniform Encoder block, the Bits and
Peak parameters of the Uniform Decoder block should be set to the same
values as the Bits and Peak parameters of the Uniform Encoder block. The
Overflow mode parameter specifies the Uniform Decoder block’s behavior
when the integer input is outside the range representable by B bits. If
Saturate is selected, unsigned input values greater than 2B-1 saturate at 2B-1;
signed input values greater than 2B-1-1 or less than -2B-1 saturate at those
limits. The real and imaginary components of complex inputs saturate
independently.
If Wrap is selected, unsigned input values, u, greater than 2B-1 are wrapped
back into the range [0, 2B-1] using mod-2B arithmetic.
u = mod(u,2^B) % Equivalent MATLAB code

5-466
 Uniform Decoder

Signed input values, u, greater than 2B-1-1 or less than -2B-1 are wrapped back
into that range using mod-2B arithmetic.
u = (mod(u+2^B/2,2^B)-(2^B/2)) % Equivalent MATLAB code

The real and imaginary components of complex inputs wrap independently.

The Output type parameter specifies whether the decoded floating-point
output is single or double precision. Either level of output precision can be used
with any of the six integer input data types.

Example Consider a Uniform Decoder block with the following parameter settings:

• Peak = 2
• Bits = 3

The input to the block is the uint8 output of a Uniform Encoder block with
comparable settings: Peak = 2, Bits = 3, and Output type = Unsigned.
(Comparable settings ensure that inputs to the Uniform Decoder block do not
saturate or wrap. See the example on the Uniform Encoder reference page for
more about these settings.)
The real and complex components of each input are independently mapped to
one of 23 distinct levels in the range [-2.0,1.5].
0 is mapped to -2.0
1 is mapped to -1.5
2 is mapped to -1.0
3 is mapped to -0.5
4 is mapped to 0.0
5 is mapped to 0.5
6 is mapped to 1.0
7 is mapped to 1.5

5-467
Uniform Decoder

Dialog Box

Peak
The largest amplitude represented in the encoded input. To correctly
decode values encoded with the Uniform Encoder block, set the Peak
parameters in both blocks to the same value.
Bits
The number of input bits, B, used to encode the data. (This can be less than
the total number of bits supplied by the input data type.) To correctly
decode values encoded with the Uniform Encoder block, set the Bits
parameters in both blocks to the same value.
Overflow mode
The block’s behavior when the integer input is outside the range
representable by B bits. Out-of-range inputs can either saturate at the
extreme value, or wrap back into range.
Output type
The precision of the floating-point output, single or double.

References General Aspects of Digital Transmission Systems: Vocabulary of Digital

Transmission and Multiplexing, and Pulse Code Modulation (PCM) Terms,
International Telecommunication Union, ITU-T Recommendation G.701,
March, 1993

Supported Single-precision floating point

Data Types Double-precision floating point

5-468
 Uniform Decoder

See Also Data Type Conversion Simulink

Quantizer Simulink
Uniform Encoder DSP Blockset
udecode Signal Processing Toolbox
uencode Signal Processing Toolbox

5-469
Uniform Encoder

Purpose 5Uniform Encoder

Quantize and encode a floating-point input to an integer output.

Library Quantizers

Description The Uniform Encoder block performs the following two operations on each
floating-point sample in the input vector or matrix:

1 Quantizes the value using the same precision

2 Encodes the quantized floating-point value to an integer value

In the first step, the block quantizes an input value to one of 2B uniformly
spaced levels in the range [-V, (1-21-B)V], where B is specified by the Bits
parameter and V is specified by the Peak parameter. The quantization process
rounds both positive and negative inputs downward to the nearest
quantization level, with the exception of those that fall exactly on a
quantization boundary. The real and imaginary components of complex inputs
are quantized independently.
The number of bits, B, can be any integer value between 2 and 32, inclusive.
Inputs greater than (1-21-B)V or less than -V saturate at those respective
values. The real and imaginary components of complex inputs saturate
independently.
In the second step, the quantized floating-point value is uniquely mapped
(encoded) to one of 2B integer values. If the Output type is set to Unsigned
integer, the smallest quantized floating-point value, -V, is mapped to the
integer 0, and the largest quantized floating-point value, (1-21-B)V, is mapped
to the integer 2B-1. Intermediate quantized floating-point values are linearly
(uniformly) mapped to the intermediate integers in the range [0, 2B-1]. For
efficiency, the block automatically selects an unsigned output data type (uint8,
uint16, or uint32) with the minimum number of bits equal to or greater
than B.
If the Output type is set to Signed integer, the smallest quantized
floating-point value, -V, is mapped to the integer -2B-1, and the largest
quantized floating-point value, (1-21-B)V, is mapped to the integer 2B-1-1.
Intermediate quantized floating-point values are linearly mapped to the
intermediate integers in the range [-2B-1, 2B-1-1]. The block automatically
selects a signed output data type (int8, int16, or int32) with the minimum
number of bits equal to or greater than B.

5-470
 Uniform Encoder

Inputs can be real or complex, double or single precision. The output data types
that the block uses are shown in the table below. Note that most of the blocks
in the DSP Blockset accept only double precision inputs. Use the Simulink
Data Type Conversion block to convert integer data types to double precision.
See “Working with Data Types” in the Simulink documentation for a complete
discussion of data types, as well as a list of Simulink blocks capable of
reduced-precision operations.

Bits Unsigned Integer Signed Integer

2 to 8 uint8 int8

9 to 16 uint16 int16

17 to 32 uint32 int32

The Uniform Encoder block operations adhere to the definition for uniform
encoding specified in ITU-T Recommendation G.701.

Example The figure below illustrates uniform encoding with the following parameter
settings:

• Peak = 2
• Bits = 3
• Output type = Unsigned

7
Output Value (real or imaginary component)

−1
−3 −2 −1 0 1 2 3
Input Value (real or imaginary component)

5-471
Uniform Encoder

The real and complex components of each input (horizontal axis) are
independently quantized to one of 23 distinct levels in the range [-2,1.5] and
then mapped to one of 23 integer values in the range [0,7].
-2.0 is mapped to 0
-1.5 is mapped to 1
-1.0 is mapped to 2
-0.5 is mapped to 3
0.0 is mapped to 4
0.5 is mapped to 5
1.0 is mapped to 6
1.5 is mapped to 7

The table below shows the results for a few particular inputs.

Input Quantized Input Output Notes

1.6 1.5+0.0i 7+4i

-0.4 -0.5+0.0i 3+4i

-3.2 -2.0+0.0i 4i Saturation (real)

0.4-1.2i 0.0-1.5i 4+i

0.4-6.0i 0.0-2.0i 4 Saturation (imaginary)

-4.2+3.5i -2.0+2.0i 7i Saturation (real and imag)

The output data type is automatically set to uint8, the most efficient format for
this input range.

5-472
 Uniform Encoder

Dialog Box

Peak
The largest input amplitude to be encoded, V. Real or imaginary input
values greater than (1-21-B)V or less than -V saturate (independently for
complex inputs) at those limits.
Bits
The number of levels at which to quantize the floating-point input. (Also
the number of bits needed to represent the integer output.)
Output type
The data type of the block’s output, Unsigned integer or Signed integer.
Unsigned outputs are uint8, uint16, or uint32, while signed outputs are
int8, int16, or int32.

References General Aspects of Digital Transmission Systems: Vocabulary of Digital

Transmission and Multiplexing, and Pulse Code Modulation (PCM) Terms,
International Telecommunication Union, ITU-T Recommendation G.701,
March, 1993

Supported Single-precision floating point

Data Types Double-precision floating point

See Also Data Type Conversion Simulink

Quantizer Simulink
Uniform Decoder DSP Blockset
udecode Signal Processing Toolbox
uencode Signal Processing Toolbox

5-473
Unwrap

Purpose 5Unwrap
Unwrap the phase of a signal.

Library Signal Operations

Description The Unwrap block unwraps each input channel by adding or subtracting
appropriate multiples of 2π to each channel element. The input can be any
matrix or 1-D vector, and must have radian phase entries. The block recognizes
phase discontinuities larger than the Tolerance parameter setting.
The block preserves the input size, dimension, and frame status, and the
output port rate equals the input port rate.
For a detailed discussion of the Unwrap block, see the following sections:
• “Acceptable Inputs and Corresponding Output Characteristics” on
page 5-474
• “The Two Unwrap Modes” on page 5-475
• “Unwrap Method” on page 5-479
• “Definition of Phase Unwrap” on page 5-479

Acceptable Inputs and Corresponding Output Characteristics

The Unwrap block preserves the input size, dimension, and frame status, and
the output port rate equals the input port rate.

Characteristics of Valid Input Characteristics of Corresponding

Output

• Input elements must be phase • Output elements are phase

values in radians. values in radians.
• Sample- or frame-based • Same frame status as input
• M-by-N 2-D matrix or a 1-D vector • Same size and dimension as input
• Output port rate = input port rate

5-474
 Unwrap

The Two Unwrap Modes

You must specify the unwrap mode by setting the parameter, Do not unwrap
phase discontinuities between successive frames. The unwrap modes are
summarized in the next table.

5-475
Unwrap

Two Unwrap Modes

In both unwrap modes, the block adds 2πk to each input channel’s elements, where it updates k
at each phase discontinuity. (For more on the updating of k, see “Unwrap Method” on
page 5-479.) The number of times that k is reset to 0 depends on the unwrap mode.
Default Unwrap Mode: Nondefault Unwrap Mode:
Initialize k to 0 For Only the First Input Frame Set k to 0 For Each Successive Input Matrix
or Input Vector

In this mode, k is initialized to 0 for only the In this mode, k is reset to 0 for each
first input matrix or input vector. As k gets successive input matrix or input vector. As k
updated, the value of k is retained between gets updated, the value of k is only retained
successive input matrices or input vectors. That within the current input matrix or vector.
is, the block unwraps each input’s channel by That is, the block unwraps each input’s
considering phase discontinuities in all channel by considering phase discontinuities
previous frames and the current frame. in the current input matrix or input vector
only, ignoring discontinuities in previous
inputs.

Depending on input characteristics, the block Depending on input characteristics, the block
unwraps the columns or each individual unwraps the columns or rows of the input:
element of the input:
• Frame-based inputs — unwrap columns
• Frame-based inputs — unwrap columns • Sample-based nonrow inputs — unwrap
• Sample-based inputs — unwrap each element columns
of the input. • Sample-based row vector inputs — unwrap
• 1-D vector inputs — treat as frame-based the row.
column • 1-D vector inputs — treat as frame-based
column
See the following diagrams. See the following diagrams.

5-476
 Unwrap

The following diagrams illustrate how the two unwrap modes operate on
various inputs.

Default Unwrap Mode Operation:

Frame-Based Inputs Sample-Based Inputs

The block treats each input column as an The block treats each element of the input
independent channel. It unwraps by treating matrix as an independent channel. (The first
Channel 1 of Frame 2 as a continuation of sample in Channel 1 is in the upper left corner
Channel 1 of Frame 1. of the Sample 1 matrix. The second sample of
Channel 1 is in the corresponding corner of the
Sample 2 matrix, and so on.)

Channel 2
Channel 1
0 0
Tolerance parameter =π 0 0
Tolerance parameter =π
2π 2π
Channel 1
Frame 1 --- 0
3
--- 0
3 Ch 3
–2 π 4π 00 Ch 4 00
----- 0 --- 0
3 Phase discontinuity (jump in 3 Sample 1 00 00

0 0
adjacent phase values greater 2π 2π
than the value of the
6π
--- 0 --- 0
3
Phase discontinuity --- 0
3
Frame 2
2π
--- 0 3 Sample 2 0 0
3 Tolerance parameter) 8π
--- 0
0 0
–2 π 3
----- 0 4π
3 10π – 2π --- 0
3
----- 0
3 Sample 3 ----- 0
3 0 0
0 0 0 0
2π
Frame 3 --- 0
3
12π
----- 0 00
6π
--- 0
–2 π
3 Sample 4 3
----- 0 14π 00 0 0
3 ----- 0
3
2π 8π
16π Sample 5 --- 0 --- 0
----- 0 3 3
3
0 0 0 0

5-477
Unwrap

Nondefault Unwrap Mode Operation:

Frame-Based Inputs and

Sample-Based (Nonrow) Inputs Sample-Based Row Vector Inputs

The block unwraps each column, treating each The block unwraps each row, treating each
input matrix as completely unrelated to the input row vector as completely independent of
other input matrices. the other input row vectors.

0 0 Tolerance parameter =π 0 0 Tolerance parameter =π

2π 2π
Input 1 --- 0
3
--- 0
3 Input 1 2π – 2 π 2π – 2 π
0 --- ----- 0 --- -----
2π 4π 6π 8π 10π
0 --- --- --- --- -----
3 3 3 3 3 3 3 3 3
–2 π 4π
----- 0
3 Phase discontinuity (jump in --- 0
3
Input 2 2π – 2 π 2π – 2 π 2π 4π 6π 8π 10π
adjacent phase values greater 0 --- ----- 0 --- -----
3 3 3 3
0 --- --- --- --- -----
3 3 3 3 3
0 0 0 0
2π than the value of the 2π
Input 2 --- 0
Tolerance parameter)
--- 0
2π – 2 π 2π – 2 π 2π 4π 6π 8π 10π
3 3 Input 3 0 --- ----- 0 --- ----- 0 --- --- --- --- -----
3 3 3 3 3
–2 π 4π 3 3 3 3
----- 0 --- 0
3 3

0 0 0 0
2π 2π
Input 3 --- 0
3
--- 0
3
–2 π 4π
----- 0 --- 0
3 3

5-478
 Unwrap

Unwrap Method
The Unwrap block unwraps each channel of its input matrix or input vector by
adding 2πk to each successive channel element, and updating k at each phase
jump. See the following steps to the unwrap method for details.
Relevant Unwrap Terms:
• ui — ith element of the input channel on which the algorithm operates
• α — Tolerance parameter value
• phase jump or phase discontinuity — difference between phase values of
two adjacent channel entries that exceeds α . The diagram in the next
section indicates phase jumps with red arrows.

Steps to the Unwrap Method:

1 Set k to 0 (See “The Two Unwrap Modes” on page 5-475 for more on how
often this step occurs.)
2 Check for a phase jump between adjacent channel elements ui and ui+1:
- If there is no phase jump between ui and ui+1 ( u i + 1 – u i ≤ α ) , add 2πk
to ui, and then repeat step 2 to continue checking for phase jumps.
- If there is a phase jump between ui and ui+1 ( u i + 1 – u i > α ) , add 2πk
to ui, and then go to step 3 to update k.
3 Update k as follows when there is a phase jump between ui and ui+1. Then
go back to step 2 to add the updated 2πk value to ui+1 and succeeding
channel elements until the next phase jump:
- If u i + 1 < u i (phase jump is negative), increment k.
- If u i + 1 > u i (phase jump is positive), decrement k.

Definition of Phase Unwrap

Algorithms that compute the phase of a signal often only output phases
between – π and π . For instance, such algorithms compute the phase of
sin ( 2π + 3 ) to be 3, since sin ( 3 ) = sin ( 2π + 3 ) , and since the actual phase,
2π + 3 , is not between – π and π . Such algorithms compute the phases of
sin ( – 4 π + 3 ) and sin ( 16π + 3 ) to be 3 as well.
Phase unwrap or unwrap is a process often used to reconstruct a signal’s
original phase. Unwrap algorithms add appropriate multiples of 2π to each
phase input to restore original phase values, as illustrated in the following

5-479
Unwrap

diagram. For more on phase unwrap, see the previous section, “Unwrap
Method” on page 5-479.

5-480
 Unwrap

Unwrapping Phase Data Ranging Between π and -π

Signal data with instantaneous phase values that range over all numbers Calculate Phases of Signal Data:
Input: [ sin ( θ 0 ), sin ( θ 1 ), …, sin ( θ N ) ]
30

25 Output: [ θ ′0, θ ′1, …, θ ′N ]

where sin ( θ ′n ) = sin ( θ n )
20

and – π < θ ′n ≤ π
[ sin ( 0 ), sin  ------ , sin  ------ , sin  ------ , …, sin 15---------- ]
2π 4π 6π 28π
0 pi
 5 2pi
 5 3pi
 5 4pi
 5  5pi 6pi
Restricted Phases (Radians)

10

Phase data of the signal restricted to range between π and -π.

5
Unwrap Restricted Phases: 4π ⁄ 5
2π ⁄ 5 Time
Input: [ θ ′0, θ ′1, …, θ ′N ] 0 0

–2 π ⁄ 5
Output: [ θ 0, θ 1, …, θ N ] – 4π ⁄5
−5
0 2 4 6 8 10 12 14 16
where θ n = θ ′n + 2πk
2π 4π – 4 π – 2π 2π 4π – 4 π – 2π 2π 4π – 4 π – 2π
Update the value of k after every large [0,------, ------, ----------, ----------, 0, ------, ------, ----------, ----------, 0, ------, ------, ----------, ----------]
5 5 5 5 5 5 5 5 5 5 5 5
jump in phase value, indicated by .
Add 2π Add 4π Add 6π

2π 4π 6π 8π 12π 14π 16π 18π 22π 24π 26π 28π

[0,------, ------, ------, ------, 2π, ----------, ----------, ----------, ----------, 4π, ----------, ----------, ----------, ----------]
5 5 5 5 5 5 5 5 5 5 5 5

30
Unwrapped phase data ranging over all numbers.
28π ⁄ 5
25
Unwrapped Phases (Radians)

20 4π

15

10 2π

2π ⁄ 5 Time
0 0

5-481
Unwrap

Range of restricted phase data: – π < θ ′ ≤ π Range of unwrapped phase data: all numbers
sin ( θ ′ ) sin ( θ )
2π 2π 12π 22π
4π ------ ------, ----------, ----------, …
------ 5 4π 14π 24π 5 5 5
5 ------, ----------, ----------, …
5 5 5
Large jump in π θ′ 0 cos ( θ ′ ) θ 0, 2π, 4π, … cos ( θ )
phase value ( –π )
6π 16π 26π
– 4π ------, ----------, ----------, …
---------- 5 5 5
5 – 2π 8π 18π 28π
---------- ------, ----------, ----------, …
5 5 5 5

Limitations The Unwrap block detects branch cut crossings, but can be fooled by sparse,
rapidly changing phase values.

Dialog Box

5-482
 Unwrap

Do not unwrap phase discontinuities between successive frames

When this parameter is cleared, the block unwraps each input’s channels
(the input channels are the columns of frame-based inputs and each
element of sample-based inputs). When this parameter is set, the block
unwraps each row of sample-based row vector inputs, and unwraps the
columns of all other inputs, where each input matrix or input vector is
treated as completely unrelated to the other input matrices or input
vectors. 1-D vector inputs are always treated as frame-based column
vectors. See “The Two Unwrap Modes” on page 5-475.
Tolerance
The jump size that the block recognizes as a true phase discontinuity. The
default is set to π (rather than a smaller value) to avoid altering legitimate
signal features. To increase the block’s sensitivity, set Tolerance to a value
slightly less than π.

Supported Double-precision floating point

Data Types

See Also unwrap MATLAB

5-483
Upsample

Purpose 5Upsample
Resample an input at a higher rate by inserting zeros.

Library Signal Operations

Description The Upsample block resamples each channel of the Mi-by-N input at a rate
L times higher than the input sample rate by inserting L-1 zeros between
consecutive samples. The integer L is specified by the Upsample factor
parameter. The Sample offset parameter delays the output samples by an
integer number of sample periods D, where 0 ≤ D < (L-1), so that any of the L
possible output phases can be selected.

Sample-Based Operation
When the input is sample-based, the block treats each of the M∗N matrix
elements as an independent channel, and upsamples each channel over time.
The Frame-based mode parameter must be set to Maintain input frame size.
The output sample rate is L times higher than the input sample rate
(Tso = Tsi/L), and the input and output sizes are identical.

Frame-Based Operation
When the input is frame-based, the block treats each of the N input columns as
a frame containing Mi sequential time samples from an independent channel.
The block upsamples each channel independently by inserting L-1 rows of
zeros between each row in the input matrix. The Frame-based mode
parameter determines how the block adjusts the rate at the output to
accommodate the added rows. There are two available options:
• Maintain input frame size
The block generates the output at the faster (upsampled) rate by using a
proportionally shorter frame period at the output port than at the input port.
For upsampling by a factor of L, the output frame period is L times shorter
than the input frame period (Tfo = Tfi/L), but the input and output frame
sizes are equal.

The model below shows a single-channel input with a frame period of

1 second being upsampled by a factor of 4 to a frame period of 0.25 seconds.
The input and output frame sizes are identical.

5-484
 Upsample

• Maintain input frame rate

The block generates the output at the faster (upsampled) rate by using a
proportionally larger frame size than the input. For upsampling by a factor
of L, the output frame size is L times larger than the input frame size
(Mo = Mi∗L), but the input and output frame rates are equal.
The model below shows a single-channel input of frame size 16 being
upsampled by a factor of 4 to a frame size of 64. The input and output frame
rates are identical.

5-485
Upsample

Latency and Initial Conditions

Zero Latency. The Upsample block has zero tasking latency for all single-rate
operations. The block is single-rate for the particular combinations of sampling
mode and parameter settings shown in the table below.

Sampling Mode Parameter Settings

Sample-based Upsample factor parameter, L, is 1.

Upsample factor parameter, L, is 1, or

Frame-based Frame-based mode parameter is Maintain input
frame rate.

The block also has zero latency for all multirate operations in Simulink’s
single-tasking mode.
Zero tasking latency means that the block propagates the first input (received
at t=0) immediately following the D consecutive zeros specified by the Sample
offset parameter. This output (D+1) is followed in turn by the L-1 inserted
zeros and the next input sample. The Initial condition parameter value is not
used.

Nonzero Latency. The Upsample block has tasking latency only for multirate
operation in Simulink’s multitasking mode:

• In sample-based mode, the initial condition for each channel appears as

output sample D+1, and is followed by L-1 inserted zeros. The channel’s first
input appears as output sample D+L+1. The Initial condition value can be
an Mi-by-N matrix containing one value for each channel, or a scalar to be
applied to all signal channels.
• In frame-based mode, the first row of the initial condition matrix appears as
output sample D+1, and is followed by L-1 inserted rows of zeros, the second
row of the initial condition matrix, and so on. The first row of the first input
matrix appears in the output as sample MiL+D+1. The Initial condition
value can be an Mi-by-N matrix, or a scalar to be repeated across all elements
of the Mi-by-N matrix. See the example below for an illustration of this case.

5-486
 Upsample

See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Example Construct the frame-based model shown below.

Adjust the block parameters as follows:

• Configure the Signal From Workspace block to generate a two-channel

signal with frame size of 4 and sample period of 0.25. This represents an
output frame period of 1 (0.25∗4). The first channel should contain the
positive ramp signal 1, 2, ..., 100, and the second channel should contain the
negative ramp signal -1, -2, ..., -100.
- Signal = [(1:100)' (-1:-1:-100)']
- Sample time = 0.25
- Samples per frame = 4
• Configure the Upsample block to upsample the two-channel input by
increasing the output frame rate by a factor of 2 relative to the input frame
rate. Set a sample offset of 1, and an initial condition matrix of

11 – 11
12 – 12
13 – 13
14 – 14

- Upsample factor = 2
- Sample offset = 1
- Initial condition = [11 -11;12 -12;13 -13;14 -14]
- Frame-based mode = Maintain input frame size

5-487
Upsample

• Configure the Probe blocks by deselecting the Probe width and Probe
complex signal check boxes (if desired).

This model is multirate because there are at least two distinct frame rates, as
shown by the two Probe blocks. To run this model in Simulink’s multitasking
mode, select Fixed-step and discrete from the Type controls in the Solver
panel of the Simulation Parameters dialog box, and select MultiTasking from
the Mode parameter. Also set the Stop time to 30.
Run the model and look at the output, yout. The first few samples of each
channel are shown below.
yout =

0 0
11 -11
0 0
12 -12
0 0
13 -13
0 0
14 -14
0 0
1 -1
0 0
2 -2
0 0
3 -3
0 0
4 -4
0 0
5 -5
0 0

Since we ran this frame-based multirate model in multitasking mode, the first
row of the initial condition matrix appears as output sample 2
(i.e., sample D+1, where D is the Sample offset value). It is followed by the
other three initial condition rows, each separated by L-1 inserted rows of zeros,
where L is the Upsample factor value of 2. The first row of the first input
matrix appears in the output as sample 10 (i.e., sample MiL+D+1, where Mi is
the input frame size).

5-488
 Upsample

Dialog Box

Upsample factor
The integer factor, L, by which to increase the input sample rate.
Sample offset
The sample offset, D, which must be an integer in the range [0,L-1].
Initial condition
The value with which the block is initialized for cases of nonzero latency, a
scalar or matrix. This value (first row in frame-based mode) appears in the
output as sample D+1.
Frame-based mode
For frame-based operation, the method by which to implement the
upsampling: Maintain input frame size (i.e., increase the frame rate), or
Maintain input frame rate (i.e., increase the frame size). The Framing
parameter must be set to Maintain input frame size for sample-base
inputs.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-489
Upsample

See Also Downsample DSP Blockset

FIR Interpolation DSP Blockset
FIR Rate Conversion DSP Blockset
Repeat DSP Blockset

5-490
 Variable Fractional Delay

Purpose 5Variable Fractional Delay

Delay an input by a time-varying fractional number of sample periods.

Library Signal Operations

Description The Variable Fractional Delay block delays each channel of the Mi-by-N input
matrix, u, by a variable (possibly noninteger) number of sample intervals.
The block computes the value for each channel of the output based on the
stored samples in memory most closely indexed by the Delay input, v, and the
interpolation method specified by the Mode parameter. In Linear
Interpolation mode, the block stores the D+1 most recent samples received at
the In port for each channel, where D is the Maximum delay. In FIR
Interpolation mode, the block stores the D+P+1 most recent samples received
at the In port for each channel, where P is the Interpolation filter
half-length.

See the Variable Integer Delay block for further discussion of how input
samples are stored in the block’s memory. The Variable Fractional Delay block
differs only in the way that these stored sample are accessed; a fractional delay
requires the computation of a value by interpolation from the nearby samples
in memory.

Sample-Based Operation
When the input is sample-based, the block treats each of the Mi∗N matrix
elements as an independent channel. The input to the Delay port, v, is an
Mi-by-N matrix of floating-point values in the range 0 ≤ v ≤ D that specifies the
number of sample intervals to delay each channel of the input.
A 1-D vector input is treated as an Mi-by-1 matrix, and the output is 1-D.
The Initial conditions parameter specifies the values in the block’s memory at
the start of the simulation in the same manner as for the Variable Integer
Delay block. See the section on sample-based initial conditions there for
complete information.

Frame-Based Operation
When the input is frame-based, the block treats each of the N input columns as
a frame containing Mi sequential time samples from an independent channel.

5-491
Variable Fractional Delay

The input to the Delay port, v, contains floating-point values in the range
0 ≤ v ≤ D specifying the number of sample intervals to delay the current input.
The input to the Delay port can be:

• An Mi-by-N matrix containing the number of sample intervals to delay each

sample in each channel of the current input
• An Mi-by-1 matrix containing the number of sample intervals to delay each
sample in every channel of the current input
• A 1-by-N matrix containing the number of sample intervals to delay every
sample in each channel of the current input

For example, if v is the Mi-by-1 matrix [v(1) v(2) ... v(Mi)]', the earliest
sample in the current frame is delayed by v(1) fractional sample intervals, the
following sample in the frame is delayed by v(2) fractional sample intervals,
and so on. The set of fractional delays contained in v is applied identically to
every channel of a multichannel input.
The Initial conditions parameter specifies the values in the block’s memory at
the start of the simulation in the same manner as for the Variable Integer
Delay block. See the section on frame-based initial conditions there for
complete information.

Interpolation Modes
The delay value specified at the Delay port is used as an index into the block’s
memory, U, which stores the D+1 most recent samples received at the In port
for each channel. For example, an integer delay of 5 on a scalar input sequence
retrieves and outputs the fifth most recent input sample from the block’s
memory, U(6). Fractional delays are computed by interpolating between stored
samples; the two available interpolation modes are described below.

Linear Interpolation Mode. For noninteger delays, at each sample time the Linear
Interpolation mode uses the two samples in memory nearest to the specified
delay to compute a value for the sample at that time. If v is the specified
fractional delay for a scalar input, the output sample, y, is computed as follows.
vi = floor(v) % vi = integer delay
vf = v-vi % vf = fractional delay
y = (1-vf)*U(vi) + vf*U(vi+1)

5-492
 Variable Fractional Delay

Delay values less than 0 are clipped to 0, and delay values greater than D are
clipped to D, where D is the Maximum delay. Note that a delay value of 0
causes the block to pass through the current input sample, U(1), in the same
simulation step that it is received.

FIR Interpolation Mode. In FIR Interpolation mode, the block computes a value
for the sample at the desired delay by applying an FIR filter of order 2P to the
stored samples on either side of the desired delay, where P is the Interpolation
filter half-length. For periodic signals, a larger value of P (i.e., a higher order
filter) yields a better estimate of the sample at the specified delay. A value
between 4 and 6 for this parameter (i.e. a 7th to 11th order filter) is usually
adequate.
A vector of 2P filter tap weights is precomputed at the start of the simulation
for each of Q-1 discrete points between input samples, where Q is specified by
the Interpolation points per input sample parameter. For a delay
corresponding to one of the Q interpolation points, the unique filter computed
for that interpolation point is applied to obtain a value for the sample at the
specified delay. For delay times that fall between interpolation points, the
value computed at the nearest interpolation point is used. Since Q controls the
number of locations where a unique interpolation filter is designed, a larger
value results in a better estimate of the sample at a given delay.
Note that increasing the Interpolation filter half length (P) increases the
number of computations performed per input sample, as well as the amount of
memory needed to store the filter coefficients. Increasing the Interpolation
points per input sample (Q) increases the simulation’s memory requirements
but does not affect the computational load per sample.
The Normalized input bandwidth parameter allows you to take advantage of
the bandlimited frequency content of the input. For example, if you know that
the input signal does not have frequency content above Fs/4, you can specify a
value of 0.5 for the Normalized input bandwidth to constrain the frequency
content of the output to that range.
(Each of the Q interpolation filters can be considered to correspond to one
output phase of an “upsample-by-Q” FIR filter. In this view, the Normalized
input bandwidth value is used to improve the stopband in critical regions, and
to relax the stopband requirements in frequency regions where there is no
signal energy.)

5-493
Variable Fractional Delay

For delay values less than P/2-1, the output is computed using linear
interpolation. Delay values greater than D are clipped to D, where D is the
Maximum delay.

The block uses the intfilt function in the Signal Processing Toolbox to
compute the FIR filters.

Note When the Variable Fractional Delay block is used in a feedback loop, at
least one block with nonzero delay (e.g., an Integer Delay block with
Delay > 0) should be included in the loop as well. This prevents the occurrence
of an algebraic loop if the delay of the Variable Fractional Delay block is
driven to zero.

Examples The dspafxf demo illustrates an audio flanger system built around the
Variable Fractional Delay block.

Dialog Box

Mode
The method by which to interpolate between adjacent stored samples to
obtain a value for the sample indexed by the input at the Delay port.

5-494
 Variable Fractional Delay

Maximum delay
The maximum delay that the block can produce, D. Delay input values
exceeding this maximum are clipped at the maximum.
Interpolation filter half-length
Half the number of input samples to use in the FIR interpolation filter.
Interpolation points per input sample
The number of points per input sample, Q, at which a unique FIR
interpolation filter is computed.
Normalized input bandwidth
The bandwidth to which the interpolated output samples should be
constrained. A value of 1 specifies half the sample frequency.
Initial conditions
The values with which the block’s memory is initialized. See the Variable
Integer Delay block for more information.

Supported Double-precision floating point

Data Types

See Also Integer Delay DSP Blockset

Unit Delay Simulink
Variable Integer Delay DSP Blockset

5-495
Variable Integer Delay

Purpose 5Variable Integer Delay

Delay the input by a time-varying integer number of sample periods.

Library Signal Operations

Description The Variable Integer Delay block delays the discrete-time input at the In port
by the integer number of sample intervals specified by the input to the
Delay port. The Delay port input rate must be an integer multiple of the
In port input rate. The delay for a sample-based input sequence is a scalar
value to uniformly delay every channel. The delay for a frame-based input
sequence can be a scalar value to uniformly delay every sample in every
channel, a vector containing one delay value for each sample in the input
frame, or a vector containing one delay value for each channel in the input
frame.
The delay values should be in the range of 0 to D, where D is the Maximum
delay. Delay values greater than D or less than 0 are clipped to those
respective values and noninteger delays are rounded to the nearest integer
value.
The Variable Integer Delay block differs from the Integer Delay block in the
following ways.

Variable Integer Delay Integer Delay

Delay is provided as an input to the Delay is specified as a parameter

Delay port. setting in the dialog box.

Delay can vary with time; for Delay cannot vary with time; for
example, for a frame-based input, example, for a frame-based input,
the nth element’s delay in the first the nth element’s delay is the same
input frame can differ from the nth for every input frame.
element’s delay in the second input
frame.

Sample-Based Operation
When the input is an M-by-N sample-based matrix, the block treats each of the
M∗N matrix elements as an independent channel, and applies the delay at the
Delay port to each channel.

5-496
 Variable Integer Delay

The Variable Integer Delay block stores the D+1 most recent samples received
at the In port for each channel. At each sample time the block outputs the
stored sample(s) indexed by the input to the Delay port.
For example, if the input to the In port, u, is a scalar signal, the block stores a
vector, U, of the D+1 most recent signal samples. If the current input sample
is U(1), the previous input sample is U(2), and so on, then the block’s output is
y = U(v+1); % Equivalent MATLAB code

where v is the input to the Delay port. Note that a delay value of 0 (v=0) causes
the block to pass through the sample at the In port in the same simulation step
that it is received. The block’s memory is initialized to the Initial conditions
value at the start of the simulation (see below).
The figure below shows the block output for a scalar ramp sequence at the In
port, a Maximum delay of 5, an Initial conditions of 0, and a variety of
different delays at the Delay port.
In Delay Memory (U) Output

0 3 [0 0 0 0 0 0] i.c. 0
1 1 [1 0 0 0 0 0] 0
2 0 [2 1 0 0 0 0] 2
3 2 [3 2 1 0 0 0] 1
4 1 [4 3 2 1 0 0] 3
Simulation time

5 2 [5 4 3 2 1 0] 3
6 2.3 [6 5 4 3 2 1] 4
7 3 rounded to 2 [7 6 5 4 3 2] 4
8 –1 [8 7 6 5 4 3] 8
9 4 clipped to 0 [9 8 7 6 5 4] 5
10 10 [10 9 8 7 6 5] 5
...

...

...

...

clipped to 5

Note that the current input at each time-step is immediately stored in memory
as U(1). This allows the current input to be available at the output for a delay
of 0 (v=0).
The Initial conditions parameter specifies the values in the block’s memory at
the start of the simulation. Unlike the Integer Delay block, the Variable

5-497
Variable Integer Delay

Integer Delay block does not have a fixed initial delay period during which the
initial conditions appear at the output. Instead, the initial conditions are
propagated to the output only when they are indexed in memory by the value
at the Delay port. Both fixed and time-varying initial conditions can be
specified in a variety of ways to suit the dimensions of the input sequence.

Fixed Initial Conditions. The settings shown below specify fixed initial conditions.
For a fixed initial condition, the block initializes each of D samples in memory
to the value entered in the Initial conditions parameter. A fixed initial
condition in sample-based mode can be specified in one of the following ways:

• Scalar value with which to initialize every sample of every channel in

memory. For a general M-by-N input and the parameter settings below,

the block initializes 100 M-by-N matrices in memory with zeros.

• Array of size M-by-N-by-D. In this case, you can specify different fixed initial
conditions for each channel. See the Array bullet in “Time-Varying Initial
Conditions” below for details.
Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions. The following settings specify time-varying initial

conditions. For a time-varying initial condition, the block initializes each of D
samples in memory to one of the values entered in the Initial conditions
parameter. This allows you to specify a unique output value for each sample in
memory. A time-varying initial condition in sample-based mode can be
specified in one of the following ways:
• Vector containing D elements with which to initialize memory samples
U(2:D+1), where D is the Maximum delay. For a scalar input and the
parameters shown below,

5-498
 Variable Integer Delay

the block initializes U(2:6) with values [-1, -1, -1, 0, 1].
• Array of dimension M-by-N-by-D with which to initialize memory samples
U(2:D+1), where D is the Maximum delay and M and N are the number of
rows and columns, respectively, in the input matrix. For a 2-by-3 input and
the parameters below,

the block initializes memory locations U(2:5) with values

U(2) = 1 1 1 , U(3) = 2 2 2 , U(4) = 3 3 3 , U(5) = 4 4 4

111 222 333 444

An array initial condition can only be used with matrix inputs.

Initial conditions cannot be specified by full matrices.

Frame-Based Operation
When the input is an M-by-N frame-based matrix, the block treats each of the
N input columns as a frame containing M sequential time samples from an
independent channel.
In frame-based mode, the input at the Delay port can be a scalar value to
uniformly delay every sample in every channel. It can also be a length-M
vector, v = [v(1) v(2) ... v(M)], containing one delay for each sample in
the input frame(s). The set of delays contained in vector v is applied identically
to every channel of a multichannel input. The Delay port entry can also be a
length-N vector, containing one delay for each channel.
Vector v does not specify when the samples in the current input frame will
appear in the output. Rather, v indicates which previous input samples (stored
in memory) should be included in the current output frame. The first sample in
the current output frame is the input sample v(1) intervals earlier in the

5-499
Variable Integer Delay

sequence, the second sample in the current output frame is the input sample
v(2) intervals earlier in the sequence, and so on.

The illustration below shows how this works for an input with a sample period
of 1 and frame size of 4. The Maximum delay (Dmax) is 5, and the Initial
conditions parameter is set to -1. The delay input changes from [1 3 0 5] to
[2 0 0 2] after the second input frame. Note that the samples in each output
frame are the values in memory indexed by the elements of v.
y(1) = U(v(1)+1)
y(2) = U(v(2)+1)
y(3) = U(v(3)+1)
y(4) = U(v(4)+1)

In Delay (v) Memory (U) Out

1 1 [ 1 -1 -1 -1 -1 -1] –1 U(2)
2 3 [ 2 1 -1 -1 -1 -1] –1 U(4)
(t=0) [ 3 2 1 -1 -1 -1] U(1)
3 0 3
4 5 [ 4 3 2 1 -1 -1] –1 U(6)

5 1 [ 5 4 3 2 1 -1] 4 U(2)
6 3 [ 6 5 4 3 2 1] 3 U(4)
(t=4) [ 7 6 5 4 3 2] U(1)
7 0 7
Simulation time

8 5 [ 8 7 6 5 4 3] 3 U(6)

9 2 [ 9 8 7 6 5 4] 7 U(3)
10 0 [10 9 8 7 6 5] 10 U(1)
(t=8) [11 10 9 8 7 6] U(1)
11 0 11
12 2 [12 11 10 9 8 7] 10 U(3)

13 2 [13 12 11 10 9 8] 11 U(3)
14 0 [14 13 12 11 10 9] 14 U(1)
(t=12) [15 14 13 12 11 10] U(1)
15 0 15
16 2 [16 15 14 13 12 11] 14 U(3)

The Initial conditions parameter specifies the values in the block’s memory at
the start of the simulation. Both fixed and time-varying initial conditions can
be specified.

5-500
 Variable Integer Delay

Fixed Initial Conditions. The settings shown below specify fixed initial conditions.
For a fixed initial condition, the block initializes each of D samples in memory
to the value entered in the Initial conditions parameter. A fixed initial
condition in frame-based mode can be one of the following:

• Scalar value with which to initialize every sample of every channel in

memory. For a general M-by-N input with the parameter settings below,

the block initializes five samples in memory with zeros.

• Array of size 1-by-N-by-D. In this case, you can specify different fixed initial
conditions for each channel. See the Array bullet in “Time-Varying Initial
Conditions” below for details.
Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions. The following setting specifies a time-varying

initial condition. For a time-varying initial condition, the block initializes each
of D samples in memory to one of the values entered in the Initial conditions
parameter. This allows you to specify a unique output value for each sample in
memory. A time-varying initial condition in frame-based mode can be specified
in the following way:

• Vector of dimensions 1-by-D. In this case, all channels have the same set of
time-varying initial conditions specified by the entries of the vector. For the
ramp input [100; 100]' with a frame size of 4, delay of 5, and the parameter
settings below,

the block outputs the following sequence of frames at the start of the
simulation.

5-501
Variable Integer Delay

–1 –1 –5 –5 4 4
–2 –2 , 1 1 , 5 5 , …
–3 –3 2 2 6 6
–4 –4 3 3 7 7

• Array of size 1-by-N-by-D. In this case, you can specify different time-varying
initial conditions for each channel. For the ramp input [100; 100]' with a
frame size of 4, delay of 5, and the parameter settings below,

the block outputs the following sequence of frames at the start of the
simulation.

–1 – 11 –5 – 55 44
–2 – 22 , 1 1 , 5 5 ,…
–3 – 33 2 2 66
–4 – 44 3 3 77

Note that by specifying a 1-by-N-by-D initial condition array such that each
1-by-N vector entry is identical, you can implement different fixed initial
conditions for each channel.
Initial conditions cannot be specified by full matrices.

Dialog Box

5-502
 Variable Integer Delay

Maximum delay
The maximum delay that the block can produce for any sample. Delay
input values exceeding this maximum are clipped at the maximum.
Initial conditions
The values with which the block’s memory is initialized.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Integer Delay DSP Blockset

Variable Fractional Delay DSP Blockset

5-503
Variable Selector

Purpose 5Variable Selector

Select a subset of rows or columns from the input.

Library Signal Management / Indexing

Description The Variable Selector block extracts a subset of rows or columns from the
M-by-N input matrix at the In port, u.
When the Select parameter is set to Rows, the Variable Selector block
extracts rows from the input matrix, while if the Select parameter is set to
Columns, the block extracts columns.
When the Selector mode parameter is set to Variable, the length-L vector
input to the Idx port selects L rows or columns of u to pass through to the
output. The elements of the indexing vector can be updated at each sample
time, but the vector length must remain the same throughout the simulation.
When the Selector mode parameter is set to Fixed, the Idx port is disabled,
and the length-L vector specified in the Elements parameter selects L rows or
columns of u to pass through to the output. The Elements parameter is
tunable, so you can change the values of the indexing vector elements at any
time during the simulation; however, the vector length must remain the same.
For both variable and fixed indexing modes, the row selection operation is
equivalent to
y = u(idx,:) % Equivalent MATLAB code

and the column selection operation is equivalent to

y = u(:,idx) % Equivalent MATLAB code

where idx is the length-L indexing vector. The row selection output size is
L-by-N and the column selection output size is M-by-L. Input rows or columns
can appear any number of times in the output, or not at all.
When the input is a 1-D vector, the Select parameter is ignored; the output is
a 1-D vector of length L containing those elements specified by the length-L
indexing vector.
When an element of the indexing vector references a nonexistent row or column
of the input, the block reacts with the behavior specified by the Invalid index
parameter. The following options are available:

5-504
 Variable Selector

• Clip index – Clip the index to the nearest valid value, and do not issue an
alert. Example: For a 64-by-N input, an index of 72 is clipped to 64; an index
of -2 is clipped to 1.
• Clip and warn – Display a warning message in the MATLAB command
window, and clip as above.
• Generate error – Display an error dialog box and terminate the simulation.

Note The Variable Selector block always copies the selected input rows to a
contiguous block of memory (unlike the Simulink Selector block).

Dialog Box

Select
The dimension of the input to select, Rows or Columns. Tunable.
Selector mode
The type of indexing operation to perform, Variable or Fixed. Variable
indexing uses the input at the Idx port to select rows or columns from the
input at the In port. Fixed indexing uses the Elements parameter value to
select rows from the input at the In port, and disables the Idx port.

5-505
Variable Selector

Elements
A vector containing the indices of the input rows or columns that will
appear in the output matrix. This parameter is available when Fixed is
selected in the Selector mode parameter. Tunable.
Invalid index
Response to an invalid index value. Tunable.

Supported Fixed-point Only supported by input port In

Data Types Custom data types Only supported by input port In
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Multiport Selector DSP Blockset

Permute Matrix DSP Blockset
Selector Simulink
Submatrix DSP Blockset

5-506
 Variance

Purpose 5Variance
Compute the variance of an input or sequence of inputs.

Library Statistics

Description The Variance block computes the variance of each column in the input, or
tracks the variance of a sequence of inputs over a period of time. The Running
variance parameter selects between basic operation and running operation.

Basic Operation
When the Running variance check box is not selected, the block computes the
variance of each column in M-by-N input matrix u independently at each
sample time.
y = var(u) % Equivalent MATLAB code

For convenience, length-M 1-D vector inputs and sample-based length-M row
vector inputs are both treated as M-by-1 column vectors. (A scalar input
generates a zero-valued output.)
The output at each sample time, y, is a 1-by-N vector containing the variance
for each column in u. For purely real or purely imaginary inputs, the variance
of the jth column is the square of the standard deviation:
M

∑
2
u ij – µ j
2 i=1
y j = σ j = ----------------------------------- 1≤j≤N
M–1

where µj is the mean of the jth column. For complex inputs, the output is the
total variance for each column in u, which is the sum of the real and imaginary
variances for that column:
2 2 2
σ j = σ j, Re + σ j, Im

The frame status of the output is the same as that of the input.

Running Operation
When the Running variance check box is selected, the block tracks the
variance of each channel in a time-sequence of M-by-N inputs. For
sample-based inputs, the output is a sample-based M-by-N matrix with each

5-507
Variance

element yij containing the variance of element uij over all inputs since the last
reset. For frame-based inputs, the output is a frame-based M-by-N matrix with
each element yij containing the variance of the jth column over all inputs since
the last reset, up to and including element uij of the current input.
If the Reset port parameter is set to Non-zero sample, the optional Rst port
is enabled and the block resets the running variance when the scalar input at
the Rst port is nonzero. (The Rst port can be disabled by setting the Reset port
parameter to None.)
As in basic operation, length-M 1-D vector inputs and sample-based length-M
row vector inputs are both treated as M-by-1 column vectors.

Example The Variance block in the model below calculates the running variance of a
frame-based 3-by-2 (two-channel) matrix input, u. The running variance is
reset at t=2 by an impulse to the block’s Rst port.

The Variance block has the following settings:

• Running variance =
• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where
u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

• Delay (samples) = 2

5-508
 Variance

• Sample time = 1
• Samples per frame = 1

The block’s operation is shown in the figure below.

In Rst Output

ch1 ch2 ch1 ch2

61 0 0
First
13 t=0 0 First output 12.50 2.00
input 39 6.33 17.33

–7 2 30.92 12.92
2 4 t=1 0 23.50 9.70
5 1 21.47 9.07

8 6 0 0
Simulation time

0 2 t=2 1 Reset 32.00 8.00

–1 5 24.33 4.33

–3 0 23.33 7.58
2 4 t=3 0 17.70 5.80
1 17 14.17 35.47

The statsdem demo illustrates the operation of several blocks from the
Statistics library.

Dialog Box

Running variance
Enables running operation when selected.

5-509
Variance

Reset port
Enables the Rst input port when set to Non-zero sample, and disables the
Rst input port when set to None.

Supported Double-precision floating point

Data Types

See Also Mean DSP Blockset

RMS DSP Blockset
Standard Deviation DSP Blockset
var MATLAB

5-510
 Vector Scope

Purpose 5Vector Scope

Display a vector or matrix of time-domain, frequency-domain, or user-defined
data.

Library DSP Sinks

Description The Vector Scope block is a comprehensive tool, similar to a digital oscilloscope,
for displaying time-domain, frequency-domain, or user-defined signals. The
scope window, display-property settings, axis-property settings, and
line-property settings are shared with the Spectrum Scope block.
The input to this block can be any M-by-N matrix or 1-D vector, where 1-D
vectors are treated as column vectors. The frame-status for inputs are ignored;
the input to the block is always assumed to be a data frame, even if the input
is not identified as a frame. Thus, any M-by-N matrix input is interpreted as
having N independent channels of data, each with M consecutive samples to be
plotted sequentially across the horizontal axis of the plot.
The Vector Scope is most commonly used to plot consecutive time samples
(from a frame-based vector). However, it is just as appropriate to use the Vector
Scope to plot vectors containing data such as filter coefficients or spectral
magnitudes.

Displaying Data
The domain of the data is specified by the Input domain parameter under the
Scope properties check box, and can be Time, Frequency, or User-defined.

When displaying an M-by-N matrix containing time-domain data, the block

assumes that each of the N input frames (columns) represent a succession of M
consecutive samples taken from a time-series. That is, each data point in the
input frame is assumed to correspond to a unique time value.
When displaying an N-by-M matrix of frequency-domain data, the block
assumes that each of the N input frames (columns) is a vector of spectral
magnitude data corresponding to M consecutive ascending frequency indices.
That is, if the input is a single column vector, u, each value in the input
frame, u(i), is assumed to correspond to a unique frequency value, f(i),
where f(i+1)>f(i).
When displaying user-defined data, the block does not make any assumptions
about the nature of the data in the input frame. In particular, it does not

5-511
Vector Scope

assume that it is time-domain or frequency-domain data. The dialog box

parameters give you complete freedom to plot the data in the most appropriate
manner.
The scope updates the display for each new input frame. The number of
sequential frames displayed on the scope is specified by the Time display span
parameter for time-domain signals, and the Horizontal display span
parameter for user-defined signals. Setting either parameter to 1 plots the
current input frame’s data across the entire width of the scope. Setting these
display-span parameters to larger numbers allows you to see a broader section
of the signal by fitting more frames of data into the display region. A single
frame is the smallest unit that can be displayed, so neither parameter can be
less than 1.

Time display span = 4

➀ ➁ ➂ ➃

Scaling the Horizontal Axis for Time-Domain Signals

Scaling of the horizontal (time) axis for time-domain signals is automatic. The
range of the time axis is [0,S∗Tfi], where Tfi is the input frame period, and S is
the Time display span parameter. The spacing between time points is
Tfi/(M-1).

5-512
 Vector Scope

Scaling the Horizontal Axis for User-Defined Signals

To correctly scale the horizontal axis for user-defined signals, the block needs
to know the spacing of the data in the input. This is specified by the Increment
per sample in input frame parameter, Is. This parameter represents the
numerical interval between adjacent x-axis points corresponding to the input
data. For example, an input signal sampled at 500 Hz has an increment per
sample of 0.002 second. The actual units of this interval (seconds, meters,
Volts, etc.) are not needed for axis scaling.
When the Inherit sample increment from input check box is selected, the
block scales the horizontal axis by computing the horizontal interval between
samples in the input frame from the frame period of the input. For example, if
the input frame period is 1, and there are 64 samples per input frame, the
interval between samples is computed to be 1/64. Computing the interval this
way is usually only valid if the following conditions hold:

• The input is a nonoverlapping time-series; the x-axis on the scope represents

time.
• The input’s sample period (1/64 in the above example) is equal to the period
with which the physical signal was originally sampled.

In other cases, the frame rate and frame size do not provide enough
information for the block to correctly scale the horizontal axis, and you should
specify the appropriate value for the Increment per sample in input frame
parameter. The range of the horizontal axis is [0,M∗Is∗S], where M is the
number of samples in each consecutive input frame, and S is the Horizontal
display span parameter.

Scaling the Horizontal Axis for Frequency-Domain Signals

In order to correctly scale the horizontal (frequency) axis for frequency-domain
signals, the Vector Scope block needs to know the sample period of the original
time-domain sequence represented by the frequency-domain data. This is
specified by the Sample time of original time series parameter.
When the Inherit sample time from input check box is selected, the block
scales the frequency axis by reconstructing the frequency data from the
frame-period of the frequency-domain input. This is valid when the following
conditions hold:

5-513
Vector Scope

• Each frame of frequency-domain data shares the same length as the frame
of time-domain data from which it was generated; for example, when the
FFT is computed on the same number of points as are contained in the
time-domain input.
• The sample period of the time-domain signal in the simulation is equal to the
period with which the physical signal was originally sampled.
• Consecutive frames containing the time-domain signal do not overlap each
other; that is, a particular signal sample does not appear in more than one
sequential frame.

In cases where not all of these conditions hold, you should specify the
appropriate value for the Sample time of original time-series parameter.
The Frequency units parameter specifies whether the frequency axis values
should be in units of Hertz or rad/sec, and the Frequency range parameter
specifies the range of frequencies over which the magnitudes in the input
should be plotted. The available options are [0..Fs/2], [-Fs/2..Fs/2], and [0..Fs],
where Fs is the original time-domain signal’s sample frequency.
The Vector Scope block assumes that the input data spans the range [0,Fs), as
does the output from an FFT. To plot over the range [0..Fs/2] the scope
truncates the input vector leaving only the first half of the data, then plots
these remaining samples over half the frequency range. To plot over the range
[-Fs/2..Fs/2], the scope reorders the input vector elements such that the last
half of the data becomes the first half, and vice versa; then it relabels the x-axis
accordingly.
If the Frequency units parameter specifies Hertz, the spacing between
frequency points is 1/(M∗Ts). For Frequency units of rad/sec, the spacing
between frequency points is 2π/(M∗Ts). The Amplitude scaling parameter
allows you to select Magnitude or dB scaling along the y-axis.

Scope Properties
The Vector Scope block allows you to plot time-domain, frequency-domain, or
user-defined data, and adjust the frame span of the plot. Selecting the Scope
Properties check box displays the Input domain parameter, which specifies
the domain of the input data. In addition, for time-domain data, a Time
display span parameter allows you to specify the number of frames to be
displayed across the width of the scope window at any given time. For

5-514
 Vector Scope

user-defined data, a Horizontal display span parameter serves the same

function. Both of these parameters must be 1 or greater. See “Displaying Data”
on page 5-511 for more information.

Display Properties
The Vector Scope and Spectrum Scope blocks offer a similar collection of
display property settings. These can be exposed in the parameter dialog box by
selecting the Display properties check box. Many of the properties can be
accessed under the Axes menu in the unzoomed scope view (when Compact
display is deselected), or by right-clicking on the scope window.

The Show grid parameter toggles the background grid on and off. This option
can also be set in the Axes menu of the scope window.
When Persistence is selected, the window maintains successive displays. That
is, the scope does not erase the display after each frame (or collection of
frames), but overlays successive input frames in the scope display. This option
can also be set in the Axes menu of the scope window.
When Frame number is selected, the number of the current frame in the input
sequence is displayed on the scope window, incrementing the count as each
new input is received. Counting starts at 1 with the first input frame, and
continues until the simulation stops.
When Channel legend is selected, a legend indicating the line color, style, and
marker of each channel’s data is added. If the input signal is labeled, that label
is displayed in the channel legend. If the input signal is not labeled, but comes
from a Matrix Concatenation block with labeled inputs, those labels are
displayed in the channel legend. Otherwise, each channel in the legend is
labeled with the channel number (CH 1, CH 2, etc.). Click and drag on the legend

5-515
Vector Scope

to reposition it in the scope window; double click on the line label to edit the
text. Note that when the simulation is rerun, the new edits are lost and the
labels revert to the defaults. The Channel legend option can also be set in the
Axes menu of the scope window.

When Compact display is selected, the scope completely fills the containing
figure window. Menus and axis titles are not displayed, and the numerical axis
labels are shown within the axes. When Compact display is deselected, the
axis labels and titles are displayed in a gray border surrounding the scope axes,
and the window’s menus (including Axes and Channels) and toolbar are
visible. This option can also be set in the Axes menu of the scope window.
When Open scope at start of simulation is selected, the scope opens at the
start of the simulation. When this parameter is deselected, the scope does not
open automatically during the simulation. To view the scope, double-click on
the Vector Scope block, which brings up the scope as well as the block
parameter dialog box. This feature is useful when you have several scope
blocks in a model, and you do not want to view all the associated scopes during
the simulation.
Open scope immediately allows you to open the scope from the Vector Scope
parameters dialog box while the simulation is running. If the simulation is
running and the scope window is not visible, you can double-click on the scope
block to expose the scope window and the parameters dialog box. If you close
the scope window during simulation, you can make it visible again by checking
the Open scope immediately check box as long as the simulation is running.
The check box will become deselected as soon as the scope opens.
The Scope position parameter specifies a four-element vector of the form
[left bottom width height]

specifying the position of the scope window on the screen, where (0,0) is the
lower-left corner of the display. See the MATLAB figure command for more
information.

Axis Properties
The Vector Scope and Spectrum Scope blocks also share a similar collection of
axis property settings. For the Vector Scope, the parameters listed under the
Axis properties check box vary with the domain of the input. The dialogue box
below shows the parameters available for frequency-domain data.

5-516
 Vector Scope

Minimum Y-limit and Maximum Y-limit set the range of the vertical axis. If
Autoscale is selected from the right-click pop-up menu or from the Axes menu
option, the Minimum Y-limit and Maximum Y-limit values are automatically
recalculated to best fit the range of the data on the scope. Both of these
parameters are available for all input domains.
Y-axis title is the text to be displayed to the left of the y-axis. This parameter
is available for all input domains. X-axis title is an analogous parameter
available only when plotting user-defined data (this parameter is not visible in
the dialog box shown).
Frequency-domain and user-defined data need extra information to scale the
horizontal axis. For user-defined data, the parameters that provide this
information are Inherit sample increment from input and Increment in
sample in input frame. See “Scaling the Horizontal Axis for User-Defined
Signals” on page 5-513 for more information. For frequency-domain data, an
analogous pair of parameters, Inherit sample time from input and Sample
time of original time series, must be specified. See “Scaling the Horizontal
Axis for Frequency-Domain Signals” on page 5-513 for more information.
Three other parameters related to scaling the x-axis for frequency-domain
signals are Frequency units, Frequency range, and Amplitude scaling.
These are also described in “Scaling the Horizontal Axis for Frequency-Domain
Signals” on page 5-513.

5-517
Vector Scope

Line Properties
Both the Vector Scope and Spectrum scope also offer a similar collection of line
property settings. These can be exposed in the parameter dialog box by
selecting the Line properties check box. These properties can also be accessed
under the Channels menu in the unzoomed scope view (when Compact
display is deselected), or by right-clicking on the scope window.

The Line properties setting are typically used to help distinguish between two
or more independent channels of data on the scope.
The Line visibilities parameter specifies which channels’ data is displayed on
the scope, and which is hidden. The syntax specifies the visibilities in list form,
where the term on or off as a list entry specifies the visibility of the
corresponding channel’s data. The list entries are separated by the pipe
symbol, |.
For example, a five-channel signal would ordinarily generate five distinct plots
on the scope. To disable plotting of the third and fifth lines, enter the following
visibility specification.
on | on | off | on | off
➀ ➁ ➂ ➃ ➄

Note that the first (leftmost) list item corresponds to the first signal channel
(leftmost column of the input matrix).
The Line styles parameter specifies the line style with which each channel’s
data is displayed on the scope. The syntax specifies the channel line styles in
list form, with each list entry specifying a style for the corresponding channel’s
data. The list entries are separated by the pipe symbol, |.

5-518
 Vector Scope

For example, a five-channel signal would ordinarily generate all five plots with
a solid line style. To instead plot each line with a different style, enter
- | -- | : | -. | -
➀ ➁ ➂ ➃ ➄

These settings plot the signal channels with the following styles.

Line Style Appearance

Solid

Dashed

Dotted

Dash-dot

Solid

Note that the first (leftmost) list item, '-', corresponds to the first signal
channel (leftmost column of the input matrix). See LineStyle property of the
line function in the MATLAB documentation for more information about the
style syntax. To specify a marker for the individual sample points, use the Line
markers parameter, described below.

The Line markers parameter specifies the marker style with which each
channel’s samples are represented on the scope. The syntax specifies the
channels’ marker styles in list form, with each list entry specifying a marker
for the corresponding channel’s data. The list entries are separated by the pipe
symbol, |.
For example, a five-channel signal would ordinarily generate all five plots with
no marker symbol (i.e., the individual sample points are not marked on the
scope). To instead plot each line with a different marker style, you could enter
* | . | x | s | d
➀ ➁ ➂ ➃ ➄

5-519
Vector Scope

These settings plot the signal channels with the following styles.

Marker Style Appearance

Asterisk

Point

Cross

Square

Diamond

Note that the first (leftmost) list item, '*', corresponds to the first signal
channel (leftmost column of the input matrix). See the Marker property of the
line function in the MATLAB documentaion for more information about the
available markers.
Type the word stem instead of one of the basic Marker shapes to produce a stem
plot for the data in a particular channel.
The Line colors parameter specifies the color in which each channel’s data is
displayed on the scope. The syntax specifies the channel colors in list form,
with each list entry specifying a color (in one of MATLAB’s ColorSpec formats)
for the corresponding channel’s data. The list entries are separated by the pipe
symbol, |.
For example, a five-channel signal would ordinarily generate all five plots in
the color black. To instead plot the lines with the color order below, enter
[0 0 0] | [0 0 1] | [1 0 0 ] | [0 1 0] | [.7529 0 .7529]
➀ ➁ ➂ ➃ ➄

or
'k' | 'b' | 'r' | 'g' | [.7529 0 .7529]
➀ ➁ ➂ ➃ ➄

5-520
 Vector Scope

These settings plot the signal channels in the following colors (8-bit RGB
equivalents shown in the center column).

Color RGB Equivalent Appearance

Black (0,0,0)

Blue (0,0,255)

Red (255,0,0)

Green (0,255,0)

Dark purple (192,0,192)

Note that the first (leftmost) list item, 'k', corresponds to the first signal
channel (leftmost column of the input matrix). See ColorSpec in the online
MATLAB documentaion for more information about the color syntax.

Scope Window
The scope title (in the window title bar) is the same as the block title. The axis
scaling is set by parameters listed under the Axis properties check box in the
dialog box.
In addition to the standard MATLAB figure window menus (File, Edit,
Window, Help), the Vector Scope window has an Axes and a Channels menu.

The properties listed in the Axes menu apply to all channels. Many of the
parameters in this menu are also accessible through the block parameter
dialog box. These are Persistence, Show grid, Compact display, Frame
number, and Channel legend; see “Display Properties” on page 5-515 for more
information. Below are descriptions of the other parameters listed in the Axes
menu:
• Refresh erases all data on the scope display, except for the most recent trace.
This command is useful in conjunction with the Persistence setting.
• Autoscale resizes the y-axis to best fit the vertical range of the data. The
numerical limits selected by the autoscale feature are displayed in the
Minimum Y-limit and Maximum Y-limit parameters in the parameter
dialog box. You can change them by editing those values.

5-521
Vector Scope

• Save Position automatically updates the Scope position parameter in the

Axis properties field to reflect the scope window’s current position and size.
To make the scope window open at a particular location on the screen when
the simulation runs, simply drag the window to the desired location, resize
it as needed, and select Save Position. Note that the parameter dialog box
must be closed when you select Save Position in order for the Scope
position parameter to be updated.

The properties listed in the Channels menu apply to a particular channel. The
parameters listed in this menu are Visible, Style, Marker, and Color; they
correspond to the parameters listed in the dialog box under the Line
properties check box. See “Line Properties” on page 5-518 for more
information.
Many of these options can also be accessed by right-clicking with the mouse
anywhere on the scope display. The menu that pops up contains a combination
of the options available in both the Axes and Channels menus. The right-click
menu is very helpful when the scope is in zoomed mode, when the Axes and
Channels menus are not visible.

5-522
 Vector Scope

Dialog Box Scope Properties Dialog Box

Scope properties
Select to expose Scope properties panel. Tunable.
Input domain
The domain of the input; Time, Frequency, or User-defined. Tunable.
Time display span
The number of consecutive frames to display (horizontally) on the scope at
any one time. (Visible when the Input domain parameter is Time.)
Horizontal display span
(Not visible in the dialog box shown; appears under Scope properties
when the Input domain parameter is User-defined.) The number of
consecutive frames to display (horizontally) on the scope at any one time.

5-523
Vector Scope

Display Properties Dialog Box

Display properties
Select to expose Display properties panel. Tunable.
Show grid
Toggles the scope grid on and off. Tunable.
Persistence
Causes the window to maintain successive displays. That is, the scope does
not erase the display after each frame (or collection of frames), but overlays
successive input frames in the scope display. Tunable.
Frame number
Displays the number of the current frame in the input sequence, when
selected with Compact display off. The frame number is not shown when
Compact display is selected. Tunable.

Channel legend
Toggles the legend on and off. Tunable.
Compact display
Resizes the scope to fill the window. Tunable.
Open scope at start of simulation
Opens the scope at the start of the simulation. When this parameter is
deselected, the scope will not open automatically during the simulation; to
view the scope, double click on the Vector Scope block during the
simulation. This will bring up the scope as well as the block parameter
dialog box. Tunable.

5-524
 Vector Scope

Open scope immediately

Opens the scope from the Vector Scope parameters dialog box while the
simulation is running. The check box becomes deselected automatically
after use. Tunable.
Scope position
A four-element vector of the form [left bottom width height] specifying
the position of the scope window. (0,0) is the lower-left corner of the
display. Tunable.

Axis properties Dialog Box

Axis properties
Select to expose the Axis Properties panel. Tunable.
Frequency units
The frequency units for the x-axis, Hertz or rad/sec. (Visible when the
Input domain parameter is Frequency.) Tunable.

Frequency range
The frequency range over which to plot the data, [0..Fs/2], [-Fs/2..Fs/2],
or [0..Fs], where Fs is the sample frequency of the original time-domain
signal, 1/Ts. (Visible when the Input domain parameter is Frequency.)
Tunable.
Inherit sample time from input
Computes the time-domain sample period from the frame period and frame
size of the frequency-domain input; use only if the length of the each frame

5-525
Vector Scope

of frequency-domain data is the same as the length of the frame of

time-domain data from which is was generated. (Visible when the Input
domain parameter is Frequency.) Tunable.

Sample time of original time series

The sample period of the original time-domain signal, Ts. (Visible when the
Input domain parameter is Frequency.) Tunable.

Inherit sample increment from input

(Not visible in the dialog box shown; appears under Axis properties when
the Input domain parameter is User-defined.) Scales the horizontal axis
by computing the horizontal interval between samples in the input frame
from the frame period of the input; use only if the input’s sample period is
equal to the period with which the physical signal was originally sampled.
Tunable.
Increment per sample in input frame
(Not visible in the dialog box shown; appears under Axis properties when
the Input domain parameter is User-defined.) The numerical interval
between adjacent x-axis points corresponding to the user-defined input
data. Tunable.
Amplitude scaling
The scaling for the y-axis, dB or Magnitude. (Visible when the Input
domain parameter is Frequency.) Tunable.
Minimum Y-limit
The minimum value of the y-axis. Tunable.
Maximum Y-limit
The maximum value of the y-axis. Tunable.
Y-Axis title
The text to be displayed to the left of the y-axis. Tunable.
X-Axis title
(Not visible in the dialog box shown; appears under Axis properties when
the Input domain parameter is User-defined.) The text to be displayed
below the x-axis. Tunable.

5-526
 Vector Scope

Line Properties Dialog Box

Line properties
Select to expose the Line Properties panel. Tunable.
Line visibilities
The visibility of the various channels’ scope traces, on or off. Channels are
separated by a pipe (|) symbol. Tunable.
Line styles
The line styles of the various channels’ scope traces. Channels are
separated by a pipe (|) symbol. Tunable.
Line markers
The line markers of the various channels’ scope traces. Channels are
separated by a pipe (|) symbol. Tunable.
Line colors
The colors of the various channels’ scope traces, in one of the ColorSpec
formats. Channels are separated by a pipe (|) symbol. Tunable.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

5-527
Vector Scope

See Also Matrix Viewer DSP Blockset

Spectrum Scope DSP Blockset

See “Viewing Signals” on page 3-80 for related information.

5-528
 Wavelet Analysis

Purpose 5Wavelet Analysis

Decompose a signal into components of logarithmically decreasing frequency
intervals and sample rates (requires the Wavelet Toolbox).

Library Filtering / Multirate Filters

Description The Wavelet Analysis block uses the wfilters function from the Wavelet
Toolbox to construct a dyadic analysis filter bank that decomposes a broadband
signal into a collection of successively more bandlimited components. An
n-level filter bank structure is shown below, where n is specified by the
Number of levels parameter.

Wavelet Analysis Filter Bank, n Levels

u HP ↓2 2Ts y1

LP ↓2 HP ↓2 4Ts y2

LP ↓2 HP ↓2 8Ts y3

LP ↓2 ... HP ↓2 yn

Tsi = Ts LP ↓2 yn+1

HP: highpass filter with fc ≈ 1/2 Nyquist

Tso = (2k)Ts for output yk, 1 ≤ k ≤ n
LP: lowpass filter with fc ≈ 1/2 Nyquist
↓2: downsample by 2 Tso = (2n)Ts for output yn+1

At each level, the low-frequency output of the previous level is decomposed into
adjacent high- and low-frequency subbands by a highpass (HP) and lowpass
(LP) filter pair. Each of the two output subbands is half the bandwidth of the
input to that level. The bandlimited output of each filter is maximally
decimated by a factor of 2 to preserve the bit rate of the original signal.

5-529
Wavelet Analysis

Filter Coefficients
The filter coefficients for the highpass and lowpass filters are computed by the
Wavelet Toolbox function wfilters, based on the wavelet specified in the
Wavelet name parameter. The table below lists the available options.

Wavelet Name Sample Wavelet Function Syntax

Haar wfilters('haar')

Daubechies wfilters('db4')

Symlets wfilters('sym3')

Coiflets wfilters('coif1')

Biorthogonal wfilters('bior3.1')

Reverse Biorthogonal wfilters('rbio3.1')

Discrete Meyer wfilters('dmey')

The Daubechies, Symlets, and Coiflets options enable a secondary Wavelet

order parameter that allows you to specify the wavelet order. For example, if
you specify a Daubechies wavelet with Wavelet order equal to 6, the Wavelet
Analysis block calls the wfilters function with input argument 'db6'.
The Biorthogonal and Reverse Biorthogonal options enable a secondary
Filter order [synthesis / analysis] parameter that allows you to
independently specify the wavelet order for the analysis and synthesis filter
stages. For example, if you specify a Biorthogonal wavelet with Filter order
[synthesis / analysis] equal to [2 / 6], the Wavelet Analysis block calls the
wfilters function with input argument 'bior2.6'.

See the Wavelet Toolbox decantation for more information about the wfilters
function. If you want to explicitly specify the FIR coefficients for the analysis
filter bank, use the Dyadic Analysis Filter Bank block.

Tree Structure
The wavelet tree structure has n+1 outputs, where n is the number of levels.
The sample rate and bandwidth of the top output are half the input sample rate
and bandwidth. The sample rate and bandwidth of each additional output

5-530
 Wavelet Analysis

(except the last) are half that of the output from the previous level. In general,
for an input with sample period Tsi = Ts, and bandwidth BW, output yk has
sample period Tso,k and bandwidth BWk.

 k
 ( 2 )T s (1 ≤ k ≤ n)
T so, k = 
 ( 2 n )T (k = n + 1)
 s

 BW
 ---------- (1 ≤ k ≤ n)
 2
k
BW k = 
 BW
---------- (k = n + 1)
 n
 2

Note that in frame-based mode, the change in the sample period of output yk is
reflected by its frame size, Mo,k, rather than by its frame rate.


 Mi
 ------- (1 ≤ k ≤ n)
 2
k
M o, k = 
 Mi
 ------- (k = n + 1)
n
 2


The bottom two outputs (yn and yn+1) share the same sample period,
bandwidth, and frame size because they originate at the same tree level.

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block filters each channel independently over time. The
output at each port is the same size as the input, one output channel for each
input channel. As described earlier, each output port has a different sample
period.
The figure below shows the input and output sample periods for a 64-channel
sample-based input to a three-level filter bank. The input has a period of 1, so
the fastest output has a period of 2.

5-531
Wavelet Analysis

Tso = 2

Tso = 4
Tsi = 1
Tso = 8

Tso = 8

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block filters each channel independently over time. The input frame
size Mi must be a multiple of 2n, and n is the number of filter bank levels. For
example, a frame size of 8 would be appropriate for a three-level tree (23=8).
The number of columns in each output is the same as the number of columns
in the input.
Each output port has the same frame period as the input. The reduction in the
output sample rates results from the smaller output frame sizes, as shown in
the example below for a four-channel input to a three-level filter bank.

Tso = 1/32)

Tfi = 1 Tso = 1/16)

Tsi = 1/64 Tfo = 1
Tso = 1/8)

Tso = 1/8)

Latency

Zero Latency. The Wavelet Analysis block has no tasking latency for frame-based
operation, which is always single-rate. The block therefore analyzes the first
input sample (received at t=0) to produce the first output sample at each port.

Nonzero Latency. For sample-based operation, the Wavelet Analysis block is

multirate and has 2n-1 samples of latency in both Simulink tasking modes. As
a result, the block repeats a zero initial condition in each channel for the first

5-532
 Wavelet Analysis

2n-1 output samples, before propagating the first analyzed input sample
(computed from the input received at t=0).
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

The parameters displayed in the dialog box vary for different wavelet types.
Only some of the parameters listed below are visible in the dialog box at any
one time.
Wavelet name
The wavelet used in the analysis.
Wavelet order
The order for the Daubechies, Symlets, and Coiflets wavelets. This
parameter is available only when one of these wavelets is selected in the
Wavelet name menu.

Filter order [synthesis / analysis]

The filter orders for the synthesis and analysis stages of the Biorthogonal
and Reverse Biorthogonal wavelets. For example, [2 / 6] selects a
second-order synthesis stage and a sixth-order analysis stage. The Filter
order parameter is available only when one of the above wavelets is
selected in the Wavelet name menu.
Number of levels
The number of filter bank levels. An n-level structure has n+1 outputs.

5-533
Wavelet Analysis

References Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter

Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.
Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA:
Wellesley-Cambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ:
Prentice Hall, 1993.

Supported Double-precision floating point

Data Types

See Also Dyadic Analysis Filter Bank DSP Blockset

Wavelet Synthesis DSP Blockset
wfilters Wavelet Toolbox

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

• “Multirate Filters” on page 4-9

5-534
 Wavelet Synthesis

Purpose 5Wavelet Synthesis

Reconstruct a signal from its multirate bandlimited components (requires the
Wavelet Toolbox).

Library Filtering / Multirate Filters

Description The Wavelet Synthesis block uses the wfilters function from the Wavelet
Toolbox to reconstruct a signal that was decomposed by the Wavelet Analysis
block. The reconstruction or synthesis process is the inverse of the analysis
process, and restores the original signal by upsampling, filtering, and summing
the bandlimited inputs in stages corresponding to the analysis process. An
n-level synthesis filter bank structure is shown below, where n is specified by
the Number of levels parameter.
Wavelet Synthesis Filter Bank, n Levels

u1 2Ts ↑2 HP Σ y

u2 4Ts ↑2 HP Σ ↑2 LP

u3 8Ts ↑2 HP Σ ↑2 LP

un ↑2 HP Σ ... ↑2 LP

un+1 ↑2 LP Tso = Ts

Tsi = (2k)Ts for input uk, 1 ≤ k ≤ n HP: highpass filter with fc ≈ 1/2 Nyquist
LP: lowpass filter with fc ≈ 1/2 Nyquist
Tsi = (2n)Ts for input un+1
↑2: upsample by 2

At each level, the two bandlimited inputs (one low-frequency, one

high-frequency, both with the same sample rate) are upsampled by a factor of 2
to match the sample rate of the input to the next stage. They are then filtered
by a highpass (HP) and lowpass (LP) filter pair with coefficients calculated to
cancel (in the subsequent summation) the aliasing introduced in the
corresponding analysis filter stage. The output from each
(upsample-filter-sum) level has twice the bandwidth and twice the sample rate
of the input to that level.

5-535
Wavelet Synthesis

For perfect reconstruction, the Wavelet Synthesis and Wavelet Analysis blocks
must have the same parameter settings.

Filter Coefficients
The filter coefficients for the highpass and lowpass filters are computed by the
Wavelet Toolbox function wfilters, based on the wavelet specified in the
Wavelet name parameter. The table below lists the available options.

Wavelet Name Sample Wavelet Function Syntax

Haar wfilters('haar')

Daubechies wfilters('db4')

Symlets wfilters('sym3')

Coiflets wfilters('coif1')

Biorthogonal wfilters('bior3.1')

Reverse Biorthogonal wfilters('rbio3.1')

Discrete Meyer wfilters('dmey')

The Daubechies, Symlets, and Coiflets options enable a secondary Wavelet

order parameter that allows you to specify the wavelet order. For example, if
you specify a Daubechies wavelet with Wavelet order equal to 6, the Wavelet
Synthesis block calls the wfilters function with input argument 'db6'.
The Biorthogonal and Reverse Biorthogonal options enable a secondary
Filter order [synthesis / analysis] parameter that allows you to
independently specify the wavelet order for the analysis and synthesis filter
stages. For example, if you specify a Biorthogonal wavelet with Filter order
[synthesis / analysis] equal to [2 / 6], the Wavelet Synthesis block calls the
wfilters function with input argument 'bior2.6'.

See the Wavelet Toolbox documentation for more information about the
wfilters function. If you want to explicitly specify the FIR coefficients for the
synthesis filter bank, use the Dyadic Synthesis Filter Bank block.

5-536
 Wavelet Synthesis

Tree Structure
The wavelet tree structure has n+1 inputs, where n is the number of levels. The
sample rate and bandwidth of the output are twice the sample rate and
bandwidth of the top input. The sample rate and bandwidth of each additional
input (except the last) are half that of the input to the previous level.

T si, k + 1 = 2T si, k 1≤k<n

BW k
BW k + 1 = ------------- 1≤k<n
2

The bottom two inputs (un and un+1) should have the same sample rate and
bandwidth since they are processed by the same level.

T si, n + 1 = T si, n

BW n + 1 = BW n

Note that in frame-based mode, the sample period of input uk is reflected by its
frame size, Mi,k, rather than by its frame rate.

M i, k
M i, k + 1 = ------------ 1≤k<n
2

M i, n + 1 = M i, n

Sample-Based Operation
An M-by-N sample-based matrix input is treated as M∗N independent
channels, and the block filters each channel independently over time. The
output is the same size as the input at each port, one output channel for each
input channel. As described earlier, each input port has a different sample
period.

5-537
Wavelet Synthesis

The figure below shows the input and output sample periods for the four
64-channel sample-based inputs to a three-level filter bank. The fastest input
has a period of 2, so the output period is 1.

Tsi = 2

Tsi = 4
Tso = 1
Tsi = 8

Tsi = 8

Frame-Based Operation
An Mi-by-N frame-based matrix input is treated as N independent channels,
and the block filters each channel independently over time. The number of
columns in the output is the same as the number of columns in the input.
All inputs must have the same frame period, which is also the output frame
period. The different input sample rates should be represented by the input
frame sizes: If the input to the top port has frame size Mi, the input to the
second-from-top port should have frame size Mi/2, the input to the
third-from-top port should have frame size Mi/4, and so on. The input to the
bottom port should have the same frame size as the second-from-bottom port.
The increase in the sample rate of the output is also represented by its frame
size, which is twice the largest input frame size.
The relationship between sample periods, frame periods, and frame sizes is
shown below for a four-channel frame-based input to a 3-level filter bank.

(Tsi=1/32)

(Tsi=1/16) Tfo = 1
Tfi = 1
Tso = 1/64
(Tsi=1/8)

(Tsi=1/8)

5-538
 Wavelet Synthesis

Latency

Zero Latency. The Wavelet Synthesis block has no tasking latency for
frame-based operation, which is always single-rate. The block therefore uses
the first input samples (received at t=0) to synthesize the first output sample.

Nonzero Latency. For sample-based operation, the Wavelet Synthesis block is

multirate and has the following tasking latencies:

• 2n-2 samples in Simulink’s single-tasking mode

• 2n samples in Simulink’s multitasking mode

In the above cases, the block repeats a zero initial condition in each channel for
the first D output samples, where D is the latency shown above. For example,
in single-tasking mode the block generates 2n-2 zero-valued output samples in
each channel before propagating the first synthesized output sample
(computed from the inputs received at t=0).
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-91 and “The
Simulation Parameters Dialog Box” in the Simulink documentation for more
information about block rates and Simulink’s tasking modes.

Dialog Box

The parameters displayed in the dialog box vary for different wavelet types.
Only some of the parameters listed below are visible in the dialog box at any
one time.
Wavelet name
The wavelet used in the synthesis.

5-539
Wavelet Synthesis

Wavelet order
The order for the Daubechies, Symlets, and Coiflets wavelets. This
parameter is available only when one of these wavelets is selected in the
Wavelet name menu.

Filter order [synthesis / analysis]

The filter orders for the synthesis and analysis stages of the Biorthogonal
and Reverse Biorthogonal wavelets. For example, [2 / 6] selects a
second-order synthesis stage and a sixth-order analysis stage. The Filter
order parameter is available only when one of the above wavelets is
selected in the Wavelet name menu.
Number of levels
The number of filter bank levels. An n-level structure has n+1 outputs.

References Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter

Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.
Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA:
Wellesley-Cambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ:
Prentice Hall, 1993.

Supported Double-precision floating point

Data Types

See Also Dyadic Synthesis Filter Bank DSP Blockset

Wavelet Analysis DSP Blockset
wfilters Wavelet Toolbox

See the following sections for related information:

• “Converting Sample Rates and Frame Rates” on page 3-20

• “Multirate Filters” on page 4-9

5-540
 Window Function

Purpose 5Window Function

Compute a window, and/or apply a window to an input signal.

Library DSP Sources, Signal Operations

Description The Window Function block has three modes of operation, selected by the
Operation parameter as described below.

Operation Modes
In each mode, the block first creates a window vector, w, by sampling the
window specified in the Window type parameter at M discrete points. The
Operation modes are:

• Apply window to input

In this mode the block computes an M-by-1 window vector, w, and multiplies
the vector element-wise with each of the N channels in the M-by-N input
matrix u.
y = repmat(w,1,N) .* u % Equivalent MATLAB code

A length-M 1-D vector input is treated as an M-by-1 matrix. The output, y,

always has the same dimension as the input. If the input is frame-based, the
output is frame-based; otherwise, the output is sample-based.
• Generate window
In this mode the block generates a sample-based 1-D window vector, w, with
length M specified by the Window length parameter. The In port is disabled.
• Generate and apply window
In this mode the block computes an M-by-1 window vector, w, and multiplies
the vector element-wise with each of the N channels in the M-by-N input
matrix u.
y = repmat(w,1,N) .* u % Equivalent MATLAB code

A length-M 1-D vector input is treated as an M-by-1 matrix. The block

produces two outputs:
- At the Out port, the block produces the result of the multiplication, y,
which has the same dimension as the input. If the input is frame-based,
output y is frame-based; otherwise, output y is sample-based.
- At the Win port, the block produces the M-by-1 window vector, w. Output w
is always sample-based.

5-541
Window Function

Window Sampling
For the generalized-cosine windows (Blackman, Hamming, and Hann), the
Sampling parameter determines whether the window samples are computed
in a periodic or a symmetric manner. For example, if Sampling is set to
Symmetric, a Hamming window of length M is computed as
w = hamming(M) % Symmetric (aperiodic) window

If Sampling is set to Periodic, the same window is computed as

w = hamming(M+1) % Periodic (asymmetric) window
w = w(1:M)

Window Type
The available window types are shown in the table below. The Stopband
attenuation in dB and Beta parameters specify the characteristics of the
Chebyshev and Kaiser windows, respectively, and are only available when
those window designs are selected.
When Window type is set to User defined, the Window function block
computes the user-defined window specified by the Window function name
parameter. If the user-defined window requires parameters other than the
window length, select the Additional parameters for user defined window
check box. The cell array entered in Window function parameters determines
the values of the additional parameters.
For complete information about the other window functions, consult the Signal
Processing Toolbox documentation.

Window Description
Type

Bartlett Computes a Bartlett window.

w = bartlett(M)

Blackman Computes a Blackman window.

w = blackman(M)

5-542
 Window Function

Window Description
Type

Rectangular Computes a rectangular window.

w = rectwin(M)

Chebyshev Computes a Chebyshev window with stopband ripple R.

w = chebwin(M,R)

Hamming Computes a Hamming window.

w = hamming(M)

Hann Computes a Hann window (also known as a Hanning

window).
w = hann(M)

Hanning Obsolete. This window option is included only for

compatibility with older models. Use the Hann option
instead of Hanning whenever possible.
Kaiser Computes a Kaiser window with Kaiser parameter beta.
w = kaiser(M,beta)

Triang Computes a triangular window.

w = triang(M)

User Defined Computes the user-defined window function specified by the

entry in the Window function name parameter, usrwin.
w = usrwin(M) % window takes no extra parameters
w = usrwin(M,x1,...,xn) % window takes extra
parameters {x1 ... xn}

5-543
Window Function

Dialog Box

Operation
The block’s operation: Apply window to input, Generate window, or
Generate and apply window. The input/output port configuration is
updated to match the parameter setting.
Window type
The type of window to apply. Tunable.
Window length
The length of the window to apply. This parameter is available only when
Generate window is selected in the Operation menu. Otherwise, the
window vector length is computed to match the input frame size, M.
Sampling
The window sampling for generalized-cosine windows, Symmetric or
Periodic. Tunable.

Stopband attenuation in dB
(Not shown in dialog above. Visible for the Chebyshev window.) The level
(dB) of stopband attenuation, Rs. Tunable.
Beta
(Not shown in dialog above. Visible for the Kaiser window.) The Kaiser
window β parameter. Increasing β widens the mainlobe and decreases the
amplitude of the window sidelobes in the window’s frequency magnitude
response. Tunable.

5-544
 Window Function

Window function name

(Not shown in dialog above. Visible for User defined windows.) The name
of the user-defined window function to be calculated by the block.
Additional parameters for user defined window
(Not shown in dialog above. Visible for User defined windows.) Enables
the Window function parameters when selected. Select when the
user-defined window requires parameters other than the window length.
Window function parameters
(Not shown in dialog above.Visible for User defined windows.) The extra
parameters required by the user-defined window function (besides the
window length), enabled when Additional parameters for user defined
window is selected. The entry must be a cell array.

Supported Single-precision floating point

Data Types Double-precision floating point

See Also FFT DSP Blockset

bartlett Signal Processing Toolbox
blackman Signal Processing Toolbox
rectwin Signal Processing Toolbox
chebwin Signal Processing Toolbox
hamming Signal Processing Toolbox
hann Signal Processing Toolbox
kaiser Signal Processing Toolbox
triang Signal Processing Toolbox

5-545
Yule-Walker AR Estimator

Purpose 5Yule-Walker AR Estimator

Compute an estimate of AR model parameters using the Yule-Walker method.

Library Estimation / Parametric Estimation

Description The Yule-Walker AR Estimator block uses the Yule-Walker AR method, also
called the autocorrelation method, to fit an autoregressive (AR) model to the
windowed input data by minimizing the forward prediction error in the
least-squares sense. This formulation leads to the Yule-Walker equations,
which are solved by the Levinson-Durbin recursion.
The Yule-Walker AR Estimator block can output the AR model coefficients as
polynomial coefficients, reflection coefficients, or both. The input is a
sample-based vector (row, column, or 1-D) or frame-based vector (column only)
representing a frame of consecutive time samples from a single-channel signal,
which is assumed to be the output of an AR system driven by white noise. The
block computes the normalized estimate of the AR system parameters, A(z),
independently for each successive input frame.

G G
H ( z ) = ------------ = -------------------------------------------------------------------------------
A(z) –1
1 + a ( 2 )z + … + a ( p + 1 )z
–p

When Inherit estimation order from input dimensions is selected, the

order, p, of the all-pole model is one less that the length of the input vector.
Otherwise, the order is the value specified by the Estimation order
parameter. The Yule-Walker AR Estimator and Burg AR Estimator blocks
return similar results for large frame sizes.
When Output(s) is set to A, port A is enabled. Port A outputs a column vector
of length p+1 that contains the normalized estimate of the AR model
coefficients in descending powers of z,
[1 a(2) ... a(p+1)]

When Output(s) is set to K, port K is enabled. Port K outputs a length-p column

vector whose elements are the AR model reflection coefficients. When
Output(s) is set to A and K, both port A and K are enabled, and each port
outputs its respective column vector of AR model coefficients. The outputs at
both ports A and K are always 1-D vectors.
The square of the model gain, G (a scalar), is provided at port G.

5-546
 Yule-Walker AR Estimator

Dialog Box

Output(s)
The type of AR model coefficients output by the block. The block can output
polynomial coefficients (A), reflection coefficients (K), or both (A and K).
Tunable.
Inherit estimation order from input dimensions
When selected, sets the estimation order p to one less than the length of the
input vector. Tunable.
Estimation order
The order of the AR model, p. This parameter is enabled when Inherit
estimation order from input dimensions is not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

5-547
Yule-Walker AR Estimator

See Also Burg AR Estimator DSP Blockset

Covariance AR Estimator DSP Blockset
Modified Covariance AR Estimator DSP Blockset
Yule-Walker Method DSP Blockset
aryule Signal Processing Toolbox

5-548
 Yule-Walker Method

Purpose 5Yule-Walker Method

Compute a parametric estimate of the spectrum using the Yule-Walker AR
method.

Library Estimation / Power Spectrum Estimation

Description The Yule-Walker Method block estimates the power spectral density (PSD) of
the input using the Yule-Walker AR method. This method, also called the
autocorrelation method, fits an autoregressive (AR) model to the windowed
input data by minimizing the forward prediction error in the least-squares
sense. This formulation leads to the Yule-Walker equations, which are solved
by Levinson-Durbin recursion.
The input is a sample-based vector (row, column, or 1-D) or frame-based vector
(column only) representing a frame of consecutive time samples from a
single-channel signal. The block’s output (a column vector) is the estimate of
the signal’s power spectral density at Nfft equally spaced frequency points in
the range [0,Fs), where Fs is the signal’s sample frequency.
When Inherit estimation order from input dimensions is selected, the order
of the all-pole model is one less that the input frame size. Otherwise, the order
is the value specified by the Estimation order parameter. The spectrum is
computed from the FFT of the estimated AR model parameters.
When Inherit FFT length from estimation order is selected, Nfft is specified
by (estimation order + 1), which must be a power of 2. When Inherit FFT
length from estimation order is not selected, Nfft is specified as a power of 2
by the FFT length parameter, and the block zero pads or truncates the input
to Nfft before computing the FFT. The output is always sample-based.
See the Burg Method block reference for a comparison of the Burg Method,
Covariance Method, Modified Covariance Method, and Yule-Walker AR
Estimator blocks. The Yule-Walker AR Estimator and Burg Method blocks
return similar results for large buffer lengths.

5-549
Yule-Walker Method

Dialog Box

Inherit estimation order from input dimensions

When selected, sets the estimation order to one less than the length of the
input vector.
Estimation order
The order of the AR model. This parameter is enabled when Inherit
estimation order from input dimensions is not selected.

Inherit FFT length from estimation order

When selected, uses the estimation order to determine the number of data
points, Nfft, on which to perform the FFT. Sets Nfft equal to (estimation
order + 1). Note that Nfft must be a power of 2, so (estimation order + 1)
must be a power of 2.
FFT length
The number of data points, Nfft, on which to perform the FFT. If Nfft
exceeds the input frame size, the frame is zero-padded as needed. This
parameter is enabled when Inherit FFT length from estimation order is
not selected.

References Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood

Cliffs, NJ: Prentice-Hall, 1988.
Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood
Cliffs, NJ: Prentice-Hall, 1987.

Supported Double-precision floating point

Data Types

5-550
 Yule-Walker Method

Supported Double-precision floating point

Data Types

See Also Burg Method DSP Blockset

Covariance Method DSP Blockset
Levinson-Durbin DSP Blockset
Autocorrelation LPC DSP Blockset
Short-Time FFT DSP Blockset
Yule-Walker AR Estimator DSP Blockset
pyulear Signal Processing Toolbox

See “Power Spectrum Estimation” on page 4-15 for related information.

5-551
Zero Pad

Purpose 5Zero Pad

Alter the input size by zero-padding or truncating rows and/or columns.

Library Signal Operations

Description The Zero Pad block changes the size of the input matrix from Mi-by-Ni to
Mo-by-No by zero-padding or truncating along the rows, the columns, or both
dimensions. The dimensions of the output, Mo and No, are specified by the
Number of output rows and Number of output columns parameters,
respectively. You can set Action when truncation occurs so that the block
gives a warning or an error when truncation occurs.
The Zero pad along parameter specifies how the input should be altered. The
options are:
• Columns
When Columns is selected, the Number of output rows parameter (Mo) is
enabled, and the block pads or truncates each input column by an equal
amount. If Mo>Mi, the block pads by adding Mo-Mi rows of zeros to the
bottom of the matrix. If Mo<Mi, the block truncates by deleting Mi-Mo rows
from the bottom of the matrix. In both cases, the number of columns is
unchanged (No=Ni). A 1-D vector input is zero padded or truncated at the
“bottom,” and the output is a 1-D vector.
• Rows
When Rows is selected, the Number of output columns parameter (No) is
enabled, and the block pads or truncates each input row by an equal amount.
If No>Ni, the block pads by adding No-Ni columns of zeros to the right side of
the matrix. If No<Ni, the block truncates by deleting Ni-No columns from the
right side of the matrix. In both cases, the number of rows is unchanged
(Mo=Mi). A 1-D vector input is zero padded or truncated at the “bottom,” and
the output is a 1-D vector.
• Columns and rows
When Columns and rows is selected, both the Number of output rows
parameter (Mo) and the Number of output columns parameter (No) are
enabled, and the block pads or truncates rows and columns as specified. A
length-Mi 1-D vector input is treated as an Mi-by-1 matrix and the output is
an Mo-by-No matrix.

5-552
 Zero Pad

• None
When None is selected, the input is passed through to the output without
padding or truncation.

Example In the model below, the 3-by-3 input is zero-padded along the column
dimension to 5-by-3. The parameter settings in the Zero Pad block are:

• Zero pad along = Columns

• Number of output rows = 5

Dialog Box

Zero pad along

The direction along which to pad or truncate. Columns specifies that the
row dimension should be changed to Mo; Rows specifies that the column
dimension should be changed to No; Columns and rows specifies that both

5-553
Zero Pad

column and row dimensions should be changed; None disables padding and
truncation and passes the input through to the output unchanged.
Number of output rows
The desired number of rows in the output, Mo. This parameter is enabled
when Columns or Columns and rows is selected in the Zero pad along
menu.
Number of output columns
The desired number of columns in the output, No. This parameter is
enabled when Rows or Columns and rows is selected in the Zero pad
along menu.

Action When Truncation Occurs

The block’s behavior when the input matrix is truncated. It gives a
Warning, an Error, or gives no indication of the truncation when set to
None.

Supported Fixed-point
Data Types Custom data types
Boolean
8-, 16-, and 32-bit signed integer
8-, 16-, and 32-bit unsigned integer
Single-precision floating point
Double-precision floating point

See Also Matrix Concatenation Simulink

Pad DSP Blockset
Repeat DSP Blockset
Submatrix DSP Blockset
Upsample DSP Blockset
Variable Selector DSP Blockset

5-554
 6

DSP Function Reference

DSP Blockset Utility Functions . . . . . . . . . . . 6-2
6 DSP Function Reference

DSP Blockset Utility Functions

In addition to the blocks contained in the DSP Blockset libraries, a number of
utility functions and scripts are provided in the toolbox\dspblks\dspblks
directory. The key functions are listed below and described on the following
pages:
• dsp_links
• dsplib
• dspstartup
• liblinks
• rebuffer_delay

6-2
 dsp_links

Purpose 6dsp_links
Display library link information for blocks linked to the DSP Blockset.

Syntax dsp_links
dsplinks(sys)
dsplinks(sys,mode)

Description dsp_links displays library link information for blocks linked to the DSP
Blockset. For each block in the current model, dsp_links replaces the block
name with the full pathname to the block’s library link in the DSP Blockset.
Blocks linked to v4 or later DSP Blockset blocks are highlighted in green while
blocks linked to v3 DSP Blockset blocks are highlighted in yellow. Blocks at all
levels of the model are analyzed.
A summary report indicating the number of blocks linked to each blockset
version is also displayed in the MATLAB command window. The highlighting
and link display is disabled when the model is executed or saved, or when
dsp_links is executed a second time from the MATLAB command line.

dsp_links(sys) toggles the display of block links in system sys. If sys is the
current model (gcs), this is the same as the plain dsp_links syntax.

dsp_links(sys,mode) directly sets the link display state, where mode can be
'on', 'off', or 'toggle'. The default is 'toggle'.

See Also liblinks DSP Blockset

6-3
dsplib

Purpose 6dsplib
Open the main DSP Blockset library.

Syntax dsplib
dsplib ver

Description dsplib opens the current version of the main DSP Blockset library.

dsplib ver opens version ver of the DSP Blockset library, where ver can be 2,
3, or 4.

When you launch an older version of the DSP Blockset, MATLAB displays a
message reminding you that a newer version exists.

6-4
 dspstartup

Purpose 6dspstartup
Configure the Simulink environment for DSP systems.

Syntax dspstartup

Description dspstartup configures a number of Simulink environment parameters with

settings appropriate for a typical DSP project. When the Simulink
environment has successfully been configured, the function displays the
following message in the command window.
Changed default Simulink settings for DSP systems (dspstartup.m).

To automatically configure the Simulink environment at startup, add a call to

dspstartup.m from your startup.m file. If you do not have a startup.m file on
your path, you can create one from the startupsav.m template in the
toolbox/local directory.

To edit startupsav.m, simply replace the load matlab.mat command with a

call to dspstartup.m, and save the file as startup.m. The result should look
like this.
%STARTUP Startup file
% This file is executed when MATLAB starts up,
% if it exists anywhere on the path.

dspstartup;

For more information, see the description for the startup command in the
MATLAB documentation, “Using dspstartup.m” on page 2-12.
The dspstartup.m script sets the following Simulink environment parameters.
See Appendix A, “Model and Block Parameters,” in the Simulink
documentation for complete information about a particular setting.

Parameter Setting

SingleTaskRate error
TransMsg

Solver fixedstepdiscrete

SolverMode SingleTasking

6-5
dspstartup

Parameter Setting

StartTime 0.0

StopTime inf

FixedStep auto

SaveTime off

SaveOutput off

AlgebraicLoopMsg error

InvariantConstants on

RTWOptions [get_param(0,'RTWOptions')',
-aRollThreshold=2']

See Also startup MATLAB

6-6
 liblinks

Purpose 6liblinks
Display library link information for blocks linked to the DSP Blockset.

Syntax liblinks
liblinks(sys)
liblinks(sys,mode,lib)
liblinks(sys,mode,lib,clrs)
blks = liblinks(...)

Description Please see the command line help for liblinks. Type
help liblinks

in the MATLAB command window.

See Also dsp_links DSP Blockset

6-7
rebuffer_delay

Purpose 6rebuffer_delay
Compute the number of samples of delay introduced by buffering and
unbuffering operations.

Syntax d = rebuffer_delay(f,n,m)
d = rebuffer_delay(f,n,m,'singletasking')

Description d = rebuffer_delay(f,n,m) returns the delay (in samples) introduced by the

buffering and unbuffering blocks in multitasking operations, where f is the
input frame size, n is the Buffer size parameter setting, and m is the Buffer
overlap parameter setting.

The blocks whose delay can be computed by rebuffer_delay are:

• Buffer
• Unbuffer

d = rebuffer_delay(f,n,m,'singletasking') returns the delay (in

samples) introduced by these blocks in single-tasking operations.
The table below shows the appropriate rebuffer_delay parameter values to
use in computing delay for the two blocks.

Block Parameter Values

Buffer f = input frame size (f=1 for sample-based mode)

n = Buffer size
m = Buffer overlap

Unbuffer f = input frame size

n = 1
m = 0

See Also Buffer DSP Blockset

Unbuffer DSP Blockset

6-8
 Index

Symbols
Numerics
f (linear frequency). See frequencies 0s
fnyq (Nyquist frequency). See frequencies inserting 5-200, 5-207, 5-484
Fs (sample frequency or rate) outputting
See sample periods Counter block 5-105
M (frame size). See frame sizes and matrices Discrete Impulse block 5-138
Mi (input frame size). See frame sizes Integer Delay block 5-244
Mo (output frame size). See frame sizes N-Sample Enable block 5-325
N (number of channels) Signal From Workspace block 5-388, 5-457
See sample vectors and matrices padding with 3-27, 3-31
ω (digital frequency). See frequencies 1s, outputting 5-325
Ω (angular frequency). See frequencies 2-norm 5-405
Ωp (passband edge frequency)
See edge frequencies
Ωp1 (lower passband edge frequency) A
See edge frequencies acquiring data, blocks for 5-10
Ωp2 (upper passband edge frequency) adaptive filter designs
See edge frequencies blocks for 1-4
Ωs (stopband edge frequency) FIR 5-268
See edge frequencies Kalman 5-249
Ωs1 (lower stopband edge frequency) LMS 5-268
See edge frequencies RLS 5-375
Ωs2 (upper stopband edge frequency) adaptive filters 4-3
See edge frequencies Adaptive Filters library 5-9
Rp (passband ripple). See passband ripple addition, cumulative 5-116
Rs (stopband attenuation) algebraic loop errors 3-92
See stopband attenuation algorithmic delay 3-86
T (signal period). See periods adjustable 3-90
T (tunable parameter). See tuning parameters and initial conditions 3-90
Tf (frame period). See frame periods basic 3-89
Tfi (input frame period). See frame periods excess 3-91
Tfo (output frame period). See frame periods relation to latency 3-91
Ts (sample period). See sample periods zero 3-87
Tsi (input sample period). See sample periods Analog Filter Design block 4-7, 5-23
Tso (output sample period). See sample periods analog filter designs 5-23, 5-24
See also filter designs, continuous-time

I-1
 Index

analytic signal 5-27 band configurations

Analytic Signal block 5-27 See filter band configurations
angular frequency bandpass filter designs
defined 3-5 analog, available parameters 4-8
See also periods using Analog Filter Design block 5-23
arrays bandstop filter designs
exporting matrix data to 3-73 analog, available parameters 4-8
importing 3-65 using Analog Filter Design block 5-23
attenuation, stopband 4-8 Bartlett windows 5-542
audio basic operations 4-21
exporting 3-79, 5-444, 5-449 batch processing 1-3
importing 5-217, 5-222 binary clock signals 5-319
autocorrelation bins, histogram 5-224
and Levinson-Durbin recursion 5-265 Biquadratic Filter block 5-37
of a real vector 5-29 bit-reversed order 5-177
sequence 5-549 Blackman windows 5-542
Autocorrelation block 5-29 block diagrams, creating 2-5, 2-6
Autocorrelation LPC block 5-31 blocks
autocorrelation method 5-546 connecting 2-7
auto-promoting rates 3-9 multirate 3-92
autoregressive models parameters for 2-7
using Burg AR Estimator block 5-48 single-rate 3-91
using Burg Method block 5-50 Buffer block 3-25, 3-27, 5-41
using the Covariance AR Estimator block initial state of 5-45
5-111 Buffer overlap parameter 3-48
using the Covariance Method block 5-113 negative values for 3-50
using the Modified Covariance AR Estimator buffering 3-24, 3-47, 5-41
block 5-314 and rate conversion 3-47
using the Modified Covariance Method block blocks for 3-25
5-316 causing unintentional rate conversions 3-31
using the Yule-Walker AR Estimator block example 3-47
5-546 FIFO (first input, first output) register 5-353
using the Yule-Walker Method block 5-549 internally 3-49
LIFO (last input, first output) register 5-413
overlapping 3-25, 3-50
B to create a frame-based signal 3-47
Backward Substitution block 5-35 with alteration of the signal 3-26, 3-28

I-2
 Index

with Delay Line block 5-124 clocks

with preservation of the signal 3-25 binary 5-319
with Queue block 5-353 multiphase 5-319
with Stack block 5-413 code generation 5-6
with Triggered Delay Line block 5-453 and contiguous memory 5-91
Buffers library 5-10 generic real-time (GRT) 3-86
Burg AR Estimator block 5-48 minimizing size of 2-15
Burg Method block 5-50 using Real Time Workshop (RTW) 1-5
butter 4-8 code generation in the DSP Blockset
Butterworth filter designs embedded real-time (ERT), generic real-time
analog 4-8 (GRT) 5-6
band configurations for 4-8 color coding sample periods 3-19
using Analog Filter Design block 5-23 complex analytic signal 5-27
Complex Cepstrum block 5-84
Complex Exponential block 5-86
C complex exponentials 5-86, 5-398
C code, generating 1-5 computational delay 3-85
canonical forms 5-134, 5-433 concatenating
channels to create multichannel signals 3-43, 3-54
in a frame-matrix 1-10 Constant Diagonal Matrix block 5-87
of a sample-based signal 3-11 Constant Ramp block 5-89
cheby1 4-8 constants
cheby2 4-8 generating 3-33
Chebyshev type I filter designs invariant (non-tunable) 2-13
analog 4-8 matrix 5-87, 5-230
band configurations for 4-8 precomputing 2-13
using Analog Filter Design block 5-23 ramp 5-89
Chebyshev type II filter designs Contiguous Copy block 5-91
analog 4-8 contiguous memory
band configurations for 4-8 defined 5-91
using Analog Filter Design block 5-23 continuous-time signals 3-9
Chebyshev windows 5-542, 5-543 continuous-time source blocks 3-9
Check Signal Attributes block 5-54 control signals
Chirp block 5-61 for Triggered Shift Register block 5-453
Cholesky Factorization block 5-78 for Triggered Signal From Workspace block
Cholesky Inverse block 5-80 5-456
Cholesky Solver block 5-82

I-3
 Index

for Triggered Signal To Workspace block dBm, converting to 5-118

5-460 DC component of an analytic signal 5-27
controller canonical forms 5-24 DCT block 5-122
conventions DCTs
technical 1-10 computing 5-122
time and frequency 3-4 decimation
conventions in our documentation (table) 1-12 process of 5-193
Convert 1-D to 2-D block 5-93 using FIR Decimation block 5-193
Convert 2-D to 1-D block 5-95 using FIR Rate Conversion block 5-207
Convert Complex DSP To Simulink block 5-96 default settings, Simulink 2-11
Convert Complex Simulink To DSP block 5-98 delay
converting algorithmic 3-86
frame rates. See rate conversion computational 3-85
sample rates. See rate conversion fractional 5-491, 5-496
convolution generating 5-241, 5-491, 5-496
of two real vectors 5-100 integer 5-241
Convolution block 5-100 rebuffering 3-53, 6-8
correlation relation to latency 3-91
of two real vectors 5-102 types of 3-85
Correlation block 5-102 Delay Line block 3-25, 3-27, 5-124
correlation matrices 5-250 demos
Counter block 5-104 MATLAB 4-24
Covariance AR Estimator block 5-111 running 1-7
Covariance Method block 5-113 Demos library 1-6
Create Diagonal Matrix block 5-115 Detrend block 5-128
creating signals 3-33 diagonal matrix constants 5-87
Cumulative Sum block 5-116 dialog boxes, opening 1-8
Difference block 5-129
difference, between elements in a vector 5-129
D Digital Filter Design block 5-131
data types digital frequency
customizing 5-3 defined 3-5
fixed-point 5-3 See also periods
supported by DSP Blockset 5-3 Direct-Form II Transpose Filter block 5-134
dB Conversion block 5-118 initial conditions for 5-135
dB Gain block 5-120 discrete cosine transforms. See DCTs
dB, converting to 5-118 Discrete Impulse block 5-138

I-4
 Index

discrete sample time, defined 3-10 Dyadic Analysis Filter Bank block 3-22, 5-151
discrete-time blocks Dyadic Synthesis Filter Bank block 3-22, 5-159
nonsource 3-10
source 3-10
discrete-time signals E
characteristics 3-4 Edge Detector block 5-166
defined 3-3 edge frequencies
terminology 3-4, 3-5 of analog filters 4-8
See also signals edge frequencies, of analog filters 4-8
discretizing a continuous-time signal 3-10 ellip 4-8
Display block 5-10 elliptic filter designs
displaying analog 4-8
blocks for 5-10 band configurations for 4-8
frame-based data 5-511 using Analog Filter Design block 5-23
matrices as images 5-292 errors
doc 1-8 algebraic loop 3-92
documentation discrete-time source block 3-10
Signal Processing Toolbox 5-542 due to continuous-time input to a discrete-time
Downsample block 3-22, 3-23, 5-141 block 3-10
downsampling 5-141, 5-193, 5-207 due to insufficient audio buffer size 5-446
See also rate conversion sample-rate mismatch 3-7
DSP Blockset ERT 5-6
accessing 1-8 estimation
documentation 1-9 nonparametric 5-277, 5-385
features 1-3 parametric 1-5
getting started with 1-8 using Burg AR Estimator block 5-48
installation 1-7 using Burg Method block 5-50
organization 1-6 using Covariance AR Estimator block 5-111
overview 1-3 using Covariance Method block 5-113
required products 1-13 using Modified Covariance AR Estimator
DSP Constant block 5-148 block 5-314
DSP Sinks library 5-9 using Modified Covariance Method block
DSP Sources library 5-9 5-316
dsp_links 6-3 using Yule-Walker AR Estimator block
dsplib 1-6, 1-8, 6-4 5-546
dspstartup M-file 2-11, 2-15, 6-5 using Yule-Walker Method block 5-549
editing 2-12 Estimation library 5-9

I-5
 Index

Event-Count Comparator block 5-168 filter band configurations

events, triggering bandpass 4-8
for N-Sample Enable block 5-325, 5-327 using Analog Filter Design block 5-23
for Sample and Hold block 5-383 bandstop 4-8
for Stack block 5-354, 5-414 using Analog Filter Design block 5-23
for Triggered Shift Register block 5-453 highpass 4-8
for Triggered Signal From Workspace block using Analog Filter Design block 5-23
5-456 lowpass 4-8
for Triggered Signal To Workspace block using Analog Filter Design block 5-23
5-460 filter designs
exponentials, complex 5-86, 5-398 analog. See filter designs, continuous-time
exporting Butterworth 4-8
blocks for 3-72, 5-10 using Analog Filter Design block 5-23
sample-based signals 3-73 using butter 4-8
using Triggered Signal To Workspace block Chebyshev type I
5-460 band configurations for 4-8
exporting signals 3-72 using Analog Filter Design block 5-23
Extract Diagonal block 5-170 using cheby1 4-8
Extract Triangular Matrix block 5-171 Chebyshev type II
band configurations for 4-8
using Analog Filter Design block 5-23
F using cheby2 4-8
f (linear frequency) continuous-time 4-8, 5-23
defined 3-4 available parameters 4-8
See also frequencies band configurations for 4-8
fast Fourier transform (FFT) 5-173 edge frequency for 4-8
FDATool passband ripple for 4-8
and the Digital Filter Design block 5-131 stopband attenuation for 4-8
using with DSP Blockset 5-131 elliptic
features of DSP Blockset 1-3 band configurations for 4-8
FFT block 5-173 using Analog Filter Design block 5-23
FFT length parameter 3-30 using ellip 4-8
FFTs FIR
and overlap-add filtering 5-331 using Levinson-Durbin block 5-266
and overlap-save filtering 5-334 with prescribed autocorrelation sequence
computing 5-173 5-266
filter architectures. See filter realizations IIR

I-6
 Index

continuous-time 4-7 defined 3-4

working with 4-3 See also frequencies
Filter Designs library 4-4, 5-9 Forward Substitution block 5-213
designing digital filters 4-5 frame
designing filters with various filter structures defined 1-11
4-6 See also frame-based signals
Filter Realization Wizard 5-183 frame periods
filter realizations altered by buffering 3-47
canonical forms 5-134, 5-433 altered by unbuffering 3-60
lattice 5-438 constant 3-21, 3-23
transposed direct-form II IIR 5-134, 5-433 converting. See rate conversion
using Filter Realization Wizard 5-183 defined 3-4, 3-20
filtering inspecting 3-17
adaptive. See adaptive filter designs inspecting, using the Simulink Probe block
by overlap-add method 5-331 3-18
by overlap-save method 5-334 multiple 3-21
multirate related to sample period and frame size 3-16,
using Direct-Form II Transpose Filter block 3-20
5-134, 5-433 frame rates
using Time-Varying Lattice Filter block 5-438 auto-promoting 3-9
Filtering library 5-9 See also frame periods
filters frame sizes
adaptive 4-3 constant 3-21, 3-23
FIR Decimation block 3-22, 5-193 converting 3-47
FIR filter designs by direct rate conversion 3-21
using Levinson-Durbin block 5-266 by rebuffering 3-21
with prescribed autocorrelation sequence to maintain constant frame rate 3-21, 3-23
5-266 to maintain constant sample rate 3-24, 3-25
FIR Interpolation block 3-22, 5-200 See also rate conversion
FIR Rate Conversion block 3-22, 5-207 defined
first-input, first-output (FIFO) registers 5-353 related to sample period and frame period
fixed-step solvers 2-15, 3-7 3-16
Flip block 5-211 frame status
fn (normalized frequency) converting 3-31
defined 3-5 Frame Status Conversion block 5-215
See also frequencies frame-based processing 1-3
fnyq (Nyquist frequency) and latency 3-15

I-7
 Index

benefits 3-86 generated code

frame-based signals and contiguous memory 5-91
benefits of 3-14 generic real-time (GRT) 3-86
changing frame size 3-47 size of 2-15
converting to sample-based signals 3-31, 3-60 generating signals 3-33
creating 3-47 GRT 5-6
creating from sample-based signals 3-47
unbuffering 3-60
frame-matrices H
format of 3-12 Hamming windows 5-543
frames Hann windows 5-543
changing size of 5-41 help
unbuffering to scalars 5-463 accessing block reference pages online 5-2
Framing parameter 3-21 Help Browser, accessing 1-8
frequencies help, accessing 1-8, 1-9
normalized 4-8 helpdesk 1-8
normalized linear 3-5 highpass filter designs
terminology 3-4 continuous-time 4-8
See also periods using Analog Filter Design block 5-23
frequency distributions 5-224 Hilbert transformer filter designs 5-27
computing 5-224 Histogram block 4-21, 5-224
From Wave Device block 5-217 histograms, computing 5-224
From Wave File block 5-222 Hz (Hertz)
Fs (sample frequency or rate) defined 3-4
defined 3-4 See also sample periods
See also sample periods
functions, utility 6-2
dsp_links 6-3 I
dsplib 6-4 IDCT block 5-228
dspstartup 2-11, 2-15, 6-5 IDCTs 5-228
rebuffer_delay 6-8 computing 5-228
startup 2-12 identity matrices 5-230
startupsav 2-12 Identity Matrix block 5-230
IFFT block 5-232
IFFTs
G computing 5-232
gain, applying in dB 5-120 IIR filter designs

I-8
 Index

continuous-time 4-7 K
images, displaying matrices as 5-292 Kaiser windows 5-542, 5-543
importing Kalman Adaptive Filter block 5-249
arrays 3-65
blocks for 5-10
frame-based signals 3-68 L
pages of an array 3-65 last-input, first-output (LIFO) registers 5-413
sample-based matrices 3-65 latency 3-91
sample-based signals 3-63, 3-65, 3-68 due to frame-based processing 3-15
sample-based vectors 3-63 example 3-93
scalars 5-222 predicting 3-92
signals 3-62, 5-388, 5-456 reducing 3-91
vectors 5-222 relation to delay 3-91
indexing lattice filters 5-438
to deconstruct multichannel signals 3-55 LDL Factorization block 5-254
Indexing library 5-10 LDL Inverse block 5-257
inf parameter setting 2-6 LDL Solver block 5-259
info 1-9 least mean-square algorithm 5-268
Inherit Complexity block 5-239 Least Squares Polynomial Fit block 5-261
inheriting sample periods 3-10 length of a vector
initial conditions, with basic algorithmic delay defined 1-11
3-90 See also frame sizes
Inline Parameters check box 2-14 Levinson-Durbin block 5-264
input frame periods libraries
defined 3-16 Adaptive Filters 5-9
See also frame periods Buffers 5-10
input frame sizes. See frame sizes Demos 1-6
input periods. See also frame periods displaying link information 6-3
input sample periods. See sample periods DSP Sinks 5-9
installing the DSP Blockset 1-7 DSP Sources 5-9
Integer Delay block 5-241 Estimation 5-9
initial conditions for 5-241, 5-244 Filter Designs 5-9
interpolating 5-200, 5-207 Filtering 5-9
procedure 5-200 Indexing 5-10
InvariantConstants parameter 2-13 Linear Prediction 5-9
inverse discrete cosine transforms. See IDCTs Linear System Solvers 5-9
listed 5-9

I-9
 Index

Math Functions 5-9 M

Math Operations 5-9 M (frame size). See frame sizes and matrices
Matrices and Linear Algebra 5-9 Magnitude FFT block 5-277
Matrix Factorizations 5-9 magnitude response
Matrix Functions 5-9 of Butterworth filters 5-23
Matrix Inverses 5-9 of Chebyshev type I filters 5-23
Matrix Operations 5-9 of Chebyshev type II filters 5-23
Multirate Filters 5-9 of elliptic filters 5-23
opening 1-8 magnitudes
Parametric Estimation 5-9 converting to dB 5-118
Polynomial Functions 5-9 Math Functions library 5-9
Power Spectrum Estimation 5-9 Math Operations library 5-9
Quantizers 5-9 MATLAB
Signal Attributes 5-10 Demos window 1-6, 4-24
Signal Management 5-9 matrices
Signal Operations 5-10 2-norm 5-405
Simulink 2-3, 2-5 diagonal 5-87, 5-115
Statistics 4-21, 5-10 dimensions
Switches and Counters 5-10 defined 1-10
Transforms 5-10 displaying
Library Browser, using 2-4 as images 5-292
line widths extracting diagonal of 5-170
displaying 3-22 extracting triangle from 5-171
linear algebra 1-5 frame-based
Linear Prediction library 5-9 format of 3-12
linear prediction, using LPC block 5-31 generated by buffering 3-47
Linear System Solvers library 5-9 identity 5-87, 5-230
LMS Adaptive Filter block 5-268 multiplying 5-282
LMS algorithm 5-268 multiplying within 5-284
loop-rolling 2-14 normalizing 5-280
lowpass filter designs number of channels in 1-10
continuous-time 4-8 permuting 5-339
using Analog Filter Design block 5-23 scaling 5-286
LU Factorization block 5-272 selecting elements from 5-422
LU Inverse block 5-274 summing 5-290
LU Solver block 5-275 support for 1-4
Toeplitz 5-442

I-10
 Index

transposing 5-451 multirate 3-21

Matrices and Linear Algebra library 5-9 simulating 2-8
Matrix 1-Norm block 5-280 modes, tasking 3-91
Matrix Concatenation block 5-14 Modified Covariance AR Estimator block 5-314
Matrix Factorizations library 5-9 Modified Covariance Method block 5-316
Matrix Functions library 5-9 mono inputs 3-79
Matrix Inverses library 5-9 multichannel signals
Matrix Multiply block 5-282 constructing 3-43, 3-54
Matrix Operations library 5-9 deconstructing 3-55
Matrix Product block 5-284 See also signals
Matrix Scaling block 5-286 Multiphase Clock block 5-319
Matrix Square block 5-288 multiplying
Matrix Sum block 5-290 by dB gain 5-120
in tutorial 2-6 matrices 5-282
Matrix Viewer block 3-83, 5-292 Multi-port Selector block 5-322
maximum 4-21 multirate blocks 3-92
Maximum block 5-298 multirate filtering
mean 4-21 Multirate Filters library 5-9
computing 5-303 multirate models 3-21, 3-92
Mean block 4-21, 5-303 multi-tasking mode 3-7
Median block 5-307 multitasking mode 3-91
memory
conserving 2-13
contiguous 5-91 N
M-files N (number of channels)
dspstartup 2-11, 2-15, 6-5 See sample vectors and matrices 1-10
running simulations from 2-10 Normalization block 5-329
startup 2-12 normalized frequencies
startupsav 2-12 defined
Mi (input frame size). See frame sizes See also frequencies
minimum 4-21 norms, 2-norm 5-405
Minimum block 5-309 N-Sample Enable block 5-325
MMSE 5-249 N-Sample Switch block 5-327
Mo (output frame size). See frame sizes n-step forward linear predictors 5-31
models Nyquist frequency
building 2-5 defined 3-4
defining 2-5 Nyquist rate

I-11
 Index

defined 3-4 overlap-save method 5-334

overview of DSP Blockset 1-3

O
ω (digital frequency) P
defined 3-5 Pad block 5-337
See also frequencies pages of an array
Ω (angular frequency) defined 1-11
defined 3-5 exporting 3-73
See also frequencies pages of an array, importing 3-65
Ωp (passband edge frequency) parameters
See edge frequencies Buffer overlap, negative values for 3-50
Ωp1 (lower passband edge frequency) continuous-time filter 4-8
See edge frequencies definition of 2-7
Ωp2 (upper passband edge frequency) InvariantConstants 2-13
See edge frequencies normalized frequency 4-8
Ωs (stopband edge frequency) RTWOptions 2-15
See edge frequencies SaveOutput 2-13
Ωs1 (lower stopband edge frequency) SaveTime 2-13
See edge frequencies setting 2-7
Ωs2 (upper stopband edge frequency) Simulink 2-11
See edge frequencies Solver 2-15
ones, outputting 5-325 StopTime 2-15
online help 1-8 tuning 2-9, 5-3
Out block, suppressing output 2-13 with T symbol 5-3
Output check box 2-13 parametric estimation 1-5
output frame periods Parametric Estimation library 5-9
defined 3-16 Partial Unbuffer block 3-27
See also frame periods partial unbuffering 3-25
output frame sizes. See frame sizes passband ripple
output periods. See frame periods analog filter 4-8
output sample periods. See sample periods performance, improving 2-13, 3-14, 3-86
Overlap-Add FFT Filter block 5-331, 5-332 periodograms 5-277
overlap-add method 5-331 periods
overlapping buffers 3-25, 3-50 defined 3-4
causing unintentional rate conversions 3-31 See sample periods and frame periods
Overlap-Save FFT Filter block 5-334, 5-335 Permute Matrix block 5-339

I-12
 Index

phase angles, unwrapping 5-474 by buffering 3-47

phase unwrap 5-474 by unbuffering 3-60
Polynomial Evaluation block 5-343 direct 3-21, 3-22
Polynomial Functions library 5-9 overview 3-20
Polynomial Stability Test block 5-345 to avoid rate-mismatch errors 3-7
polyphase filter structures 5-193, 5-200, 5-207 unintentional 3-21, 3-28
ports, connecting 2-7 rate types
power spectrum estimation block 3-91
using the Burg method 5-50, 5-113, 5-316 model 3-92
using the short-time, fast Fourier transform rates
(ST-FFT) 5-385 auto-promoting 3-9
using the Yule-Walker AR method 5-549 See also sample periods and frame periods
Power Spectrum Estimation library 5-9 Real Cepstrum block 5-365
prediction, linear 5-31 Real-Time Workshop
predictor algorithm 5-249 and contiguous memory 5-91
Probe block 3-17 and loop-rolling 2-14
example 3-18 generating generic real-time (GRT) code 3-86
Pseudoinverse block 5-347 Real-Time Workshop panel 2-14
rebuffer_delay 3-53, 6-8
rebuffering 3-21, 3-24, 5-41
Q blocks for 3-25
QR Factorization block 5-349 causing unintentional rate conversions 3-31
QR Solver block 5-351 delay 3-53, 6-8
Quantizer block 5-15 computing 3-53
Quantizers library 5-9 procedure 3-48
Queue block 5-353 with alteration of the signal 3-26, 3-28
Quicksort algorithm 5-407 with preservation of the signal 3-25, 3-26
Reciprocal Condition block 5-367
rectangular windows 5-543
R recursive least-squares (RLS) algorithm 5-375
radians 3-5 Remez exchange algorithm 5-27
ramp signal 5-89 Repeat block 3-22, 5-369
random signals 5-358 resampling 5-141, 5-193, 5-200, 5-207, 5-369
Random Source block 5-358 by inserting zeros 5-484
random-walk Kalman filter 5-250 procedure 5-207
rate conversion 3-21, 3-23 ripple, passband 4-8
blocks for 3-22 RLS (recursive least-squares) algorithm 5-375

I-13
 Index

RLS Adaptive Filter block 5-375 maintaining constant 3-24, 3-25

RMS block 4-21, 5-379 of source blocks 3-9
RMS, computing 5-379 output, defined 3-4
root-mean-square. See RMS related to frame period and frame size 3-16,
Rp (passband ripple) 3-20
See passband ripple See also frame periods and sample times
Rs (stopband attenuation) sample rates
See stopband attenuation auto-promoting 3-9
RTW. See Real-Time Workshop changing 5-141, 5-369
RTWOptions parameter 2-15 defined 3-3, 3-4
running operations 4-23 inherited 3-10
overview 3-16
See also sample periods
S Sample time colors option 3-19
Sample and Hold block 5-383 Sample time of original time series parameter
sample frequency 3-31
definition 3-4 Sample time parameter 3-10
See also sample periods sample times
sample modes 3-92 color coding 3-19
sample periods defined 3-3, 3-5, 3-6
altered by buffering 3-47 shifting with sample-time offsets 3-9
altered by unbuffering 3-60 See also sample periods and frame periods
color coding 3-19 sample-based signals 3-11, 3-12
continuous-time 3-9 converting to frame-based signals 3-47
converting 3-26, 3-28 creating from frame-based signals 3-60
See also rate conversion importing 3-63, 3-68
defined 3-3, 3-4, 3-5, 3-20 samples
discrete-time 3-10 adding 3-25, 3-27
for Buffer block 3-27 defined 3-3
for frame-based signals 3-16 deleting 3-25, 3-27
for nonsource blocks 3-10 rearranging 3-27
for Rebuffer block 3-27 sampling 5-383
inherited 3-10 See also sample periods and frame periods
input, defined 3-4 SaveOutput parameter 2-13
inspecting 3-17 SaveTime parameter 2-13
using color coding 3-19 scalars
using the Simulink Probe block 3-17, 3-18 converting to vectors 5-124, 5-453

I-14
 Index

creating from vectors 5-463 frame-based

exporting 5-460 benefits 3-14
importing 5-222, 5-388 converting to sample-based 3-31, 3-60
Scope block 2-7 multichannel 3-12
scopes 3-80 frequency of, defined 3-4, 3-5
scripts 6-2 generating 3-33
seconds 3-4 importing 3-62, 5-456
selecting sample-based 3-65
elements of a vector 5-504 multichannel 3-11, 3-12
Selector block 5-15 Nyquist frequency, defined 3-4
sequences Nyquist rate, defined 3-4
defining a discrete-time signal 3-3 period of, defined 3-4
settings, Simulink 2-11 random 5-358
Shift Register block sample-based 3-11, 3-12
initial state of 5-126 converting to frame-based 3-47
Short-Time FFT block 5-385 Simulation Parameters dialog box 2-6, 2-13, 2-14,
short-time, fast Fourier transform (ST-FFT) 3-5
method 5-385 accessing 2-6
Signal Attributes library 5-10 simulations
Signal dimensions 2-8 accelerating 2-13, 3-14, 3-86
Signal From Workspace block 5-388 running 2-8
compared to Simulink To Workspace block from M-file 2-10
5-388 from the command line 3-86
Signal Management library 5-9 size of generated code 2-15
Signal Operations library 5-10 stopping 2-15
Signal Processing Toolbox Simulink
documentation 5-542 accessing 2-3
Signal To Workspace block 5-392 configuring for DSP 2-11
signals default settings 2-11
continuous-time 3-9 description 2-1
control 5-453, 5-456, 5-460 learning 1-9, 2-10
discrete-time libraries 2-3, 2-5
characteristics 3-4 parameters 2-11
defined 3-3 simulink 2-3
inspecting the sample period of 3-17 Sine Wave block 3-29, 5-398
terminology 3-4, 3-5 in tutorial 2-6
exporting 3-72 single-rate blocks 3-91

I-15
 Index

single-rate models 3-92 speed, improving 2-13, 3-14, 3-86

single-tasking mode 3-6, 3-91 Stack block 5-413
Singular Value Decomposition block 5-405 stack events 5-354, 5-414
size standard deviation 4-21
of a frame computing 5-418
See also frame sizes Standard Deviation block 4-21, 5-418
of a matrix 1-10 startup M-file 2-12
of an array 1-11 startupsav M-file 2-12
size of a vector editing 2-12
defined 1-11 state-space forms 4-8, 5-24
See also frame sizes statistics
sliding windows operations 1-5, 4-21
example 4-22 RMS 5-379
Solver options panel, recommended settings 3-5 standard deviation 5-418
Solver parameter 2-15 variance 5-507
solvers Statistics library 4-21, 5-10
fixed-step 3-7 stereo inputs 3-79
variable-step 3-7 Stereo parameter 3-79
Sort block 5-407 ST-FFT method 5-385
sound stopband, attenuation 4-8
exporting 3-79, 5-444, 5-449 stopping a simulation 2-15
importing 5-217, 5-222 StopTime parameter 2-15
source blocks Submatrix block 5-422
defined 3-9 SVD Solver block 5-430
sample periods of 3-9 swept cosine 5-67
sources swept-frequency cosine 5-61
discrete-time 3-10 Switches and Counters library 5-10
sample periods of 3-9 switching
spectral analysis between two inputs 5-327
Burg method 5-50 symbols, time and frequency 3-4
covariance method 5-113
magnitude FFT method 5-277
modified covariance method 5-316 T
See also power spectrum estimation T (signal period)
short-time FFT method 5-385 defined 3-4
Yule-Walker method 5-549 See also sample periods and frame periods
Spectrum Scope block 3-82, 5-409 T (tunable) icon 5-3

I-16
 Index

tasking latency transposing

defined 3-91 matrices 5-451
example 3-93 trends, removing 5-128
predicting 3-92 triangular windows 5-543
tasking modes 3-91 triggered blocks 3-10
technical conventions 1-10 Triggered Delay Line block 5-453
terminology, time and frequency 3-4, 3-5 Triggered Shift Register block
Tf (frame period) initial state of 5-454
defined 3-4 Triggered Signal From Workspace block 5-456
See also frame periods Triggered Signal To Workspace block 5-460
Tfi (input frame period) triggering
defined 3-4 for N-Sample Enable block 5-325, 5-327
See also frame periods for Sample and Hold block 5-383
Tfo (output frame period) for Triggered Shift Register block 5-453
defined 3-4 for Triggered Signal From Workspace block
See also frame periods 5-456
throughput rates, increasing 3-14 for Triggered Signal To Workspace block
Time check box 2-13 5-460
Time Scope Block 5-10 Ts (sample period)
Time Scope block 5-432 defined 3-3, 3-4
time-step vector, saving to workspace 2-13 See also sample periods
Time-Varying Direct-Form II Transpose Filter Tsi (input sample period)
initial conditions for 5-434 defined 3-4
Time-Varying Direct-Form II Transpose Filter See also sample periods
block 5-433 Tso (output sample period)
Time-Varying Lattice Filter block 5-438 defined 3-4
initial conditions for 5-439 See also sample periods
To Wave Device block 3-79, 5-444 tuning parameters 2-9, 5-3
To Wave File block 3-79, 5-449 typographical conventions (table) 1-12
Toeplitz block 5-442
tout vector, suppressing 2-13
transforms U
discrete cosine 5-122 Unbuffer block 3-25, 3-26, 5-463
Fourier 5-173 initial state of 5-464
Transforms library 5-10 unbuffering 3-60, 5-41, 5-463
Transpose block 5-451 and rate conversion 3-60
transposed direct-form II IIR filter 5-134, 5-433 frame-based signals 3-25

I-17
 Index

partial 3-25 exporting 5-460

to a sample-based signal 3-26 importing 5-222, 5-388
Uniform Decoder block 5-466 versions
Uniform Encoder block 5-470, 5-471 displaying information about 6-3
units of time and frequency measures 3-4 opening 6-4
Unwrap block 5-474 viewing data
unwrapping radian phase angles 5-474 with scopes 3-80
Upsample block 3-22, 5-484, 5-486 viewing in a model 2-8
upsampling 3-21, 5-200, 5-207, 5-369
by inserting zeros 5-484
See also rate conversion W
utility functions 6-2 Wavelet Analysis block 3-22, 5-529
dsp_links 6-3 Wavelet Synthesis block 3-22, 5-535
dsplib 6-4 Window Function block 5-541
dspstartup 6-5 windows
rebuffer_delay 6-8 applying 5-541
Bartlett 5-542
Blackman 5-542
V Chebyshev 5-542, 5-543
Variable Fractional Delay block 5-491 computing 5-541
initial conditions for 5-491, 5-492 Hamming 5-543
Variable Integer Delay block 5-496 Hann 5-543
initial conditions for 5-497, 5-500 Kaiser 5-542, 5-543
Variable Selector block 3-25, 3-27, 5-504, 5-505 rectangular 5-543
variable-step solver 2-15, 3-7 triangular 5-543
variance 4-21, 5-507 workspace
tracking 5-507 importing data from 3-62
Variance block 4-21, 5-507 suppressing output to 2-13
Vector Scope block 3-29, 3-80, 5-511 Workspace I/O panel 2-13
vectors
1-D 1-10, 1-11
converting to scalars 5-463 Y
creating yout, suppressing 2-13
by buffering 3-47 Yule-Walker Estimator block 5-546
from scalars 5-453 Yule-Walker Method block 5-549
defined 1-10
displaying 5-511, 5-512

I-18
 Index

Z
Zero Pad block 3-25, 3-27, 5-552
Zero-Order Hold block 3-10
zero-padding 3-30, 5-337, 5-552
causing unintentional rate conversions 3-31
zeros
inserting 5-200, 5-207, 5-484
outputting
Counter block 5-105
Discrete Impulse block 5-138
Integer Delay block 5-244
N-Sample Enable block 5-325
Signal From Workspace block 5-388, 5-457
padding with 3-27, 3-31

I-19