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Advanced DSP Course Overview

This document provides an introduction to an advanced signals and systems lecture. It outlines the contents to be covered over the semester, including discrete signals, random processes, spectra, systems, and generalizations. Literature references are provided. The lecture will cover boundary conditions like exams and credits. Notation for signals, systems, random variables, correlation, and white noise is also introduced. The introduction concludes by previewing the topics of discrete signals and random processes to be covered in the next part of the lecture.

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159 views15 pages

Advanced DSP Course Overview

This document provides an introduction to an advanced signals and systems lecture. It outlines the contents to be covered over the semester, including discrete signals, random processes, spectra, systems, and generalizations. Literature references are provided. The lecture will cover boundary conditions like exams and credits. Notation for signals, systems, random variables, correlation, and white noise is also introduced. The introduction concludes by previewing the topics of discrete signals and random processes to be covered in the next part of the lecture.

Uploaded by

vondutchlg
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Advanced Signals and Systems

Part 1: Introduction

Gerhard Schmidt
Christian-Albrechts-Universität zu Kiel
Faculty of Engineering
Institute of Electrical Engineering and Information Engineering
Digital Signal Processing and System Theory
Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction
Contents of the Lecture

Today:

 Boundary conditions of the lecture


 Contents
 Literature hints
 Exams
 Start with first part (discrete signals and processes) of the lecture

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-2
Contents of the Lecture

Entire Semester:

 Introduction
 Discrete signals and random processes
 Spectra
 Discrete systems
 Idealized linear, shift-invariant systems
 Hilbert transform
 State-space description and system realizations
 Generalizations for signals, systems, and spectra

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-3
Literature

English (and German) Books:

Statistical signal theory:


 A. Papoulis: Probability, Random Variables, and Stochastic Processes, McGraw Hill, 1965
 E. Hänsler: Statistische Signale: Grundlagen und Anwendungen, Springer, 2001
(in German)

Discrete signal processing:


 A. V. Oppenheim, R. W. Schafer: Discrete-Time Signal Processing, 2nd edition, Prentice Hall, 1999
 J. G. Proakis, D. K. Manolakis: Digital Signal Processing, 4th edition, Prentice Hall, 2006

 K. D. Kammeyer,
K. Kroschel: Digitale Signalverarbeitung - Filterung und Spektralanalyse mit
MATLAB-Übungen, Teubner, 2002 (in German)

Signal processing:
 A. V. Oppenheim, A. S. Willsky, S. Hamid: Signals and Systems, 2nd edition, Prentice Hall, 1996
 S. Haykin, B. Van Veen: Signals and Systems, 2nd edition, Wiley, 2002

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-4
Boundary Condition of the Lecture

Credit Points, Exams, Exercises, and Lecture Notes

Credit points:
 7 ECTS points

Written exam:
 90 minutes test
 In the exams period

Exercises:
 Every week two hours (45 min) during the semester

Lecture notes:
 Printed versions will be spread at the beginning of each lecture
 In the internet as pdf files via www.dss.tf.uni-kiel.de

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-5
Introduction

Origin of this Lecture

Thanks to …

… Prof. Dr.-Ing. Ulrich Heute


(slides are based on his script)

Prof. Heute has given this


lecture until 2010.

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-6
Help

The DSS Team

People that you can ask for help


 The DSS team has no
“question hours” …
just come over,
someone will have
time for you.
 Details (where we
are located, etc.)
can be found via
www.dss.tf.uni-kiel.de.

Exercises
 M.Sc. Anne Theiß

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-7
Introduction

Some General Words about Signals and Systems

“Advanced” Signals and Systems:


We will treat the basic theory of continuous, deterministic, one-dimensional signals. We
assume that basic knowledge about continuous, stochastic, one-dimensional signals as well
as theory of continuous, one-dimensional systems with one input and one output are
known. What we will treat here are:
 Signals (discrete signals, sequences) representing (in an abstract manner) any entity
depending on any independent variable (e.g. pixel brightness on a 2-D grid). Please
note that we call signals to be digital, if a discrete signal has also a discrete (quantized)
amplitude.
 Systems are operators that are excited by input sequences, creating internal (state)
sequences and output sequences. Digital systems are operators that are working on
digital inputs with digital parameters (e.g. quantized coefficients) and quantized
states yielding digital outputs.

In the following …
… we will restrict ourselves to discrete signals and systems with a short extension towards
digital signals and some references to continuous (analog) signals and systems.

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-8
Notation – Part 1

Scalars and Vectors

Scalars: Discrete time index

 Signals: Coefficient index


 Impulse responses (time-variant):

 Example for a (real) convolution:

Vectors: Boldface and lowercase


 Signal vectors:

 Impulse response vectors (time-variant) :

 Example for a real convolution:

Matrices:

Boldface and uppercase

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-9
Notation – Part 2

Signals – Part 2

Signals (Details):
 Notation:

with Non-quantized, complex quantity!

 Signal vector versus –dimensional signals:


E.g. speed of an object (x, y, and z-direction)

E.g. brightness of a picture (M=2)

During the lecture we will focus on one-dimensional scalar signals!

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-10
Notation – Part 3

Signals and Random Processes

Random variables and processes:


 Notation:
No differences between deterministic signals and random
processes – different writing styles:

 Probability density function:

 Stationary random processes:

 Expected values of stationary random processes:

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-11
Notation – Part 4

Correlation

Auto and cross correlation for real, stationary random processes:

 Auto-correlation function:

 Cross-correlation function:

 (Auto) power spectral density:

 (Cross) power spectral density:

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-12
Notation – Part 5

White Noise

Stationary white noise:


 Auto-correlation function:

 Auto power spectral density:

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-13
Applying our Knowlegde …

A First Exercise

Please try on your own:


 A linear, causal, and (time-) shift-invariant system – specified by its impulse response – is
excited with zero-mean white noise with variance . What is the output power of the
system?

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-14
Introduction

Summary and Outlook

This part:
 Boundary conditions of the lecture
 Contents
 Literature hints
 Exams, credit points, etc.
 Notation

Next part:

 Discrete signals and random processes

Digital Signal Processing and System Theory| Advanced Signals and Systems| Introduction Slide I-15

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