LECTURE NOTES

DIGITAL SIGNAL PROCESSING

(19A04602T)

LECTURE NOTES

B.TECH

III-YEAR& II-SEM(R19)

Prepared by:

Mr.M.P.Chennaiah , Associate Professor

Department of Electronics and Communication Engineering

VEMU INSTITUTE OF TECHNOLOGY

(Approved By AICTE, New Delhi and Affiliated to JNTUA, Ananthapuramu)
Accredited By NAAC & ISO: 9001-2015 Certified Institution
Near Pakala, P. Kothakota, Chittoor- Tirupathi Highway
Chittoor, Andhra Pradesh - 517 112
Web Site: www.vemu.org
 COURSE MATERIAL
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR
B.Tech (ECE)– III-II Sem LTPC
3003
(19A04602T) DIGITAL SIGNAL PROCESSING
Course Objectives:
• To provide background and fundamental material for the analysis and processing of digital signals.
• To familiarize the relationships between continuous-time and discrete time signals and systems.
• To study fundamentals of time, frequency and Z-plane analysis and to discuss the inter-relationships of these
analytic method.• To study the designs and structures of digital (IIR and FIR) filters from analysis to synthesis
for a given specifications.
• To introduce a few real-world signal processing applications.
• To acquaint with DSP processor.

UNIT- I:
Discrete Fourier Transform: Discrete Fourier series, Properties of Discrete Fourier series,Discrete Fourier
Transform (DFT), The DFT as a linear transformation, Relationship of the DFT to other transforms, Properties
of DFT.
Fast Fourier Transforms: Efficient computation of DFT algorithms - Radix 2-Decimation-in-Time &
Decimation-in-Frequency algorithms, Inverse FFT, Illustrative problems.
Learning Outcomes:-
After completion of this unit student will
• Understand the concept of DFT and its properties.(L1)
• Find N-Point DFT/FFT for a given signal/sequence.(L2)

UNIT- II:
IIR Digital Filters: Review of analog filter design, Frequency transformation in the analog and digital
domains,Design of IIR filters from Analog filters – Approximation of derivatives, Impulse invariance, Bilinear
transformation,Design of Butterworth, Chebyshev filters, Illustrative problems.
Realization of IIR Systems: Structures for IIR systems–Direct form I& Direct form II, Transposed, Cascade
form, Parallel form and Lattice structures, Signal flow graphs.
Learning Outcomes:-
After completion of this unit student will

• Understands signal flow graph and block diagram representations of difference equations that realize
digital filters(L1)
• Realization of different structures for IIR filters(L2)
• Design of IIR filters using different techniques. (L4)
UNIT- III:
FIR Digital Filters: Linear phase FIR filter, characteristic response, location of zeros, Design ofFIR filter
using Windowing Techniques - Rectangular, Hanning, Hamming, Kaiser, Bartlett, Blackman, Design ofFIR
filter by Frequency sampling technique, Illustrative problems.
Realization of FIR Systems: Structures for FIR systems - Direct form, Cascade form and Lattice structures.
Comparison of FIR and IIR filters.
Learning Outcomes:-
After completion of this unit student will
• Understand the concept of FIR filter(L1)
• Realization of different structures for FIR filters(L2)
• FIR filter design based on windowing methods.(L4)
• Compare FIR and IIR filters (L5)
UNIT -IV:
Architectures for Programmable DSP Devices: Basic Architectural features, DSPComputational Building
Blocks, Bus Architecture and Memory, Data Addressing Capabilities, Address Generation Unit,
Programmability and Program Execution, Speed Issues.
Learning Outcomes:-
After completion of this unit student will
• Recognize the fundamentals of fixed and floating point architectures of various DSPs.(L1)
• Learn the architecture details and instruction sets of fixed and floating point DSPs.(L1)
• Illustrate the control instructions, interrupts, and pipeline operations.(L2)
UNIT- V:
Programmable Digital Signal Processors: Introduction, Commercial Digital signal-processingDevices,
Architecture of TMS320C54XX DSPs, Data Addressing modes of TMS320C54XX Processors, Memory space
of TMS320C54XX Processors, Program Control, TMS320C54XX instructions and Programming, On-Chip
Peripherals, Interrupts of TMS320C54XX processors, Pipeline Operation of TMS320C54XX Processors. 199
Page
Learning Outcomes:-
After completion of this unit student will
• Illustrate the features of on-chip peripheral devices and its interfacing along with its programming
details.(L2)
• Analyze and implement the signal processing algorithms in DSPs. (L3)

Course Outcomes
• Understand the basic concepts of IIR and FIR filters, DSP building blocks to achieve high speed in
DSP processor, DSP TMS320C54XX architecture and instructions.
• Compute the fast Fourier transforms and find the relationship with other transforms. Realization of
digital filter structures.
• Design of FIR and IIR digital filters.
• Compare FIR and IIR filters.

TEXT BOOKS:
1. John G. Proakis, Dimitris G. Manolakis, “Digital signal processing, principles, Algorithms and
applications,” Pearson Education/PHI, 4th ed., 2007.
2. Avtar Singh and S. Srinivasan, “Digital Signal Processing,” Thomson Publications, 2004.

REFERENCES:
1. Sanjit K Mitra, “Digital signal processing, A computer base approach,” Tata McGraw Hill, 3 rd edition, 2009.
2. A.V.Oppenheim and R.W. Schaffer, & J R Buck, “Discrete Time Signal Processing,” 2 nd, Pearson
Education, 2012.
3. B. P. Lathi, “Principles of Signal Processing and Linear Systems,” Oxford Univ. Press, 2011.
4. B. Venkata Ramani and M.Bhaskar, “Digital Signal Processors, Architecture, Programming and
Applications,” TMH, 2004.

REFERENCES:
1. Sanjit K Mitra, “Digital signal processing, A computer base approach,” Tata McGraw Hill, 3 rd edition, 2009.
2. A.V.Oppenheim and R.W. Schaffer, & J R Buck, “Discrete Time Signal Processing,” 2 nd, Pearson
Education, 2012.
3. B. P. Lathi, “Principles of Signal Processing and Linear Systems,” Oxford Univ. Press, 2011.
4. B. Venkata Ramani and M.Bhaskar, “Digital Signal Processors, Architecture, Programming and
Applications,” TMH, 2004.
 UNIT -1
Discrete Fourier Transform

Discrete Fourier Series

The Fourier series representation o f a continuous-time periodic signal can consist of an

infinite number of frequency components, where the frequency spacing between two successive
harmonically related frequencies is 1 / T p, and where Tp is the fundamental period.
Since the frequency range for continuous-time signals extends infinity on both sides it is
possible to have signals that contain an infinite number of frequency components.
In contrast, the frequency range for discrete-time signals is unique over the interval. A
discrete-time signal of fundamental period N can consist of frequency components separated by 2n /
N radians.
Consequently, the Fourier series representation o f the discrete-time periodic signal will
contain at most N frequency components. This is the basic difference between the Fourier series
representations for continuous-time and discrete-time periodic signals.
PROPERTIES OF DFT:

LINEAR FILTERING METHODS BASED ON THE DFT

Since the D F T provides a discrete frequency representation o f a finite-duration Sequence in

the frequency domain, it is interesting to exp lore its use as a computational tool for linear system
analysis and, especially, for linear filtering. We have already established that a system with
frequency response H { w ) y w hen excited with an input signal that has a spectrum possesses an
output spectrum.
The output sequence y(n) is determined from its spectrum via the inverse Fourier transform.
Computationally, the problem with this frequency domain approach is that are functions o f the
continuous variable. As a consequence, the computations cannot be done on a digital computer, since
the computer can only store and perform computations on quantities at discrete frequencies.
On the other hand, the DFT does lend itself to computation on a digital computer. In the discussion
that follows, we describe how the DFT can be used to perform linear filtering in the frequency
domain. In particular, we present a computational procedure that serves as an alternative to time-
domain convolution.
In fact, the frequency-domain approach based on the DFT, is computationally m ore efficient
than time-domain convolution due to the existence of efficient algorithms for computing the DFT .
These algorithms, which are described in Chapter 6, are collectively called fast Fourier transform
(FFT) algorithms.
 FAST FOURIER TRANSFORM
In this section we represent several methods for computing dft efficiently. In view of the
importance of the DFT in various digital signal processing applications such as linear filtering,
correlation analysis and spectrum analysis, its efficient computation is a topic that has received
considerably attention by many mathematicians, engineers and scientists. Basically the computation
is done using the formula method.

Divide-and-Conquer Approach to Computation of the DFT

The development of computationally efficient algorithms for the DFT is made possible if we
adopt a divide-and-conquer approach. This approach is based on the decomposition of an N-point
DFT into successively smaller DFT. This basic approach leads to a family o f computationally
efficient algorithm s know n collectively as FFT algorithms.
T o illustrate the basic notions, let us consider the computation of an N point DFT , where N can be
factored as a product of two integers, that is, N = L M
 An additional factor of 2 savings in storage of twiddle factors can be obtained by introducing
a 90° phase offset at the mid point of each twiddle array , which can be removed if necessary at the
ouput of the SRFFT computation. The incorporation of this improvement into the SRFFT results in
an other algorithm also due to price called the PFFT algorithm.

Implementation of FFT Algorithms

Now that w e has described the basic radix-2 and radix -4 F FT algorithm s, let us consider
some of the implementation issues. Our remarks apply directly to
 UNIT -II
IIR Digital Filters
IIR FILTER DESIGN
STRUCTURES FOR IIR SYSTEMS
In this section we consider different IIR system s structures described by the difference equation
given by the system function. Just as in the case o f FIR system s, there are several types o f
structures or realizations, including direct-form structures, cascade-form structures, lattice structures,
and lattice-ladder structures. In addition, IIR systems lend them selves to a parallel form realization.
We begin by describing two direct-form realizations.

DIRECT FORM STRUCTURES:

DIRECT FORM II

Signal Flow Graphs and Transposed Structures

A signal flow graph provides an alternative, N but equivalent, graphical representation to a

block diagram structure that we have been using to illustrate various system realizations. T he basic
elements o f a flow graph are branches and nodes. A signal flow graph is basically a set o f directed
branches that connect at nodes. By definition, the signal out of a branch is equal to the branch gain
(system function) times the signal into the branch. Furthermore, the signal at anode o f a flow graph
is equal to the sum o f the signals from all branches connecting to the node.
Cascade-Form Structures
Let us consider a high-order IIR system with system function given by equation. Without loss o
f generality we assume that N > M . T h e system can be factored into a cascade o f second-
order subsystem s, such that H (z) can b e expressed as
Parallel-Form Structures
A parallel-form realization o f an IIR system can be obtained by performing a partial-fraction
expansion o f H( z) . Without loss o f generality, w e again assume that N > M and that the poles are
distinct. Then, by performing a partial-fraction expansion o f H( z ), we obtain the result
The realization of second order form is given by

The general form of parallel form of structure is f\given by

Lattice and Lattice-Ladder Structures for IIR Systems

 UNIT – III
FIR DIGITAL FILTERS
The transfer function is obtained by taking Z transform of finite sample impulse response. The filters
designed by using finite samples of impulse response are called FIR filters.
Some of the advantages of FIR filter are linear phase, both recursive and non recursive, stable and
round off noise can be made smaller.
Some of the disadvantages of FIR filters are large amount of processing is required and non integral
delay may lead to problems.
DESIGN OF FIR FILTERS
STRUCTURES FOR FIR SYSTEMS

Direct-Form Structure
The direct form realization follows immediately from the non recursive difference equation given
below

Cascade-Form Structures
The cascaded realization follows naturally system function given by equation. It is simple matter to
factor H(z) into second order FIR system so that
Frequency-Sampling Structures
The frequency-sampling realization is an alternative structure for an FIR filter in which the
parameters that characterize the filter are the values o f the desired frequency response instead of the
impulse response h(n). To derive the frequency sampling structure, we specify the desired frequency
response at a set o f equally spaced frequencies, namely

The frequency response of the system is given by

Lattice Structure
In this section w e introduce another F IR filter structure, called the lattice filter or
Lattice realization. Lattice filters are used extensively in digital speech processing
And in the implementation of adaptive filters. Let us begin the development by considering a
sequence of FIR filters with system functions
The general form of lattice structure for m stage is given by’

.
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