Digital Signal Processing Using MATLAB for Students and Researchers

386 Pages·2011·15.43 MB·english

by  John W. Leis

DIGITAL SIGNAL
PROCESSING USING
MATLAB FOR
STUDENTS AND
RESEARCHERS
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DIGITAL SIGNAL
PROCESSING USING
MATLAB FOR
STUDENTS AND
RESEARCHERS
JOHN W. LEIS
University of Southern Queensland
A JOHN WILEY & SONS, INC., PUBLICATION
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Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Leis, John W. (John William), 1966-
Digital Signal Processsing Using MATLAB for Students and Researchers / John W. Leis.
p. cm
Includes bibliographical references and index.
ISBN 978-0-470-88091-3
1. Signal processing–Digital techniques. 2. Signal processing–Mathematics–Data
processing. 3. MATLAB. I. Title.
TK5102.9.L4525 2011
621.382′2–dc22
2010048285
Printed in Singapore.
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To Debbie, Amy, and Kate
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CONTENTS
PREFACE XI
CHAPTER 1 WHAT IS SIGNAL PROCESSING? 1
1.1 Chapter Objectives 1
1.2 Introduction 1
1.3 Book Objectives 2
1.4 DSP and ITS Applications 3
1.5 Application Case Studies Using DSP 4
1.6 Overview of Learning Objectives 12
1.7 Conventions Used in This Book 15
1.8 Chapter Summary 16
CHAPTER 2 MATLAB FOR SIGNAL PROCESSING 19
2.1 Chapter Objectives 19
2.2 Introduction 19
2.3 What Is MATLAB? 19
2.4 Getting Started 20
2.5 Everything Is a Matrix 20
2.6 Interactive Use 21
2.7 Testing and Looping 23
2.8 Functions and Variables 25
2.9 Plotting and Graphing 30
2.10 Loading and Saving Data 31
2.11 Multidimensional Arrays 35
2.12 Bitwise Operators 37
2.13 Vectorizing Code 38
2.14 Using MATLAB for Processing Signals 40
2.15 Chapter Summary 43
CHAPTER 3 SAMPLED SIGNALS AND DIGITAL PROCESSING 45
3.1 Chapter Objectives 45
3.2 Introduction 45
3.3 Processing Signals Using Computer Algorithms 45
3.4 Digital Representation of Numbers 47
3.5 Sampling 61
3.6 Quantization 64
3.7 Image Display 74
3.8 Aliasing 81
3.9 Reconstruction 84
3.10 Block Diagrams and Difference Equations 88
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viii CONTENTS
3.11 Linearity, Superposition, and Time Invariance 92
3.12 Practical Issues and Computational Effi ciency 95
3.13 Chapter Summary 98
CHAPTER 4 RANDOM SIGNALS 103
4.1 Chapter Objectives 103
4.2 Introduction 103
4.3 Random and Deterministic Signals 103
4.4 Random Number Generation 105
4.5 Statistical Parameters 106
4.6 Probability Functions 108
4.7 Common Distributions 112
4.8 Continuous and Discrete Variables 114
4.9 Signal Characterization 116
4.10 Histogram Operators 117
4.11 Median Filters 122
4.12 Chapter Summary 125
CHAPTER 5 REPRESENTING SIGNALS AND SYSTEMS 127
5.1 Chapter Objectives 127
5.2 Introduction 127
5.3 Discrete-Time Waveform Generation 127
5.4 The z Transform 137
5.5 Polynomial Approach 144
5.6 Poles, Zeros, and Stability 146
5.7 Transfer Functions and Frequency Response 152
5.8 Vector Interpretation of Frequency Response 153
5.9 Convolution 156
5.10 Chapter Summary 160
CHAPTER 6 TEMPORAL AND SPATIAL SIGNAL PROCESSING 165
6.1 Chapter Objectives 165
6.2 Introduction 165
6.3 Correlation 165
6.4 Linear Prediction 177
6.5 Noise Estimation and Optimal Filtering 183
6.6 Tomography 188
6.7 Chapter Summary 201
CHAPTER 7 FREQUENCY ANALYSIS OF SIGNALS 203
7.1 Chapter Objectives 203
7.2 Introduction 203
7.3 Fourier Series 203
7.4 How Do the Fourier Series Coeffi cient Equations Come About? 209
7.5 Phase-Shifted Waveforms 211
7.6 The Fourier Transform 212
7.7 Aliasing in Discrete-Time Sampling 231
7.8 The FFT as a Sample Interpolator 233
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CONTENTS ix
7.9 Sampling a Signal over a Finite Time Window 236
7.10 Time-Frequency Distributions 240
7.11 Buffering and Windowing 241
7.12 The FFT 243
7.13 The DCT 252
7.14 Chapter Summary 266
CHAPTER 8 DISCRETE-TIME FILTERS 271
8.1 Chapter Objectives 271
8.2 Introduction 271
8.3 What Do We Mean by “Filtering”? 272
8.4 Filter Specifi cation, Design, and Implementation 274
8.5 Filter Responses 282
8.6 Nonrecursive Filter Design 285
8.7 Ideal Reconstruction Filter 293
8.8 Filters with Linear Phase 294
8.9 Fast Algorithms for Filtering, Convolution, and Correlation 298
8.10 Chapter Summary 311
CHAPTER 9 RECURSIVE FILTERS 315
9.1 Chapter Objectives 315
9.2 Introduction 315
9.3 Essential Analog System Theory 319
9.4 Continuous-Time Recursive Filters 326
9.5 Comparing Continuous-Time Filters 339
9.6 Converting Continuous-Time Filters to Discrete Filters 340
9.7 Scaling and Transformation of Continuous Filters 361
9.8 Summary of Digital Filter Design via Analog Approximation 371
9.9 Chapter Summary 372
BIBLIOGRAPHY 375
INDEX 379
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PREFACE
I was once asked what signal processing is. The questioner thought it had something
to do with traffi c lights. It became clear to me at that moment that although the
theory and practice of signal processing in an engineering context has made possible
the massive advances of recent times in everything from consumer electronics to
healthcare, the area is poorly understood by those not familiar with digital signal
processing (DSP). Unfortunately, such lack of understanding sometimes extends to
those embarking on higher education courses in engineering, computer science, and
allied fi elds, and I believe it is our responsibility not simply to try to cover every
possible theoretical aspect, but to endeavor to open the student ’ s eyes to the possible
applications of signal processing, particularly in a multidisciplinary context.
With that in mind, this book sets out to provide the necessary theoretical and
practical underpinnings of signal processing, but in a way that can be readily under-
stood by the newcomer to the fi eld. The assumed audience is the practicing engineer,
the engineering undergraduate or graduate student, or the researcher in an allied fi eld
who can make use of signal processing in a research context. The examples given
to introduce the topics have been chosen to clearly introduce the motivation behind
the topic and where it might be applied. Necessarily, a great deal of detail has to be
sacrifi ced in order to meet the expectations of the audience. This is not to say that
the theory or implementation has been trivialized. Far from it; the treatment given
extends from the theoretical underpinnings of key algorithms and techniques to
computational and numerical aspects.
The text may be used in a one - term or longer course in signal processing, and
the assumptions regarding background knowledge have been kept to a minimum.
Shorter courses may not be able to cover all that is presented, and an instructor may
have to sacrifi ce some breadth in order to ensure adequate depth of coverage of
important topics. The sections on fast convolution and fi ltering, and medical image
processing, may be omitted in that case. Likewise, recursive fi lter design via analog
prototyping may be omitted or left to a second course if time does not permit
coverage.
A basic understanding of algebra, polynomials, calculus, matrices, and vectors
would provide a solid background to studying the material, and a fi rst course
in linear systems theory is an advantage but is not essential. In addition to the
aforementioned mathematical background, a good understanding of computational
principles and coding, and a working knowledge of a structured programming
language is desirable, as is prior study of numerical mathematics. Above all, these
xi
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xii PREFACE
should not be considered as a list of essential prerequisites; the reader who is lacking
in some of these areas should not be deterred.
It is hoped that the problems at the end of each chapter, in conjunction with
the various case studies, will give rise to a suffi ciently rich learning environment,
and appropriately challenging term projects may be developed with those problems
as starting points.
John W. Leis
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1
CHAPTER

WHAT IS SIGNAL
PROCESSING?
1.1 CHAPTER OBJECTIVES
On completion of this chapter, the reader should
1. be able to explain the broad concept of digital signal processing (DSP);
2. know some of the key terms associated with DSP; and
3. be familiar with the conventions used in the book, both mathematical and for
code examples.
1.2 INTRODUCTION
Signals are time - varying quantities which carry information. They may be, for
example, audio signals (speech, music), images or video signals, sonar signals or
ultrasound, biological signals such as the electrical pulses from the heart, commu-
nications signals, or many other types. With the emergence of high - speed, low -c ost
computing hardware, we now have the opportunity to analyze and process signals
via computer algorithms.
The basic idea is straightforward: Rather than design complex circuits to
process signals, the signal is fi rst converted into a sequence of numbers and pro-
cessed via software. By its very nature, software is more easily extensible and more
versatile as compared with hard - wired circuits, which are diffi cult to change.
Furthermore, using software, we can build in more “ intelligence ” into the operation
of our designs and thus develop more human - usable devices.
A vitally important concept to master at the outset is that of an a lgorithm : the
logical sequence of steps which must be followed in order to generate a useful result.
Although this defi nition is applicable to general - purpose information processing, the
key difference is in the nature of the data which are processed. In signal processing,
the data sequence represents information which is not inherently digital and is
usually imprecise.
Digital Signal Processing Using MATLAB for Students and Researchers, First Edition. John W. Leis.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.
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