DIGITAL SIGNAL PROCESSING USING MATLAB FOR STUDENTS AND RESEARCHERS

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DIGITAL SIGNAL PROCESSING USING MATLAB FOR STUDENTS AND RESEARCHERS

JOHN W. LEISUniversity 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 11.2 Introduction 11.3 Book Objectives 21.4 DSP and ITS Applications 31.5 Application Case Studies Using DSP 41.6 Overview of Learning Objectives 121.7 Conventions Used in This Book 151.8 Chapter Summary 16

CHAPTER 2 MATLAB FOR SIGNAL PROCESSING 19

2.1 Chapter Objectives 192.2 Introduction 192.3 What Is MATLAB? 192.4 Getting Started 202.5 Everything Is a Matrix 202.6 Interactive Use 212.7 Testing and Looping 232.8 Functions and Variables 252.9 Plotting and Graphing 302.10 Loading and Saving Data 312.11 Multidimensional Arrays 352.12 Bitwise Operators 372.13 Vectorizing Code 382.14 Using MATLAB for Processing Signals 402.15 Chapter Summary 43

CHAPTER 3 SAMPLED SIGNALS AND DIGITAL PROCESSING 45

3.1 Chapter Objectives 453.2 Introduction 453.3 Processing Signals Using Computer Algorithms 453.4 Digital Representation of Numbers 473.5 Sampling 613.6 Quantization 643.7 Image Display 743.8 Aliasing 813.9 Reconstruction 843.10 Block Diagrams and Difference Equations 88

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viii CONTENTS

3.11 Linearity, Superposition, and Time Invariance 923.12 Practical Issues and Computational Effi ciency 953.13 Chapter Summary 98

CHAPTER 4 RANDOM SIGNALS 103

4.1 Chapter Objectives 1034.2 Introduction 1034.3 Random and Deterministic Signals 1034.4 Random Number Generation 1054.5 Statistical Parameters 1064.6 Probability Functions 1084.7 Common Distributions 1124.8 Continuous and Discrete Variables 1144.9 Signal Characterization 1164.10 Histogram Operators 1174.11 Median Filters 1224.12 Chapter Summary 125

CHAPTER 5 REPRESENTING SIGNALS AND SYSTEMS 127

5.1 Chapter Objectives 1275.2 Introduction 1275.3 Discrete-Time Waveform Generation 1275.4 The z Transform 1375.5 Polynomial Approach 1445.6 Poles, Zeros, and Stability 1465.7 Transfer Functions and Frequency Response 1525.8 Vector Interpretation of Frequency Response 1535.9 Convolution 1565.10 Chapter Summary 160

CHAPTER 6 TEMPORAL AND SPATIAL SIGNAL PROCESSING 165

6.1 Chapter Objectives 1656.2 Introduction 1656.3 Correlation 1656.4 Linear Prediction 1776.5 Noise Estimation and Optimal Filtering 1836.6 Tomography 1886.7 Chapter Summary 201

CHAPTER 7 FREQUENCY ANALYSIS OF SIGNALS 203

7.1 Chapter Objectives 2037.2 Introduction 2037.3 Fourier Series 2037.4 How Do the Fourier Series Coeffi cient Equations Come About? 2097.5 Phase-Shifted Waveforms 2117.6 The Fourier Transform 2127.7 Aliasing in Discrete-Time Sampling 2317.8 The FFT as a Sample Interpolator 233

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CONTENTS ix

7.9 Sampling a Signal over a Finite Time Window 2367.10 Time-Frequency Distributions 2407.11 Buffering and Windowing 2417.12 The FFT 2437.13 The DCT 2527.14 Chapter Summary 266

CHAPTER 8 DISCRETE-TIME FILTERS 271

8.1 Chapter Objectives 2718.2 Introduction 2718.3 What Do We Mean by “Filtering”? 2728.4 Filter Specifi cation, Design, and Implementation 2748.5 Filter Responses 2828.6 Nonrecursive Filter Design 2858.7 Ideal Reconstruction Filter 2938.8 Filters with Linear Phase 2948.9 Fast Algorithms for Filtering, Convolution, and Correlation 2988.10 Chapter Summary 311

CHAPTER 9 RECURSIVE FILTERS 315

9.1 Chapter Objectives 3159.2 Introduction 3159.3 Essential Analog System Theory 3199.4 Continuous-Time Recursive Filters 3269.5 Comparing Continuous-Time Filters 3399.6 Converting Continuous-Time Filters to Discrete Filters 3409.7 Scaling and Transformation of Continuous Filters 3619.8 Summary of Digital Filter Design via Analog Approximation 3719.9 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

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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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