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signals and systems using matlab.pdf
Front cover
Signals and Systems Using MATLAB®
Copyright page
Dedication
Table of contents
Preface
Acknowledgments
Part 1: Introduction
Chapter 0. From the Ground Up!
0.1 Signals and Systems and Digital Technologies
0.2 Examples of Signal Processing Applications
0.3 Analog or Discrete?
0.4 Complex or Real?
0.5 Soft Introduction to MATLAB
Problems
Part 2: Theory and Application of Continuous-Time Signals and Systems
Chapter 1. Continuous-Time Signals
1.1 Introduction
1.2 Classification of Time-Dependent Signals
1.3 Continuous-Time Signals
1.4 Representation Using Basic Signals
1.5 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 2. Continuous-Time Systems
2.1 Introduction
2.2 System Concept
2.3 LTI Continuous-Time Systems
2.4 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 3. The Laplace Transform
3.1 Introduction
3.2 The Two-Sided Laplace Transform
3.3 The One-Sided Laplace Transform
3.4 Inverse Laplace Transform
3.5 Analysis of LTI Systems
3.6 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 4. Frequency Analysis: The Fourier Series
4.1 Introduction
4.2 Eigenfunctions Revisited
4.3 Complex Exponential Fourier Series
4.4 Line Spectra
4.5 Trigonometric Fourier Series
4.6 Fourier Coefficients from Laplace
4.7 Convergence of the Fourier Series
4.8 Time and Frequency Shifting
4.9 Response of LTI Systems to Periodic Signals
4.10 Other Properties of the Fourier Series
4.11 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 5. Frequency Analysis: The Fourier Transform
5.1 Introduction
5.2 From the Fourier Series to the Fourier Transform
5.3 Existence of the Fourier Transform
5.4 Fourier Transforms from the Laplace Transform
5.5 Linearity, Inverse Proportionality, and Duality
5.6 Spectral Representation
5.7 Convolution and Filtering
5.8 Additional Properties
5.9 What have We Accomplished? What is next?
Problems
Chapter 6. Application to Control and Communications
6.1 Introduction
6.2 System Connections and Block Diagrams
6.3 Application to Classic Control
6.4 Application to Communications
6.5 Analog Filtering
6.6 What Have We Accomplished? What is next?
Problems
Part 3: Theory and Application of Discrete-Time Signals and Systems
Chapter 7. Sampling Theory
7.1 Introduction
7.2 Uniform Sampling
7.3 The Nyquist-Shannon Sampling Theorem
7.4 Practical Aspects of Sampling
7.5 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 8. Discrete-Time Signals and Systems
8.1 Introduction
8.2 Discrete-Time Signals
8.3 Discrete-Time Systems
8.4 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 9. The Z-Transform
9.1 Introduction
9.2 Laplace Transform of Sampled Signals
9.3 Two-Sided Z-Transform
9.4 One-Sided Z-Transform
9.5 One-Sided Z-Transform Inverse
9.6 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 10. Fourier Analysis of Discrete-Time Signals and Systems
10.1 Introduction
10.2 Discrete-Time Fourier Transform
10.3 Fourier Series of Discrete-Time Periodic Signals
10.4 Discrete Fourier Transform
10.5 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 11. Introduction to the Design of Discrete Filters
11.1 Introduction
11.2 Frequency-Selective Discrete Filters
11.3 Filter Specifications
11.4 IIR Filter Design
11.5 FIR Filter Design
11.6 Realization of Discrete Filters
11.7 What Have We Accomplished? Where Do We Go from Here?
Problems
Chapter 12. Applications of Discrete-Time Signals and Systems
12.1 Introduction
12.2 Application to Digital Signal Processing
12.3 Application to Sampled-Data and Digital Control Systems
12.4 Application to Digital Communications
12.5 What Have We Accomplished? Where Do We Go from Here?
Appendix. Useful Formulas
Bibliography
Index
Signals and Systems
Using MATLAB
Luis F. Chaparro
Department of Electrical and Computer Engineering
University of Pittsburgh
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
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Library of Congress Cataloging-in-Publication Data
Chaparro, Luis F.
R
Signals and systems using MATLAB / Luis F. Chaparro.
p. cm.
ISBN 978-0-12-374716-7
1. Signal processing–Digital techniques. 2. System analysis. 3. MATLAB. I. Title.
TK5102.9.C472 2010
621.382’2–dc22
2010023436
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
For information on all Academic Press publications
visit our Web site at www.elsevierdirect.com
Printed in the United States of America
10 11 12 13 9 8 7 6 5 4 3 2 1
To my family, with much love.
Contents
PREFACE .....................................................................................................................
xi
ACKNOWLEDGMENTS ................................................................................................ xvi
1
Introduction
From the Ground Up! .............................................................................
Signals and Systems and Digital Technologies........................................
0.1
Examples of Signal Processing Applications ...........................................
0.2
0.2.1
Compact-Disc Player ................................................................
Software-Defined Radio and Cognitive Radio...............................
0.2.2
0.2.3
Computer-Controlled Systems ...................................................
0.3 Analog or Discrete? .............................................................................
3
3
5
5
6
8
9
Continuous-Time and Discrete-Time Representations .................. 10
Derivatives and Finite Differences ............................................. 12
Integrals and Summations......................................................... 13
Differential and Difference Equations ......................................... 16
0.4 Complex or Real? ................................................................................ 20
Complex Numbers and Vectors.................................................. 20
0.4.1
Functions of a Complex Variable................................................ 23
0.4.2
Phasors and Sinusoidal Steady State .......................................... 24
0.4.3
0.4.4
Phasor Connection ................................................................... 26
Soft Introduction to MATLAB ............................................................... 29
0.5.1 Numerical Computations .......................................................... 30
0.5.2
Symbolic Computations ............................................................ 43
Problems............................................................................................ 53
0.3.1
0.3.2
0.3.3
0.3.4
0.5
Part 1
CHAPTER 0
Part 2
CHAPTER 1 Continuous-Time Signals .........................................................................
Theory and Application of Continuous-Time
Signals and Systems
63
65
1.1
Introduction ....................................................................................... 65
1.2 Classification of Time-Dependent Signals............................................... 66
iv
Contents
v
1.4
1.3 Continuous-Time Signals ..................................................................... 67
Basic Signal Operations—Time Shifting and Reversal ................... 71
1.3.1
Even and Odd Signals .............................................................. 75
1.3.2
Periodic and Aperiodic Signals .................................................. 77
1.3.3
1.3.4
Finite-Energy and Finite Power Signals ...................................... 79
Representation Using Basic Signals....................................................... 85
Complex Exponentials .............................................................. 85
1.4.1
Unit-Step, Unit-Impulse, and Ramp Signals ................................. 88
1.4.2
Special Signals—the Sampling Signal and the Sinc ....................... 100
1.4.3
1.4.4
Basic Signal Operations—Time Scaling, Frequency Shifting,
and Windowing ....................................................................... 102
1.4.5 Generic Representation of Signals.............................................. 105
1.5 What Have We Accomplished? Where Do We Go from Here?.................... 106
Problems............................................................................................ 108
2.3
2.1
2.2
CHAPTER 2 Continuous-Time Systems ....................................................................... 117
Introduction ....................................................................................... 117
System Concept .................................................................................. 118
2.2.1
System Classification................................................................ 118
LTI Continuous-Time Systems .............................................................. 119
Linearity ................................................................................. 120
2.3.1
2.3.2
Time Invariance....................................................................... 125
2.3.3
Representation of Systems by Differential Equations.................... 130
2.3.4 Application of Superposition and Time Invariance ....................... 135
Convolution Integral................................................................. 136
2.3.5
2.3.6
Causality ................................................................................ 143
2.3.7 Graphical Computation of Convolution Integral ........................... 145
Interconnection of Systems—Block Diagrams .............................. 147
2.3.8
2.3.9
Bounded-Input Bounded-Output Stability ................................... 153
2.4 What Have We Accomplished? Where Do We Go from Here?.................... 156
Problems............................................................................................ 157
3.1
3.2
CHAPTER 3 The Laplace Transform ............................................................................ 165
Introduction ....................................................................................... 165
The Two-Sided Laplace Transform ........................................................ 166
Eigenfunctions of LTI Systems................................................... 167
3.2.1
3.2.2
Poles and Zeros and Region of Convergence ............................... 172
The One-Sided Laplace Transform ........................................................ 176
Linearity ................................................................................. 185
3.3.1
Differentiation ......................................................................... 188
3.3.2
Integration .............................................................................. 193
3.3.3
3.3.4
Time Shifting........................................................................... 194
Convolution Integral................................................................. 196
3.3.5
3.3
vi Contents
CHAPTER 4
CHAPTER 5
3.4
Inverse Laplace Transform ................................................................... 197
3.4.1
Inverse of One-Sided Laplace Transforms ................................... 197
−ρs Terms ................................ 209
Inverse of Functions Containing e
3.4.2
3.4.3
Inverse of Two-Sided Laplace Transforms ................................... 212
3.5 Analysis of LTI Systems ....................................................................... 214
LTI Systems Represented by Ordinary Differential Equations ........ 214
Computation of the Convolution Integral .................................... 221
3.6 What Have We Accomplished? Where Do We Go from Here?.................... 226
Problems............................................................................................ 226
3.5.1
3.5.2
Frequency Analysis: The Fourier Series .................................................. 237
Introduction ....................................................................................... 237
4.1
4.2
Eigenfunctions Revisited ..................................................................... 238
4.3 Complex Exponential Fourier Series ...................................................... 245
Line Spectra ....................................................................................... 248
4.4
Parseval’s Theorem—Power Distribution over Frequency ............. 248
4.4.1
4.4.2
Symmetry of Line Spectra ......................................................... 250
Trigonometric Fourier Series ................................................................ 251
4.5
4.6
Fourier Coefficients from Laplace.......................................................... 255
4.7 Convergence of the Fourier Series......................................................... 265
4.8
Time and Frequency Shifting................................................................ 270
Response of LTI Systems to Periodic Signals........................................... 273
4.9
Sinusoidal Steady State............................................................. 274
4.9.1
4.9.2
Filtering of Periodic Signals....................................................... 276
4.10 Other Properties of the Fourier Series .................................................... 279
4.10.1 Reflection and Even and Odd Periodic Signals ............................. 279
4.10.2 Linearity of Fourier Series—Addition of Periodic Signals ............... 282
4.10.3 Multiplication of Periodic Signals ............................................... 284
4.10.4 Derivatives and Integrals of Periodic Signals ............................... 285
4.11 What Have We Accomplished? Where Do We Go from Here?.................... 289
Problems............................................................................................ 290
Frequency Analysis: The Fourier Transform ........................................... 299
Introduction ....................................................................................... 299
5.1
From the Fourier Series to the Fourier Transform .................................... 300
5.2
5.3
Existence of the Fourier Transform ....................................................... 302
Fourier Transforms from the Laplace Transform ..................................... 302
5.4
Linearity, Inverse Proportionality, and Duality ........................................ 304
5.5
5.5.1
Linearity ................................................................................. 304
Inverse Proportionality of Time and Frequency............................ 305
5.5.2
5.5.3
Duality ................................................................................... 310
Contents
vii
5.6
5.8.1
5.8.2
Spectral Representation ....................................................................... 313
Signal Modulation .................................................................... 313
5.6.1
5.6.2
Fourier Transform of Periodic Signals ......................................... 317
Parseval’s Energy Conservation................................................. 320
5.6.3
5.6.4
Symmetry of Spectral Representations........................................ 322
5.7 Convolution and Filtering..................................................................... 327
Basics of Filtering .................................................................... 329
Ideal Filters ............................................................................. 332
Frequency Response from Poles and Zeros.................................. 337
Spectrum Analyzer................................................................... 341
5.8 Additional Properties .......................................................................... 344
Time Shifting .......................................................................... 344
Differentiation and Integration .................................................. 346
5.9 What Have We Accomplished? What Is Next? ....................................... 350
Problems............................................................................................ 350
5.7.1
5.7.2
5.7.3
5.7.4
6.3.1
6.3.2
CHAPTER 6 Application to Control and Communications ........................................... 359
Introduction ....................................................................................... 359
6.1
6.2
System Connections and Block Diagrams ............................................... 360
6.3 Application to Classic Control............................................................... 363
Stability and Stabilization ......................................................... 369
Transient Analysis of First- and Second-Order Control Systems ..... 371
6.4 Application to Communications ............................................................ 377
6.4.1 AM with Suppressed Carrier ..................................................... 379
6.4.2
Commercial AM....................................................................... 380
6.4.3 AM Single Sideband ................................................................. 382
6.4.4 Quadrature AM and Frequency-Division Multiplexing .................. 383
6.4.5 Angle Modulation .................................................................... 385
6.5 Analog Filtering.................................................................................. 390
Filtering Basics........................................................................ 390
Butterworth Low-Pass Filter Design........................................... 393
Chebyshev Low-Pass Filter Design ............................................ 396
Frequency Transformations ...................................................... 402
Filter Design with MATLAB ...................................................... 405
6.6 What Have We Accomplished? What Is Next? ........................................ 409
Problems............................................................................................ 409
6.5.1
6.5.2
6.5.3
6.5.4
6.5.5
Part 3
CHAPTER 7
Theory and Application of Discrete-Time
Signals and Systems
417
Sampling Theory...................................................................................... 419
Introduction ....................................................................................... 419
7.1
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