Signals and Systems (Oppenheim) 2nd Edition.pdf

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Cover

Contents

Preface

Acknowledgements

Foreword

1 Signals and Systems

1.0 Introduction

1.1 Continuous-Time and Discrete-Time Signals

1.2 Transformations of the Independent Variable

1.3 Exponential and Sinusoidal Signals

1.4 The Unit Impulse and Unit Step Functions

1.5 Continuous-Time and Discrete-Time Systems

1.6 Basic System Properties

1.7 Summary

Problems

2 Linear Time-Invariant Systems

2.0 Introduction

2.1 Discrete-Time LTI Systems: The Convolution Sum

2.2 Continuous-Time LTI Systems: The Convolution Integral

2.3 Properties of Linear Time-Invariant Systems

2.4 Causal LTI Systems Described by Differential and Difference Equations

2.5 Singularity Functions

2.6 Summary

Problems

3 Fourier Series Representation of Periodic Signals

3.0 Introduction

3.1 A Historical Perspective

3.2 The Response of LTI Systems to Complex Exponentials

3.3 Fourier Series Representation of Continuous-Time Periodic Signals

3.4 Convergence of the Fourier Series

3.5 Properties of Continuous-Time Fourier Series

3.6 Fourier Series Representation of Discrete-Time Periodic Signals

3.7 Properties of Discrete-Time Fourier Series

3.8 Fourier Series and LTI Systems

3.9 Filtering

3.10 Examples of Continuous-Time Filters Described by Differential Equations

3.11 Examples of Discrete-Time Filters Described by Difference Equations

3.12 Summary

Problems

4 The Continuous-Time Fourier Transform

4.0 Introduction

4.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform

4.2 The Fourier Transform for Periodic Signals

4.3 Properties of the Continuous-Time Fourier Transform

4.4 The Convolution Property

4.5 The Multiplication Property

4.6 Tables of Fourier Properties and of Basic Fourier Transform Pairs

4.7 Systems Characterized by Linear Constant-Coefficient Differential Equations

4.8 Summary

Problems

5 The Discrete-Time Fourier Transform

5.0 Introduction

5.1 Representation of Aperiodic Signals: The Discrete-Time Fourier Transform

5.2 The Fourier Transform for Periodic Signals

5.3 Properties of the Discrete-Time Fourier Transform

5.4 The Convolution Property

5.5 The Multiplication Property

5.6 Tables of Fourier Transform Properties and Basic Fourier Transform Pairs

5.7 Duality

5.8 Systems Characterized by Linear Constant-Coefficient Difference Equations

5.9 Summary

Problems

6 Time and Frequency Characterization of Signals and Systems

6.0 Introduction

6.1 The Magnitude-Phase Representation of the Fourier Transform

6.2 The Magnitude-Phase Representation of the Frequency Response of LTI Systems

6.3 Time-Domain Properties of Ideal Frequency-Selective Filters

6.4 Time-Domain and Frequency-Domain Aspects of Nonideal Filters

6.5 First-Order and Second-Order Continuous-Time Systems

6.6 First-Order and Second-Order Discrete-Time Systems

6.7 Examples of Time- and Frequency-Domain Analysis of Systems

6.8 Summary

Problems

7 Sampling

7.0 Introduction

7.1 Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem

7.2 Reconstruction of a Signal from Its Samples Using Interpolation

7.3 The Effect of Undersampling: Aliasing

7.4 Discrete-Time Processing of Continuous-Time Signals

7.5 Sampling of Discrete-Time Signals

7.6 Summary

Problems

8 Communication Systems

8.0 Introduction

8.1 Complex Exponential and Sinusoidal Amplitude Modulation

8.2 Demodulation for Sinusoidal AM

8.3 Frequency-Division Multiplexing

8.4 Single-Sideband Sinusoidal Amplitude Modulation

8.5 Amplitude Modulation with a Pulse-Train Carrier

8.6 Pulse-Amplitude Modulation

8.7 Sinusoidal Frequency Modulation

8.8 Discrete-Time Modulation

8.9 Summary

Problems

9 The Laplace Transform

9.0 Introduction

9.1 The Laplace Transform

9.2 The Region of Convergence for Laplace Transforms

9.3 The Inverse Laplace Transform

9.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot

9.5 Properties of the Laplace Transform

9.6 Some Laplace Transform Pairs

9.7 Analysis and Characterization of LTI Systems Using the Laplace Transform

9.8 System Function Algebra and Block Diagram Representations

9.9 The Unilateral Laplace Transform

9.10 Summary

Problems

10 The z-Transform

10.0 Introduction

10.1 The z-Transform

10.2 The Region of Convergence for the z-Transform

10.3 The Inverse z-Transform

10.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot

10.5 Properties of the z-Transform

10.6 Some Common z-Transform Pairs

10.7 Analysis and Characterization of LTI Systems Using z-Transforms

10.8 System Function Algebra and Block Diagram Representations

10.9 The Unilateral z-Transform

10.10 Problems

Problems

11 Linear Feedback Systems

11.0 Introduction

11.1 Linear Feedback Systems

11.2 Some Applications and Consequences of Feedback

11.3 Root-Locus Analysis of Linear Feedback Systems

11.4 The Nyquist Stability Criterion

11.5 Gain and Phase Margins

11.6 Summary

Problems

Appendix: Partial-Fraction Expansion

Bibliography

Answers

Index

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& SIGNALS SYSTEMS

PRENTICE HALL SIGNAL PROCESSING SERIES Alan V. Oppenheim, Series Editor ANDREWS & HUNT Digital Image Restoration BRACEWELL Two Dimensional Imaging BRIGHAM The Fast Fourier Transform and Its Applications BuRDIC Underwater Acoustic System Analysis 2/E CASTLEMAN Digital Image Processing CoHEN Time-Frequency Analysis CROCHIERE & RABINER Multirate Digital Signal Processing DuDGEON & MERSEREAU Multidimensional Digital Signal Processing HAYKIN Advances in Spectrum Analysis and Array Processing. Vols. I, II & III HAYKIN, Eo. Array Signal Processing JoHNSON & DuDGEON Array Signal Processing KAY Fundamentals of Statistical Signal Processing KAY Modern Spectral Estimation KINO Acoustic Waves: Devices, Imaging, and Analog Signal Processing LIM Two-Dimensional Signal and Image Processing LIM, Eo. Speech Enhancement LIM & OPPENHEIM, Eos. Advanced Topics in Signal Processing MARPLE Digital Spectral Analysis with Applications MccLELLAN & RADER Number Theory in Digital Signal Processing MENDEL Lessons in Estimation Theory for Signal Processing Communications and Control 2/E NIKIAS & PETROPULU Higher Order Spectra Analysis OPPENHEIM & NAWAB Symbolic and Knowledge-Based Signal Processing OPPENHEIM & WILLSKY, WITH NAWAB Signals and Systems, 2/E OPPENHEIM & ScHAFER Digital Signal Processing OPPENHEIM & ScHAFER Discrete-Time Signal Processing 0RFANIDIS Signal Processing PHILLIPS & NAGLE Digital Control Systems Analysis and Design, 3/E PICINBONO Random Signals and Systems RABINER & GoLD Theory and Applications of Digital Signal Processing RABINER & SCHAFER Digital Processing of Speech Signals RABINER & JuANG Fundamentals of Speech Recognition RoBINSON & TREITEL Geophysical Signal Analysis STEARNS & DAVID Signal Processing Algorithms in Fortran and C STEARNS & DAVID Signal Processing Algorithms in MATIAB TEKALP Digital Video Processing THERRIEN Discrete Random Signals and Statistical Signal Processing TRIBOLET Seismic Applications of Homomorphic Signal Processing VETTERLI & KovACEVIC Wavelets and Subband Coding VIADYANATHAN Multirate Systems and Filter Banks WIDROW & STEARNS Adaptive Signal Processing

SECOND EDITION SIGNALS SYSTEMS & ALAN V. OPPENHEIM ALAN S. WILLSKY MASSACHUSETTS INSTITUTE OF TECHNOLOGY WITH S. HAMID NAWAB BOSTON UNIVERSITY PRENTICE HALL UPPER SADDLE RIVER, NEW JERSEY 07458

Library of Congress Cataloging-in-Publication Data Oppenheim, Alan V. Signals and systems / Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab. - 2nd ed. cm. - Prentice-Hall signal processing series p. Includes bibliographical references and index. ISBN 0-13-814757-4 l. System analysis. I. Willsky, Alan S. II. Nawab, Syed Hamid. III. Title. IV. Series QA402.063 1996 621.382'23–dc20 2. Signal theory (Telecommunication) 96-19945 CIP Acquisitions editor: Tom Robbins Production service: TKM Productions Editorial/production supervision: Sharyn Vitrano Copy editor: Brian Baker Interior and cover design: Patrice Van Acker Art director: Amy Rosen Managing editor: Bayani Mendoza DeLeon Editor-in-Chief: Marcia Horton Director of production and manufacturing: David W. Riccardi Manufacturing buyer: Donna Sullivan Editorial assistant: Phyllis Morgan © 1997 by Alan V. Oppenheim and Alan S. Willsky © 1983 by Alan V. Oppenheim, Alan S. Willsky, and Ian T. Young Published by Prentice-Hall, Inc. Simon & Schuster / A Viacom Company Upper Saddle River, New Jersey 07458 Printed in the United States of America 10 9 8 7 6 5 4 ISBN 0-13–814757–4 Prentice-Hall International (UK) Limited, London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Simon & Schuster Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro

To Phyllis, Jason, and Justine To Susanna, Lydia, and Kate

CONTENTS PREFACE XVII ACKNOWLEDGEMENTS XXV FOREWORD XXVII 1 SIGNALS AND SYSTEMS 1 1.0 1.1 Introduction 1 Continuous-Time and Discrete-Time Signals 1 1.1.1 1.1.2 Examples and Mathematical Representation 1 Signal Energy and Power 5 1.2 Transformations of the Independent Variable 7 1.2.1 1.2.2 1.2.3 Examples of Transformations of the Independent Variable 8 Periodic Signals 11 Even and Odd Signals 13 1.3 Exponential and Sinusoidal Signals 14 1.4 The Unit Impulse and Unit Step Functions 30 Continuous-Time Complex Exponential and Sinusoidal Signals 15 Discrete-Time Complex Exponential and Sinusoidal Signals 21 Periodicity Properties of Discrete-Time Complex Exponentials 25 The Discrete-Time Unit Impulse and Unit Step Sequences 30 The Continuous-Time Unit Step and Unit Impulse Functions 32 1.3.1 1.3.2 1.3.3 1.4.1 1.4.2 1.5 Continuous-Time and Discrete-Time Systems 38 1.5.1 1.5.2 Simple Examples of Systems 39 Interconnections of Systems 41 1.6 Basic System Properties 44 1.6.1 1.6.2 1.6.3 1.6.4 1.6.5 1.6.6 Systems with and without Memory 44 Invertibility and Inverse Systems 45 Causality 46 Stability 48 Time Invariance 50 Linearity 53 1.7 Summary 56 Problems 57 2 LINEAR TIME-INVARIANT SYSTEMS 74 2.0 2.1 Introduction 74 Discrete-Time LTI Systems: The Convolution Sum 75 vii

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