SIGNALS, SYSTEMS, AND TRANSFORMS FOURTH EDITION This page intentionally left blank SIGNALS, SYSTEMS, AND TRANSFORMS FOURTH EDITION CHARLES L. PHILLIPS Emeritus Auburn University Auburn, Alabama JOHN M. PARR University of Evansville Evansville, Indiana EVE A. RISKIN University of Washington Seattle, Washington Upper Saddle River, NJ 07458 Library of Congress Cataloging-in-Publication Data Phillips, Charles L. Signals, systems, and transforms / Charles L. Phillips, John M. Parr, Eve A. Riskin.—4th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-198923-8 ISBN-10: 0-13-198923-5 1. Signal processing–Mathematical models. 2. Transformations (Mathematics) 3. System analysis. I. Parr, John M. II. Riskin, Eve A. (Eve Ann) III. Title. TK5102.9.P47 2008 621.382'2—dc22 2007021144 Vice President and Editorial Director, ECS: Art Director, Cover: Jayne Conte Marcia J. 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Pearson Education North Asia Ltd., Hong Kong Pearson Education, Inc., Upper Saddle River, New Jersey Pearson Education Canada, Inc., Toronto To Taylor, Justin, Jackson, Rebecca, and Alex Michaela, Cadence, Miriam, and Connor Duncan, Gary, Noah, and Aden This page intentionally left blank CONTENTS PREFACE xvii 1 INTRODUCTION 1 1.1 Modeling 1 1.2 Continuous-Time Physical Systems 4 Electric Circuits, 4 Operational Amplifier Circuits, 6 Simple Pendulum, 9 DC Power Supplies, 10 Analogous Systems, 12 1.3 Samplers and Discrete-Time Physical Systems 14 Analog-to-Digital Converter, 14 Numerical Integration, 16 Picture in a Picture, 17 Compact Disks, 18 Sampling in Telephone Systems, 19 Data-Acquisition System, 21 1.4 MATLAB and SIMULINK 22 2 CONTINUOUS-TIME SIGNALS AND SYSTEMS 23 2.1 Transformations of Continuous-Time Signals 24 Time Transformations, 24 Amplitude Transformations, 30 2.2 Signal Characteristics 32 Even and Odd Signals, 32 Periodic Signals, 34 vii viii Contents 2.3 Common Signals in Engineering 39 2.4 Singularity Functions 45 Unit Step Function, 45 Unit Impulse Function, 49 2.5 Mathematical Functions for Signals 54 2.6 Continuous-Time Systems 59 Interconnecting Systems, 61 Feedback System, 64 2.7 Properties of Continuous-Time Systems 65 Stability, 69 Linearity, 74 Summary 76 Problems 78 3 CONTINUOUS-TIME LINEAR TIME-INVARIANT SYSTEMS 89 3.1 Impulse Representation of Continuous-Time Signals 90 3.2 Convolution for Continuous-Time LTI Systems 91 3.3 Properties of Convolution 104 3.4 Properties of Continuous-Time LTI Systems 107 Memoryless Systems, 108 Invertibility, 108 Causality, 109 Stability, 110 Unit Step Response, 111 3.5 Differential-Equation Models 112 Solution of Differential Equations, 114 General Case, 116 Relation to Physical Systems, 118 3.6 Terms in the Natural Response 119 Stability, 120 3.7 System Response for Complex-Exponential Inputs 123 Linearity, 123 Complex Inputs for LTI Systems, 124 Impulse Response, 128 3.8 Block Diagrams 129 Direct Form I, 133 Direct Form II, 133 nth-Order Realizations, 133 Practical Considerations, 135