SignalsandSystems

For undergraduate-level courses in Signals and Systems. This comprehensive exploration of signals and systems develops continuous-time and discrete-time concepts/methods in parallel -- highlighting the similarities and differences -- and features introductory treatments of the applications of these The McGrawHill CompaniesConnectLearnwSuSIGNALS AND SYSTEMSPublished by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc, 1221 Avenue of theAmericas, New York, NY, 10020. Copyright 2014 by The McGraw-Hill Companies, Inc. All rightsreserved. Printed in the United States of America. No part of this publication may be reproduced ordistributed in any form or by any means, or stored in a database or retrieval system, without the priorwritten consent of The McGraw-Hill Companies, Inc, including, but not limited to, in any network or otherelectronic storage or transmission, or broadcast for distance learningThe author and publisher have applied their best effort in preparing this book. They make no warranty withregard to the material or programs contained in this book and shall not be liable to any damagesconsequential to its publicationSome ancillaries, including electronic and print components, may not be available to customers outside theUnited StatesThis book is printed on acid-free paper1234567890 DOC/DOC109876543ISBN978-0-07-338070-4MHID0-07-338070-9Vice President and Editor-in-Chief: Marty langeManaging Director: Thomas TimpEditorial Director: Michael langeGlobal Publisher: Raghothaman SrinivasanMarketing Manager: Curt ReynoldsDevelopment Editor: Katie NeubauerSenior project Manager Lisa A. BruflodtBuyer: Nicole baumgartnerMedia project Manager: Prashanthi nadipalleCover Designer Studio Montage, St Louis, MOCover Image: Brand X Pictures/Punchstock; Photodisc/PunchstockTypeface: 10/12 TimesCompositor: Cenveo Publisher ServicesPrinter:R.R. DonnelleyAll credits appearing on page or at the end of the book are considered to be an extension of the copyrightpagoLibrary of Congress Cataloging-in-Publication DataNahvi. Mahmood.Signals and systems Mahmood Nahvipages cmIncludes indexISBN978-0-07-338070-4(ak. paper)1. Signal processing. I. TitleTK51029N342012621.3822-dc232012038055The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a websitedoes not indicate an endorsement by the authors or McGraw-Hill, and McGraw-Hill does not guarantee theaccuracy of the information presented at these siteswww.mhhe.comABOUT THE AUTHORMahmood Nahvi is emeritus professor of electrical engineering at California polytechnic State University( Cal Poly)in San Luis Obispo, California. He earned BSc, MScand Ph. D. degrees in electrical engineering, and has more than 50 years of educational,academic, research, and industrial experience in this field. He has taught undergraduateand graduate courses on various subjects including electric circuits, electronics, signalsand systems, electromagnetics, random signals and noise, digital signal and image processing, and communications and control. Prior to joining the faculty at Cal poly, heheld positions as a guest professor and research scientist at the University of Stuttgart inGermany, working on signal processing in space communication systems, satellite microwave ranging, and synthetic aperture radar projects for the European Space Agency.In addition, he was a founding faculty member, professor, and department chair at SharifUniversity of Technology(former Aria-Mehr) in Teheran, Iran; a visiting professor atMIT; and a research scientist at UCLA, the Laboratory for Neural Control at the national Institutes of Health, and the max-Planck Institute for biological cybernetics inTubingen, Germany. He is a senior member of the Institute of Electrical and ElectronicsEngineers (ieee)Dr. Nahvi's areas of special interest and expertise include network theory, controltheory, adaptation and learning in synthetic and living systems, communication andcontrol in living systems, neural networks for pattern recognition and motor controlsatellite communication, digital signal and image processing, and engineering education.In the area of engineering education he has developed computer modules for electriccircuits, signals, and systems that improve the teaching and learning of the fundamentalsof electrical engineering. He is coauthor of Electric Circuits and Electromagnetics inSchaum's Outline Series published by McGraw-HillThis book is dedicated to the memory ofJanab nahhumanist scholar. and teacherBRIEF CONTENTSPreface xvii1 Introduction to Signals2 Sinusoids 1213 Systems, Linearity, and Time Invariance 1574 Superposition, Convolution, and Correlation 2035 Differential Equations and LTI Systems 2596 The Laplace Transform and Its applications 3137 Fourier series 3778 Fourier transform 4279 System Function, the Frequency Response, and Analog Filters 48710 Time-Domain Sampling and Reconstruction 62311 Discrete- Time Signals 68312 Linear Time-Invariant Discrete-Time Systems 73313 Discrete Convolution 76314 LTI Difference Equations 79715 The z-Transform and Its applications $2716 Discrete-Time Fourier Transform 88117 Discrete fourier transform 94718 System Function, the Frequency Response and Digital Filters 1005Appendix Electric Circuits 1093Index 1107This page intentionally left blankCONTENTSPreface xvii1.20 Weighted Integration 681.21 Window Averaging 71Chapter 11.22 Differentiation and Differences 73Introduction to Signals 11.23 Concluding Remarks 76Introduction and Summary 21.24 Problems 761.1 Discrete Versus continuous1.25 Project 1: Binary Signal in Noise 116Digital versus analog 31.26 Project 2: Signals Stored as1.2 Deterministic Versus Random 5Computer Data Files 1201.3 Examples of natural andChapter 2Societal Signals 6Sinusoids 1211.4 Voice and Speech Signals 14Introduction and Summary 1211.5 Communication Signals 1621 Sine and Cosine 1221.6 Physiologic Signals 212.2 Angles 1231.7 Electrocardiogram Signals 222.3 Series Approximations 1241.8 Electromyogram Signals 252.4 Trigonometric Identities1.9 Electroencephalogramand relations 125Signals 2625 Sinusoidal waveforms 1261.10 Electrocorticogram Signals 282.6 Sine or Cosine? 1281.11 Neuroelectric Signals fromSingle neurons 302.7 Period and Frequency 12812 Applications of2. 8 Phasors 129Electrophysiologic Signals 322.9 Lag and Lead 1291.13 Characterization and2.10 Time Shift and Phase shift 130Decomposition of Signals 322.11 Summing phasors 1301.14 Mathematical Representationsof Signals 352.12 Combination of Sinusoids 1311.15 Time Averages 482. 13 Combination of periodicSignals 1321.16 Operations on Signals 512.14 Representation of a sum1.17 Time Transformation 51of sinusoids 1321.18 Even and Odd Functions 582. 15 Power in a Sinusoid 1331.19 Integration and Smoothing 612.16 One-Sided Line spectrum 134VIIvIlIContents2.17 Complex Representation3. 16 Problems 188of sinusoids and theTwo-Sided Spectrum 1363.17 Project: Open- Loop Control 2002.18 Problems 137Chapter 42.19 Project: Trajectories, WaveSuperposition, Convolution, andPolarization, and lissajousCorrelation 203Patterns 151Introduction and Summary 203Chapter 34.1 Superposition of Responses 204Systems, Linearity, and4.2 Convolution sum 211Time Invariance 1574.3 Convolution Integral 214Introduction and Summary 1574.4 Graphical Convolution 2173.1 Formulation of Equations 1594.5 Properties of Convolution 2223.2 Classifications of Systems 1604.6 Filtering by Convolution 2263.3 Causality 16247 Matched filter 2283.4 Linearity, Time Invariance4.8 Deconvolution 231and ltI Systems 1624.9 Autocorrelation 2333.5 Derivative and integralProperties of LTI Systems 1664. 10 Cross-Correlation 2373.6 Examples from Electric4. 11 Correlation and Convolution 240Circuits 1664.12 Concluding Remarks 2413.7 Examples from Other Fields 172 4.13 Problems 2423.8 Response of LTI Systems4.14 Project: Signal Detectionto Impulse and Step Inputs 175by matched Filter 2553.9 Response of lti Systemsto Exponential Inputs 176Chapter 53.10 Response of LTI SystemsDifferential Equations and LtiSystems 259to sinusoids 1783.11 USe of SuperpositionIntroduction and Summary 260and other properties5.1 Formulation of differentialof lti Systems 179Equations 2603.12 LTI Systems and Fourier5.2 Solution in the Time domainAnalysis 181by the classical method 2703.13 Analysis and Solution Methods5.3 The Particular Solution 272for lti Systems 1825.4 The homogeneous solution 2743. 14 Complex Systems 1835.5 Composing the complete3.15 Neuronal Systems 184Solution 275Contents5.6 Examples of Complete6.2 Linearity Property 317Solutions 2756.3 Examples of the Unilateral5.7 Special Case: MultipleLaplace transform 317Roots 2796. 4 Differentiation and Integration5.8 When the Input ContainsProperties 320Natural Frequencies 2806.5 Multiplication by t 3235.9 When the Natural ResponseMay be absent 2816.6 Multiplication by ea 3245.10 Response to an exponential6.7 Time-Shift Property 324Input 2826.8 Scale Change 3255.11 The System Function 2836.9 Convolution Property 3255.12 Sinusoidal Steady-State6.10 Initial-Value and Final-ValueResponse 284Theorems 3275.13 Unit-Step Response 2856.11 Lower Limit of Integration5.14 Unit-Impulse response 2880-,0,0+3285.15 Effect of Discontinuity in the6.12 Laplace transform of the unitForcing Function 290Impulse 3285.16 Solution by Convolution 2936.13 The Inverse LaplaceTransform 3295.17 Zero-Input and Zero-State6.14 Partial Fraction ExpansionResponses 295Simple poles 3315.18 Zero-State Response and6.15 Partial Fraction ExpansionConvolution 298Multiple-Order poles 3355.19 Properties of LTI DifferentialEquations 2996.16 Summary of the laplaceTransform Properties and5.20 Solution by numericalTheorems 336Methods 2996.17 A Table of Unilateral Laplace5.21 Concluding Remarks 300Transform Pairs 3375.22 Problems 3016.18 Circuit Solution 33 85.23 Project: System of Differential6.19 Solution of dynamicalEquations 310Equations 340Chapter 66.20 Bilateral Laplace Transform 343The Laplace transform and6.21 Region of Convergence of theIts Applications 313Bilateral Laplace Transform 346Introduction and Summary 3146.22 Properties of the Bilateral LaplaceTransform 3486. 1 Definition of the laplaceTransform 3156.23 Inverse of the Bilateral LaplaceTransform 349