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Solution Signals and Systems Schaum Series Pdf

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  • 1. SCHAUMS OUTLINES OFTheory and Problems of Signals and Systems Hwei P. Hsu, Ph.D.Professor of Electrical Engineering Fairleigh Dickinson University Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1995[/DP]End of Citation

2. HWEI P. HSU is Professor of Electrical Engineering at Fairleigh Dickinson University. He receivedhis B.S. from National Taiwan University and M.S. and Ph.D. from Case Institute of Technology. Hehas published several books which include Schaums Outline of Analog and Digital Communications.Schaums Outline of Theory and Problems ofSIGNALS AND SYSTEMSCopyright 1995 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the UnitedStates of America. Except as permitted under the Copyright Act of 1976, no part of this publicationmay be reproduced or distributed in any form or by any means, or stored in a data base or retrievalsystem, without the prior written permission of the publisher.4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 BAW BAW 9 9ISBN 0-07-030641-9Sponsoring Editor: John AlianoProduction Supervisor: Leroy YoungEditing Supervisor: Maureen WalkerLibrary of Congress Cataloging-in-Publication DataHsu, Hwei P. (Hwei Piao), dateSchaums outline of theory and problems of signals and systems / Hwei P. Hsu.p. cm.(Schaums outline series)Includes index.ISBN 0-07-030641-91. Signal theory (Telecommunication)Problems, exercises, etc.I. Title.TK5102.92.H78 1995621.38223dc2094-44820 CIP Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1995[/DP]End of Citation 3. PrefaceThe concepts and theory of signals and systems are needed in almost all electrical engineering fieldsand in many other engineering and scientific disciplines as well. They form the foundation for furtherstudies in areas such as communication, signal processing, and control systems.This book is intended to be used as a supplement to all textbooks on signals and systems or for self-study. It may also be used as a textbook in its own right. Each topic is introduced in a chapter withnumerous solved problems. The solved problems constitute an integral part of the text.Chapter 1 introduces the mathematical description and representation of both continuous-time anddiscrete-time signals and systems. Chapter 2 develops the fundamental input-output relationship forlinear time-invariant (LTI) systems and explains the unit impulse response of the system andconvolution operation. Chapters 3 and 4 explore the transform techniques for the analysis of LTIsystems. The Laplace transform and its application to continuous-time LTI systems are considered inChapter 3. Chapter 4 deals with the z-transform and its application to discrete-time LTI systems. TheFourier analysis of signals and systems is treated in Chapters 5 and 6. Chapter 5 considers the Fourieranalysis of continuous-time signals and systems, while Chapter 6 deals with discrete-time signals andsystems. The final chapter, Chapter 7, presents the state space or state variable concept and analysisfor both discrete-time and continuous-time systems. In addition, background material on matrixanalysis needed for Chapter 7 is included in Appendix A.I am grateful to Professor Gordon Silverman of Manhattan College for his assistance, comments, andcareful review of the manuscript. I also wish to thank the staff of the McGraw-Hill Schaum Series,especially John Aliano for his helpful comments and suggestions and Maureen Walker for her greatcare in preparing this book. Last, I am indebted to my wife, Daisy, whose understanding and constantsupport were necessary factors in the completion of this work.HWEI P. HSUMONTVILLE, NEW JERSEY Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1995[/DP]End of Citation 4. To the StudentTo understand the material in this text, the reader is assumed to have a basic knowledge of calculus,along with some knowledge of differential equations and the first circuit course in electricalengineering.This text covers both continuous-time and discrete-time signals and systems. If the course you aretaking covers only continuous-time signals and systems, you may study parts of Chapters 1 and 2covering the continuous-time case, Chapters 3 and 5, and the second part of Chapter 7. If the courseyou are taking covers only discrete-time signals and systems, you may study parts of Chapters 1 and 2covering the discrete-time case, Chapters 4 and 6, and the first part of Chapter 7.To really master a subject, a continuous interplay between skills and knowledge must take place. Bystudying and reviewing many solved problems and seeing how each problem is approached and how itis solved, you can learn the skills of solving problems easily and increase your store of necessaryknowledge. Then, to test and reinforce your learned skills, it is imperative that you work out thesupplementary problems (hints and answers are provided). I would like to emphasize that there is noshort cut to learning except by "doing." Start of Citation[PU]McGraw-Hill Professional[/PU][DP]1995[/DP]End of Citation 5. ContentsChapter 1. Signals and Systems11.1 Introduction11.2 Signals and Classification of Signals 11.3 Basic Continuous-Time Signals 61.4 Basic Discrete-Time Signals 121.5 Systems and Classification of Systems 16Solved Problems 19Chapter 2. Linear Time-Invariant Systems562.1 Introduction562.2 Response of a Continuous-Time LTI System and the Convolution Integral 562.3 Properties of Continuous-Time LTI Systems 582.4 Eigenfunctions of Continuous-Time LTI Systems 592.5 Systems Described by Differential Equations 602.6 Response of a Discrete-Time LTI System and Convolution Sum612.7 Properties of Discrete-Time LTI Systems 632.8 Eigenfunctions of Discrete-Time LTI Systems 642.9 Systems Described by Difference Equations 65Solved Problems 66Chapter 3. Laplace Transform and Continuous-Time LTI Systems1103.1 Introduction1103.2 The Laplace Transform 1103.3 Laplace Transforms of Some Common Signals 1143.4 Properties of the Laplace Transform 1143.5 The Inverse Laplace Transform 1193.6 The System Function 1213.7 The Unilateral Laplace Transform124Solved Problems 127Chapter 4. The z-Transform and Discrete-Time LTI Systems1654.1 Introduction1654.2 The z-Transform 1654.3 z-Transforms of Some Common Sequences 1694.4 Properties of the z-Transform 1714.5 The Inverse z-Transform 1734.6 The System Function of Discrete-Time LTI Systems1754.7 The Unilateral z-Transform177Solved Problems 178Chapter 5. Fourier Analysis of Continuous-Time Signals and Systems2115.1 Introduction2115.2 Fourier Series Representation of Periodic Signals 2115.3 The Fourier Transform 2145.4 Properties of the Continuous-Time Fourier Transform 219vii 6. 5.5 The Frequency Response of Continuous-Time LTI Systems2235.6 Filtering2275.7 Bandwidth230Solved Problems231Chapter 6. Fourier Analysis of Discrete-Time Signals and Systems 2886.1 Introduction 2886.2 Discrete Fourier Series2886.3 The Fourier Transform2916.4 Properties of the Fourier Transform2956.5 The Frequency Response of Discrete-Time LTI Systems3006.6 System Response to Sampled Continuous-Time Sinusoids 3026.7 Simulation 3036.8 The Discrete Fourier Transform 305Solved Problems308Chapter 7. State Space Analysis3657.1 Introduction 3657.2 The Concept of State 3657.3 State Space Representation of Discrete-Time LTI Systems3667.4 State Space Representation of Continuous-Time LTI Systems3687.5 Solutions of State Equations for Discrete-Time LTI Systems 3717.6 Solutions of State Equations for Continuous-Time LTI Systems 374Solved Problems377Appendix A. Review of Matrix Theory428 A.1 Matrix Notation and Operations428 A.2 Transpose and Inverse 431 A.3 Linear Independence and Rank432 A.4 Determinants433 A.5 Eigenvalues and Eigenvectors435 A.6 Diagonalization and Similarity Transformation 436 A.7 Functions of a Matrix 437 A.8 Differentiation and Integration of Matrices 444Appendix B. Properties of Linear Time-Invariant Systems and Various Transforms 445 B.1 Continuous-Time LTI Systems 445 B.2 The Laplace Transform 445 B.3 The Fourier Transform 447 B.4 Discrete-Time LTI Systems 449 B.5 The z-Transform 449 B.6 The Discrete-Time Fourier Transform 451 B.7 The Discrete Fourier Transform452 B.8 Fourier Series453 B.9 Discrete Fourier Series 454Appendix C. Review of Complex Numbers455 C.1 Representation of Complex Numbers 455 C.2 Addition, Multiplication, and Division456 C.3 The Complex Conjugate 456 C.4 Powers and Roots of Complex Numbers 456Appendix D. Useful Mathematical Formulas 458 D.1 Summation Formulas458 D.2 Eulers Formulas458viii 7. D.3 Trigonometric Identities 458D.4 Power Series Expansions459D.5 Exponential and Logarithmic Functions459D.6 Some Definite Integrals460Index461ix 8. Chapter 1Signals and Systems1.1 INTRODUCTIONThe concept and theory of signals and systems are needed in almost all electricalengineering fields and in many other engineering and scientific disciplines as well. In thischapter we introduce the mathematical description and representation of signals andsystems and their classifications. We also define several important basic signals essential toour studies.1.2 SIGNALS AND CLASSIFICATION OF SIGNALSA signal is a function representing a physical quantity or variable, and typically itcontains information about the behavior or nature of the phenomenon. For instance, in aRC circuit the signal may represent the voltage across the capacitor or the current flowingin the resistor. Mathematically, a signal is represented as a function of an independentvariable t. Usually t represents time. Thus, a signal is denoted by x ( t ) .A. Continuous-Time and Discrete-Time Signals:A signal x(t) is a continuous-time signal if t is a continuous variable. If t is a discretevariable, that is, x ( t ) is defined at discrete times, then x ( t ) is a discrete-time signal. Since adiscrete-time signal is defined at discrete times, a discrete-time signal is often identified asa sequence of numbers, denoted by {x,) o r x[n], where n = integer. Illustrations of acontinuous-

Solution Signals and Systems Schaum Series Pdf

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