signals &linear systems

7/29/2019 SIGNALS &LINEAR SYSTEMS

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SIGNALSANDLINEAR SYSTEMSThird Edition

Robert A. GabelMIT Lincoln Laboratoryformerly atUniversity of Colorado at DenverRichard A. RobertsUniversity o f Colorado at Boulder

John Wiley & Sons, Inc.)AI H O C Q U O C GIA HA N O I.TRUN6 TAM THON f ^ i j H i ; VIENA - PO/ 0 5 B i


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CONTENTS1LINEAR SYSTEMS /I

1.1 Introduction /I1.2 Classification of Linear System s /21.3 Linearity /41.4 Discrete-Time Systems /lO1.5 Continuous-T ime Systems /15Problems /18

2DISCRETE-TIME SYST EM S /23

2.1 Introdu ction /232.2 Linear Difference Eq uatio ns /242-3 The General Solution of

Nonh omo geneous Difference Eq uation s /29XIU


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Xiv CONTENTSV Response Of Discrete-T.me Systems /377 4 The Frequency ResponseConvc,u.ion and .mpu.se Response /46

-n,e convolution O peration /48Finding the Impulse-Response sequence / 5 3

.62.7-? Deconvolution /63 state Vanables for Dlscre.e-TneSy.en,s / ^2.,0 The solution of S.ate-Var.able Equations P*2 11 Functions of a Matrix /752V Change of Internal System Structure /872.13 Frequency Response m Te rm s of A, B, C D /V42 14 An Application of State V ariab les:Limit Cycles in Digital Filters / 962.15 Concluding Rem arks and Fu rth er Ex am ples / 1 042.16 Summary /109

Problems /HO

3CONTINUOUS-TIME SY ST EM S /121

3.1 Linear Differential Eq ua tions /1213.2 The Frequency Response of Co ntinu ous -Tim e System s /1273.3 Convolution and the Impulse Fu nc tion /1293.4 Convolution for Co ntinuo us-T im e Systems /1343.5 Some Genera lizations ofConvolution for Continuous-Time Systems /1383.6 Finding the Impu lse-Respo nse Fu nc tion /1453.7 Frequency Response and

the Impulse-Response Function /1513.8 State Variables for Co ntinu ous-T im e System s / 1 5 33.9 Solution of the

Continuous-T.me State-Variable Equations / 1 56Frequency Response m Terms of A, B, C D /166J H Summary /167Problems /167

3.10
http://mpu.se/http://mpu.se/


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CONTENTS XV

4THE Z-TRANSFO RM /1774.1 Introduction /1774.2 The Z-Transform /1794.3 Convergence of the Z-Transform /1814.4 Properties of the Z-Transform /1854.5 Inversion of the Z-Transform / 2 0 24.6 Evaluating a System 's Frequ ency Re spon se / 2144.7 Deco nvolution Revisited /2194.8 Furthe r Ap plicat ions of the Z-Tran sform /2214.9 Summary /227

Problems /227

5FO URIER ANALYSIS /2395.1 Introduction /2395.2 Gen eralized Fo urie r Series: Orihogonal Func t ions /2415.3 Examples of O riho go na l Fu nctio ns / 2475.4 The Exp onen tial Fo urie r Series / 2 5 05.5 The Com plex Fo urie r Spe ctrum / 2 5 55.6 The Discrete-Tim e Fo urie r Tra nsfo rm / 2665.7 Properties of the Discrete-Time Fourier Transform / 27I5.8 Fo urier Analysis and the Des ign of FI R Filte rs / 2755.9 The Fou rier Tran sform /2785.10 Properties of the Fourier Transform / 2855.11 Th e Energy Sp ectrum /2975.12 Fourier Transform of Power Signals / 2985.13 Sampling of Time Signals / 3 0 75.14 Modulation /3125.J5 Transmission of Signals through Linear Filters / 315^16 Numerical Calculation of

^ - - T r a n s f o r m s - T h e Discrete Fourier Transform / 3245>7 Properi.es of the Discrete Founer Transform / 332
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XVi CONTENTS5.18 The Fast Fourier Transform /3355.19 Summary /335

Problems /336

THE LAPLACE TRANSFO RM /3496.1 Introduction /3496.2 Convergence of the Lap lace T ran sfo rm / 3 5 I6.3 The One-Sided or Un ilateral Lap lace Tr an sfo rm / 3 5 36.4 Properties of the Lap lace Tr an sfo rm / 3 5 46.5 Laplace Transform s of Simple Fu nc tio ns /3616.6 Inversion of the Lap lace T ran sfo rm / 3636.7 A pplica tions of

Laplace TransformsDifferential Equa t ions / 3 7 36.8 Stab ility in the s Domain / 3786.9 Non causal Systems and Inp uts / 3826.10 Transient and Steady -State Re spo nse ofa Linear System /3866.11 Frequency Response of Linear Systems / 3896.12 Laplace Transform Analysis of

Causal Periodic Inputs to Linear Systems /3906.13 Relationship of the Z-Transform to the Fourier andLaplace Transforms /3946.14 Summary /396

Problems /3967AN INTRO DUCTIO N TOTHE DESIGN O F DIGITAL FILTERS /40 1

7.1 Introduction /401'2 Design of FIR Dtgital Filters /402

4 ^ : i " " ' " ' ' " ' ^ ^ " ' - i a n t n R P n , e / 4 0 87 5 c^"'""^ T^^"^f Method /423

"iscrete-Time Systems /43|

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