Discrete-timesignalprocessing

This is a textbook for discrete time signal processing. Useful textEE-COMMITTEESECOND EDITIONDISCRETE- TIMESIGNALPROCESSINGALaN V OPPENHEIMMASSACHUSETTS INSTITUTE OF TECHNOLOGYRONALD W. ScHAFERGEORCIA INSTITUTE OF TECHNOLOGYWITIJoHn R. BUCKUNIVERSITY OF MASSACHUSETTS DARTMOUTHPRENTICE豆ALLUPPER SADDLE RIVER. NEW JERSEY 07458EE-COMMITTEEOppenheim, Alan VDiscrete-time signal processing/ Alan V, Oppenheim, Ronald wSchafer, with John R. Buck.-2nd edIncludes bibliographical references and indexISBN0-13-754920-21. Signal processing-Mathematics. 2. Discrete-time systemsSchafer, Ronald w. l. buck, john r. Ill. TitleTK510290671998621.3822dc2198-50398CIPAcquisitions editor: Tom RobbinsProduction service: Interactive Composition CorporationEditorial/production supervision: Sharyn VitranoCapy editor: Brian BakeCaver design: Vivian BermArt director: Amy RosenManaging editor: Eileen ClarkEditor-in-Chief marcia hortonDirector of production and manufacturing: David W. RiccardiManufacturing buyer: Pat RrowmEditorial assistant: Dan De pasqualec 1999, 1989 Alan V Oppenheim, Ronald w. SchaferPublished by Prentice-Hall, IncUpper Saddle river. New Jersey 07458All rights reserved. No part of this book may bereproduced, in any form or by any meanwithout permission in writing from the publisher.The author and publisher of this book have uscd thcir hest efforts in preparing this book. These efforts includethe development, research, and testing of the theories and programs to dctermine their effectiveness. Theauthor and publisher make no warranty of any kind, expressed or implied, with rcgard to these programsor the documentation contained in this book. The author and publisher shall not be liable in any event forincidental or consequential damages in connection wilh, or arising out of, the furnishing, performance, or useof these programs.Printed in the United States of America10987654ISBN0-13-7549202Prentice-Hall International(uk) limited londonPrentice-Hall of Australia Pty Limited, SydneyPrentice-Hall Canada Inc. TorontoPrentice-Hall Hispanoamericana, S.A., MexicoPrentice-Hall of India Private Limited, New DelhiPrentice-Hall of Japan, Inc, TokyoSimon schuster Asia Pte Ltd, SingaporeEditora prentice-hall do brasil. ltda. rio de janeiroTo Phyllis, Justine and JasonTo Dorothy, Bill, Tricia, Ken and Kateand in memory of JohnusanCOMMITTEEEE-COMMITTEECONTeNTSLIST OF EXAMPLES XVPREFACE XIXACKNOWLEDGMENTS XVINTRODUCTIONDISCRETE- TIME SIGNALS AND SYSTEMS 82.0 Introduction 82.1 Discrete- Time Signals: Sequences 92.1.1 Basic Sequences and Sequence Operations 112.2 Discrete-Time Systems 162.2.1 Memoryless Systems 182.2.2 Linear Systems 182.2.3 Time-Invariant Systems 202.2. 4 Causality 212.2.5 Stability 212.3 Linear TimeInvariant Systes 222.4 Properties of Linear Time-Invariant Systems 282.5 Linear Constant-Coefficient Difference Equations 342.6 Frequency-Domain Representation of Discrete-Time Signals andSystems 402.6.1 Eigenfunctions for Linear Time-Invariant Systems 402.7 Representation of sequences by Fourier Transforms sp2.6.2 Suddenly Applied Complex Exponential Inputs2.8 Symmetry Properties of the Fourier Transform 552.9 Fourier Transform Theorems 582.9.1 Linearity of the Fourier Transform 592.9.2 Time Shifting and Frequency Shifting 592.9.3 Time reversal 602.9.4 Differentiation in Frequency 602.9.5 Parseval's Theorem 602.9.6 The Convolution 'Theorem 602.9.7 The Modulation or Windowing Theorem 612.10 Discrete-Time Random Signals 652.11 Summary 70Problems 703 THE Z-TRANSFORM 943.0 Introduction 943.1 Z-Transform 94EE-COMMITTEEWI3.2 Properties of the Region of Convergence for the z-Transform 1053.3 The Inverse z-Transform 1113.3.1 Inspection Method 1113.3.2 Partial Fraction Expansion 1123.3.3 Power Series Expansion 1163.4 z-Transform Properties 1193.4.1 Linearity 1193.4.2 Time Shifting 1203.4.3 Multiplication by an Exponential Sequence 1213. 4. 4 Differentiation of X(z) 1223. 4.5 Conjugation of a Complex sequence 1233.4.6 Time reversal 1233.4.7 Convolution of Sequences 1243. 4.8 Initial-value Theorem 1263.4.9 Summary of Somc z-Transform Properties 1263.5 Summary 126Problems 127SAMPLING OF CONTINUOUS-TIME SIGNALS 1404.0 Introduction 1404.1 Periodic Sampling 1404.2 Frequency- Domain Representation of Sampling 1424.3 Reconstruction of a Bandlimited Signal from Its Samples 1504.4 Discrete-Time Processing of Continuous-Time Signals 1534.4.1 Linear Time-Invariant Discrete-Time Systems 1544.4.2 Impulse Invariance 1604.5 Continuous-Time Processing of Discrete-Time Signals 1634.6 Changing the Sampling Rate Using Discrete-Time Processing 1674.6.1 Sampling Rate Reduction by an Integer Factor 1674.6.2 Increasing the Sampling Rate by an Integer Factor 1724.6.3 Changing the Sampling Rate by a Noninteger Factor 1764.7 Multirate Signal Processing 1794.7.1 Interchange of Filtering and Downsampling/Upsampling 1794.7.2 Polyphase Decompositions 1804.7.3 Polyphase Implementation of Decimation Filters 1824.7.4 Polyphase Implementation of Interpolation Filters 1834.8 Digital Processing of Analog Signals 1854.8.1 Prefiltering to Avoid Aliasing 1854.8. 2 Analog-to-Digital(A/D)Conversion 1874.8.3 Analysis of Quantization Errors 1934.8. 4 D/A Conversion 1974.9 Oversampling and Noise Shaping in A/D and D/A Conversion 2014.9. 1 Oversampled A/D Conversion with DirectQuantization 2014.9.2 Oversampled A/D Conversion with Noise Shaping 2064.9.3 Oversampling and Noisc Shaping in D/A Conversion 210EE-COMMITTEEContents4.10 Summary 213Problems 214TRANSFORM ANALYSIS OF LINEAR TIME-INVARIANTSYSTEMS 2405.0 Introduction 2405.1 The Frequency response of lti Systems 2415.1.1 Ideal Frequency-Selective Filters 2415.1.2 Phase Distortion and delay 2425.2 System Functions for Systems Characterized by linearConstant-Coefi cient differenceEquations 25. 2.1 Stability and Causality 2475.2.2 Inverse Systems 2485.2.3 Impulse Response for Rational System Functions 2505.3 Frequency Response for Rational system Functions 2535.3. 1 Frequency Response of a Single Zero or Pole 2585.3.2 Examples with Multiple poles and zeros 2655.4 Relationship between Magnitude and Phase 2705.5 All-Pass Systems 2745.6 Minimum-Phase Systems 2805.6. 1 Minimum-Phase and all-Pass Decomposition 2805.6.2 Frequency-Response Compensation 2825. 6.3 Properties of Minimum-Phase Systems 2875.7 Linear Systems with Generalized linear phase 2915.7.1 Systems with Linear Phase 2925.7.2 Generalized Linear phase 2955.7.3 Causal Generalized Linear-Phase systems 2975.7.4 Relation of FIR Linear-Phase Systems to Minimum-PhaseSystems 3085.8 Summary 311Problems 312STRUCTURES FOR DISCRETE-TIME SYSTEMS 3406.0 Introduction 3406.1 Block Diagram Representation of linear Constant- CoefficientDifference Equations 3416.2 Signal Flow Graph Representation of Linear Constant-CoefficientDifference Equations 3486.3 Basic Structures for IIR Systems 3546.3. 1 Direct Forms 3546.3.2 Cascade Form 3566.3. 3 Parallel form 3596.3. 4 Feedback in IIR Systems 3616.4 Transposed Forms 3636.5 Basic Network Structures for FIR Systems 366EE-COMMITTEE6.5. 1 Direct Form 3676.5.2 Cascade form 3676.5.3 Structures for Linear-Phase FIR Systems 3686.6 Overview of finite- Precision numerical efects 3706.6. 1 Number Representations 3716.6.2 Quantization in Implementing Systems 3746.7 The Effects of Coefficient Quantization 3776.7.1 Effects of Coefficient Quantization in Iir Systems 3776.7.2 Example of Coefficient Quantization in an Elliptic Filter 3796.7 3 Poles of Quantized Sccond-Order Sections 3826.7.4 Effects of Cocfficicnt Quantization in FIR Systems 3846.7.5 Examplc of Quantization of an Optimum FIR Filter 3866. 7.6 Maintaining linear phase 3906.8 Effects of Round-off Noise in Digital Filters 3916.8.1 Analysis of the Direct-Form IIR Structures 3916.8.2 Scaling in Fixed-Point Implementations of iir Systems 3996.8. 3 Example of Analysis of a Cascade IIR Structure 4036.8.4 Analysis of Direct-Form FiR Systems 4106.8.5 Floating-Point Realizations of Discrete-Time Systems 4126.9 Zero-Input Limit Cycles in Fixed-Point Realizations of IR DigitalFilters 4136.9.1 Limit Cycles due to Round-off and Truncation 4146.9.2 Limit Cycles Due to Overflow 4166.9.3 Avoiding Limit Cycles 4176.10 Summary 418Problems 4197 FILTER DESIGN TECHNIQUES 4397.0 Introduction 4397.1 Design of Discrete- Time IIR Filters from Continuous-TimeFilters 4427.1.1 Filter Design by Impulse Invariance 4437.1.2 Bilinear Transformation 4507.1.3 Examples of Bilinear Transformation Design 4547.2 Design of FIR Filters by windowing 4657.2.1 Properties of Commonly Used Windows 4677.2.2 Incorporation of Generalized Linear Phase 4697.2.3 The Kaiser Window Filter Design Method 4747.2.4 Relationship of the Kaiser Window to Other Windows 4787.3 Examples of FIR Filter Design by the Kaiser Window Method 4787.3.1 Highpass Filter 4797.3.2 Discrete-Time Differentiators 4827.4 Optimum Approximations of FIR Filters 4867.4.1 Optimal Type I Lowpass Filters 4917.4.2 Optimal Type I Lowpass Filters 4977.4.3 The Parks-McClellan Algorithm 498