Handbook of Digital Signal Processing: Engineering Applications

1022 Pages·1988·36.834 MB·English

by  Douglas F. Elliott

Handbook of Digital
Signal Processing
Engineering Applications
This page intentionally left blank
Handbook of Digital
Signal Processing
Engineering Applications
Edited by
Douglas F. Elliott
Rockwell International Corporation
Anaheim, California
ACADEMIC PRESS, INC.
Harcourt Brace Jovanovich, Publishers
San Diego New York Berkeley Boston
London Sydney Tokyo Toronto
COPYRIGHT © 1987 BY ACADEMIC PRESS, INC.
ALL RIGHTS RESERVED
NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR
TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC
OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR
ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT
PERMISSION IN WRITING FROM THE PUBLISHER
ACADEMIC PRESS, INC.
San Diego, California 92101
United Kingdom Edition published by
ACADEMIC PRESS LIMITED
24-28 Oval Road, London NW1 7DX
Library of Congress Cataloging in Publication Data
Handbook of digital signal processing.
Includes index.
1. Signal processing-Digital techniques-Handbooks,
manuals, etc. I. Elliott, Douglas F.
TK5102.5.H32 1986 621.38'043 86-26490
ISBN 0-12-237075-9 (alk, paper)
PRINTED IN THE UNITED STATES OF AMERICA
89 90 91 9 8 7 6 5 4 32
Contents
Preface XI
Acronyms and Abbreviations xiii
Notation xvii
Chapter 1 Transforms and Transform Properties
DOUGLAS F. ELLIOTT
I. Introduction 1
II. Review of Fourier Series 2
III. Discrete-Time Fourier Transform 6
IV. z-Transform 16
V. Laplace Transform 24
VI. Table of z-Transforms and Laplace Transforms 27
VII. Discrete Fourier Transform 27
VIII. Discrete-Time Random Sequences 41
IX. Correlation and Covariance Sequences 45
X. Power Spectral Density 50
XI. Summary 51
References 53
Chapter 2 Design and Implementation of Digital FIR Filters
P. P. VAIDYANATHAN
I. Introduction 55
II. FIR Digital Filter Preliminaries 56
HI. FIR Filter Design Based on Windowing 61
IV. Equiripple Approximations for FIR Filters 71
V. Maximally Flat Approximations for FIR Filters 90
VI. Linear Programming Approach for FIR Filter Designs 95
VII. Frequency Transformations in FIR Filters 100
VIII. Two-Dimensional Linear-Phase FIR Filter Design and Implementation 112
IX. Recent Techniques for Efficient FIR Filter Design 118
X. Other Useful Types of FIR Filters 136
XI. Summary 146
Appendix A. Design Charts for Digital FIR Differentiators and Hilbert Transformers 147
Appendix B. Program Listings for Linear-Phase FIR Filter Design 150
References 170
Chapter 3 Multirate FIR Filters for Interpolating and Desampling
FREDERIC J. HARRIS
I. Introduction 173
II. Characteristics of Bandwidth-Reducing FIR Filters 180
Contents
VI
HI. Data Rate Reduction (Desampling) by 1/Af Filters 208
IV. Heterodyne Processing 223
V. Interpolating Filters 234
VI. Architectural Models for FIR Filters 245
VII. Summary 252
Appendix. Windows as Narrowband Filters 253
References 286
Chapter 4 MR Digital Fitters
NAZIR A. PASHTOON
I. Introduction 289
II. Preliminaries 290
III. Stability 291
IV. Digital Filter Realizations 295
V. Frequency Domain Design 300
VI. Analog Filter Design and Filter Types 306
VII. Frequency Transformations 331
VIII. Digital Filter Design Based on Analog Transfer Functions 332
IX. Spectral Transformations 343
X. Digital Filters Based on Continuous-Time Ladder Filters 344
XI. Summary 353
Appendix. HR Digital Filter CAD Programs 355
References 355
Chapter 5 Low-Noise and Low-Sensitivity Digital Filters
P. P. VAIDYANATHAN
I. Introduction 359
II. Binary Numbers—Representation and Quantization 361
III. Generation and Propagation of Roundoff Noise in Digital Filters 369
IV. Dynamic Range Constraints and Scaling 373
V. Signal-to-Roundoff-Noise Ratio in Simple HR Filter Structures 378
VI. Low-Noise HR Filter Sections Based on Error-Spectrum Shaping 387
VII. Signal-to-Noise Ratio in General Digital Filter Structures 395
VIII. Low-Noise Cascade-Form Digital Filter Implementation 396
IX. Noise Reduction in the Cascade Form by ESS 399
X. Low-Noise Designs via State-Space Optimization 402
XI. Parameter Quantization and Low-Sensitivity Digital Filters 412
XII. Low-Sensitivity Second-Order Sections 416
XIII. Wave Digital Filters 419
XIV. The Lossless Bounded Real Approach for the Design of Low-
Sensitivity Filter Structures 434
XV. Structural Losslessness and Passivity 443
XVI. Low-Sensitivity All-Pass-Based Digital Filter Structures 444
XVII. Digital All-Pass Functions 453
XVIII. Orthogonal Digital Filters 458
XIX. Quantization Effects in FIR Digital Filters 460
XX. Low-Sensitive FIR Filters Based on Structural Passivity 465
XXI. Limit Cycles in HR Digital Filters 469
References 475
Contents vii
Chapter 6 Fast Discrete Transforms
PAT YIP AND K. RAMAMOHAN RAO
I. Introduction 481
II. Unitary Discrete Transforms 482
III. The Optimum Karhunen Loeve Transform 483
IV. Sinusoidal Discrete Transforms 485
V. Nonsinusoidal Discrete Transforms 499
VI. Performance Criteria 510
VII. Computational Complexity and Summary 516
Appendix A. Fast Implementation of DCT via FFT 517
Appendix B. DCT Calculation Using an FFT 521
Appendix C. Walsh-Hadamard Computer Program 523
References 523
Chapter 7 Fast Fourier Transforms
DOUGLAS F. ELLIOTT
I. Introduction 527
II. DFTs and DFT Representations 528
III. FFTs Derived from the MIR 532
IV. Radix-2 FFTs 553
V. Radix-3 and Radix-6 FFTs 558
VI. Radix-4 FFTs 564
VII. Small-JVDFTs 565
VIII. FFTs Derived from the Ruritanian Correspondence (RC) 567
IX. FFTs Derived from the Chinese Remainder Theorem 571
X. Good's FFT 573
XL Kronecker Product Representation of Good's FFT 574
XII. Polynomial Transforms 579
XIII. Comparison of Algorithms 580
XIV. FFT Word Lengths 587
XV. Summary 595
Appendix A. Small-AT DFT Algorithms 596
Appendix B. FFT Computer Programs 600
Appendix C. Radix-2 FFT Program 602
Appendix D. Prime Factor Algorithm (PFA) 605
Appendix E. Highly Efficient PFA Assembly Language Computer Program 621
References 630
Chapter 8 Time Domain Signal Processing with the DFT
FREDERIC J. HARRIS
I. Introduction 633
II. The DFT as a Bank of Narrowband Filters 639
III. Fast Convolution and Correlation 666
IV. The DFT as an Interpolator and Signal Generator 683
V. Summary 698
References 698
viii Contents
Chapter 9 Spectral Analysis
JAMES A. CADZOW
I. Introduction 701
II. Rational Spectral Models 702
HI. Rational Modeling: Exact Autocorrelation Knowledge 707
IV. Overdetermined Equation Modeling Approach 714
V. Detection of Multiple Sinusoids in White Noise 716
VI. MA Modeling: Time Series Observations 721
VII. AR Modeling: Time Series Observations 723
VIII. ARMA Modeling: Time Series Observations 724
IX. ARMA Modeling: A Singular Value Decomposition Approach 726
X. Numerical Examples 731
XI. Conclusions 739
References 739
Chapter 10 Deconvolution
MANUEL T. SILVIA
I. Introduction 741
II. Deconvolution and LTI Systems with No Measurement Noise 746
III. Deconvolution and the Identification of DTLTI Systems with
Measurement Noise 760
IV. Fast Algorithms for Deconvolution Problems 766
V. Some Practical Applications of Deconvolution 777
VI. Summary 784
Appendix A. References for Obtaining Computational Algorithms 785
Appendix B. Implementing the Levinson or Toeplitz Recursion 786
Appendix C. Implementing the Lattice Form of the Levinson Recursion 787
References 787
Chapter 11 Time Delay Estimation
MANUEL T.SILVIA
I. Introduction 789
II. Time Delay Estimation for Active Sensors 793
III. Time Delay Estimation for Passive Sensors 818
IV. Cross-Correlation and Its Relationship to the Time Delay
Estimation Problem 833
V. The Implementation of Some Time Delay Estimation Algorithms
Using the Fast Fourier Transform (FFT) 837
VI. Algorithm Performance 844
VII. Summary 853
References 853
Chapter 12 Adaptive Filtering
NASIR AHMED
I. Introduction 857
II. Some Matrix Operations 858
III. A Class of Optimal Filters 860
IV. Least-Mean-Squares (LMS) Algorithm 866
Contents IX
V. LMS Lattice Algorithms 882
VI. Concluding Remarks 888
Appendix. Four FORTRAN-77 Programs 889
References 896
Chapter 13 Recursive Estimation
GENE H. HOSTETTER
I. Introduction 899
II. Least Squares Estimation 900
III. Linear Minimum Mean Square Estimation 908
IV. Discrete Kalman Filtering Examples 915
V. Extensions 922
VI. Some Computational Considerations 929
VII. Summary 938
References 938
Chapter 14 Mechanization of Digital Signal Processors
LESTER MINTZER
I. Introduction 941
II. Digital Machine Fundamentals 942
III. The Essence of Digital Signal Processing 947
IV. Number Representations 947
V. Hardware Components 950
VI. Microprogramming 959
VII. Keeping Things in Perspective 963
VIII. Distributed Arithmetic 964
IX. Summary 972
References 972
Addendum to
Chapter 3 Window Generation Computer Program 975
FREDERIC J. HARRIS
Index 987