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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley - IEEE
- Sprache: Englisch
Adaptive filtering is a topic of immense practical and theoretical value, having applications in areas ranging from digital and wireless communications to biomedical systems. This book enables readers to gain a gradual and solid introduction to the subject, its applications to a variety of topical problems, existing limitations, and extensions of current theories. The book consists of eleven parts?each part containing a series of focused lectures and ending with bibliographic comments, problems, and computer projects with MATLAB solutions.
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Seitenzahl: 1432
Veröffentlichungsjahr: 2011
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Table of Contents
Cover
Preface
AREA OF STUDY
STRUCTURE OF THE BOOK
COVERAGE AND TOPICS
DEPENDENCIES AMONG THE CORE PARTS
AUDIENCE
SOME FEATURES OF OUR TREATMENT
Notation
NOTATION
SYMBOLS
BACKGROUND MATERIAL
CHAPTER A: Random Variables
A.1 VARIANCE OF A RANDOM VARIABLE
A.2 DEPENDENT RANDOM VARIABLES
A.3 COMPLEX-VALUED RANDOM VARIABLES
A.4 VECTOR-VALUED RANDOM VARIABLES
A.5 GAUSSIAN RANDOM VECTORS
CHAPTER B: Linear Algebra
B.1 HERMITIAN AND POSITIVE-DEFINITE MATRICES
B.2 RANGE SPACES AND NULLSPACES OF MATRICES
B.3 SCHUR COMPLEMENTS
B.4 CHOLESKY FACTORIZATION
B.5 QR DECOMPOSITION
B.6 SINGULAR VALUE DECOMPOSITION
B.7 KRONECKER PRODUCTS
CHAPTER C: Complex Gradients
C.1 CAUCHY-RIEMANN CONDITIONS
C.2 SCALAR ARGUMENTS
C.3 VECTOR ARGUMENTS
PART I: OPTIMAL ESTIMATION
CHAPTER 1: Scalar-Valued Data
1.1 ESTIMATION WITHOUT OBSERVATIONS
1.2 ESTIMATION GIVEN DEPENDENT OBSERVATIONS
1.3 ORTHOGONALITY PRINCIPLE
1.4 GAUSSIAN RANDOM VARIABLES
CHAPTER 2: Vector-Valued Data
2.1 OPTIMAL ESTIMATOR IN THE VECTOR CASE
2.2 SPHERICALLY INVARIANT GAUSSIAN VARIABLES
2.3 EQUIVALENT OPTIMIZATION CRITERION
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART II: LINEAR ESTIMATION
CHAPTER 3: NORMAL EQUATIONS
3.1 MEAN-SQUARE ERROR CRITERION
3.2 MINIMIZATION BY DIFFERENTIATION
3.3 MINIMIZATION BY COMPLETION OF SQUARES
3.4 MINIMIZATION OF THE ERROR COVARIANCE MATRIX
3.5 OPTIMAL LINEAR ESTIMATOR
CHAPTER 4: Orthogonality Principle
4.1 DESIGN EXAMPLES
4.2 ORTHOGONALITY CONDITION
4.3 EXISTENCE OF SOLUTIONS
4.4 NONZERO-MEAN VARIABLES
CHAPTER 5: Linear Models
5.1 ESTIMATION USING LINEAR RELATIONS
5.2 APPLICATION: CHANNEL ESTIMATION
5.3 APPLICATION: BLOCK DATA ESTIMATION
5.4 APPLICATION: LINEAR CHANNEL EQUALIZATION
5.5 APPLICATION: MULTIPLE-ANTENNA RECEIVERS
CHAPTER 6: Constrained Estimation
6.1 MINIMUM-VARIANCE UNBIASED ESTIMATION
6.2 EXAMPLE: MEAN ESTIMATION
6.3 APPLICATION: CHANNEL AND NOISE ESTIMATION
6.4 APPLICATION: DECISION FEEDBACK EQUALIZATION
6.5 APPLICATION: ANTENNA BEAMFORMING
CHAPTER 7: Kalman Filter
7.1 INNOVATIONS PROCESS
7.2 STATE-SPACE MODEL
7.3 RECURSION FOR THE STATE ESTIMATOR
7.4 COMPUTING THE GAIN MATRIX
7.5 RICCATI RECURSION
7.6 COVARIANCE FORM
7.7 MEASUREMENT AND TIME-UPDATE FORM
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECTS OJECTS
PART III: STOCHASTIC GRADIENT ALGORITHMS
CHAPTER 8: Steepest–Descent Technique
8.1 LINEAR ESTIMATION PROBLEM
8.2 STEEPEST-DESCENT METHOD
8.3 MORE GENERAL COST FUNCTIONS
CHAPTER 9: Transient Behavior
9.1 MODES OF CONVERGENCE
9.2 OPTIMAL STEP-SIZE
9.3 WEIGHT-ERROR VECTOR CONVERGENCE
9.4 TIME CONSTANTS
9.5 LEARNING CURVE
9.6 CONTOUR CURVES OF THE ERROR SURFACE
9.7 ITERATION-DEPENDENT STEP-SIZES
9.8 NEWTON’S METHOD
CHAPTER 10: LMS Algorithm
10.1 MOTIVATION
10.2 INSTANTANEOUS APPROXIMATION
10.3 COMPUTATIONAL COST
10.4 LEAST-PERTURBATION PROPERTY
10.5 APPLICATION: ADAPTIVE CHANNEL ESTIMATION
10.6 APPLICATION: ADAPTIVE CHANNEL EQUALIZATION
10.7 APPLICATION: DECISION-FEEDBACK EQUALIZATION
10.8 ENSEMBLE-AVERAGE LEARNING CURVES
CHAPTER 11: Normalized LMS Algorithm
11.1 INSTANTANEOUS APPROXIMATION
11.2 COMPUTATIONAL COST
11.3 POWER NORMALIZATION
11.4 LEAST-PERTURBATION PROPERTY
CHAPTER 12: Other LMS-Type Algorithms
12.1 NON-BLIND ALGORITHMS
12.2 BLIND ALGORITHMS
12.3 SOME PROPERTIES
CHAPTER 13: Affine Projection Algorithm
13.1 INSTANTANEOUS APPROXIMATION
13.2 COMPUTATIONAL COST
13.3 LEAST-PERTURBATION PROPERTY
13.4 AFFINE PROJECTION INTERPRETATION
CHAPTER 14: RLS Algorithm
14.1 INSTANTANEOUS APPROXIMATION
14.2 COMPUTATIONAL COST
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECTS OJECTS
PART IV: MEAN-SQUARE PERFORMANCE
CHAPTER 15: Energy Conservation
15.1 PERFORMANCE MEASURE
15.2 STATIONARY DATA MODEL
15.3 ENERGY CONSERVATION RELATION
15.4 VARIANCE RELATION
15.A APPENDIX: ENERGY RELATION INTERPRETATIONS
CHAPTER 16: Performance of LMS
16.1 VARIANCE RELATION
16.2 SMALL STEP-SIZES
16.3 SEPARATION PRINCIPLE
16.4 WHITE GAUSSIAN INPUT
16.5 STATEMENT OF RESULTS
16.6 SIMULATION RESULTS
CHAPTER 17: Performance of NLMS
17.1 SEPARATION PRINCIPLE
17.2 SIMULATION RESULTS
17.A APPENDIX: RELATING NLMS TO LMS
CHAPTER 18: Performance of Sign-Error LMS
18.1 REAL-VALUED DATA
18.2 COMPLEX-VALUED DATA
18.3 SIMULATION RESULTS
CHAPTER 19: Performance of RLS and Other Filters
19.1 PERFORMANCE OF RLS
19.2 PERFORMANCE OF OTHER FILTERS
19.3 PERFORMANCE TABLE FOR SMALL STEP-SIZES
CHAPTER 20: Nonstationary Environments
20.1 MOTIVATION
20.2 NONSTATIONARY DATA MODEL
20.3 ENERGY CONSERVATION RELATION
20.4 VARIANCE RELATION
CHAPTER 21: Tracking Performance
21.1 PERFORMANCE OF LMS
21.2 PERFORMANCE OF NLMS
21.3 PERFORMANCE OF SIGN-ERROR LMS
21.4 PERFORMANCE OF RLS
21.5 COMPARISON OF TRACKING PERFORMANCE
21.6 COMPARING RLS AND LMS
21.7 PERFORMANCE OF OTHER FILTERS
21.8 PERFORMANCE TABLE FOR SMALL STEP-SIZES
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECTS
PART V: TRANSIENT PERFORMANCE
CHAPTER 22: Weighted Energy Conservation
22.1 DATA MODEL
22.2 DATA-NORMALIZED ADAPTIVE FILTERS
22.3 WEIGHTED ENERGY CONSERVATION RELATION
22.4 WEIGHTED VARIANCE RELATION
CHAPTER 23: LMS with Gaussian Regressors
23.1 MEAN AND VARIANCE RELATIONS
23.2 MEAN BEHAVIOR
23.3 MEAN-SQUARE BEHAVIOR
23.4 MEAN-SQUARE STABILITY
23.5 STEADY-STATE PERFORMANCE
23.6 SMALL STEP-SIZE APPROXIMATIONS
23.A APPENDIX: CONVERGENCE TIME
CHAPTER 24: LMS with non-Gaussian Regressors
24.1 MEAN AND VARIANCE RELATIONS
24.2 MEAN-SQUARE STABILITY AND PERFORMANCE
24.3 SMALL STEP-SIZE APPROXIMATIONS
24.A APPENDIX: AVERAGING ANALYSIS
CHAPTER 25: Data-Normalized Filters
25.1 NLMS FILTER
25.2 DATA-NORMALIZED FILTERS
25.A APPENDIX: STABILITY BOUND
25.B APPENDIX: STABILITY OF NLMS
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART VI: BLOCK ADAPTIVE FILTERS
CHAPTER 26: Transform Domain Adaptive Filters
26.1 TRANSFORM-DOMAIN FILTERS
26.2 DFT-DOMAIN LMS
26.3 DCT-DOMAIN LMS
26.A APPENDIX: DCT-TRANSFORMED REGRESSORS
CHAPTER 27: Efficient Block Convolution
27.1 MOTIVATION
27.2 BLOCK DATA FORMULATION
27.3 BLOCK CONVOLUTION
CHAPTER 28: Block and Subband Adaptive Filters
28.1 DFT BLOCK ADAPTIVE FILTERS
28.2 SUBBAND ADAPTIVE FILTERS
28.A APPENDIX: ANOTHER CONSTRAINED FILTER
28.B APPENDIX: OVERLAP-ADD BLOCK ADAPTIVE FILTERS
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART VII: LEAST-SQUARES METHODS
CHAPTER 29: Least-Squares Criterion
29.1 LEAST-SQUARES PROBLEM
29.2 GEOMETRIC ARGUMENT
29.3 ALGEBRAIC ARGUMENTS
29.4 PROPERTIES OF LEAST-SQUARES SOLUTION
29.5 PROJECTION MATRICES
29.6 WEIGHTED LEAST-SQUARES
29.7 REGULARIZED LEAST-SQUARES
29.8 WEIGHTED REGULARIZED LEAST-SQUARES
CHAPTER 30: Recursive Least-Squares
30.1 MOTIVATION
30.2 RLS ALGORITHM
30.3 REGULARIZATION
30.4 CONVERSION FACTOR
30.5 TIME-UPDATE OF THE MINIMUM COST
30.6 EXPONENTIALLY-WEIGHTED RLS ALGORITHM
CHAPTER 31: Kalman Filtering and RLS
31.1 EQUIVALENCE IN LINEAR ESTIMATION
31.2 KALMAN FILTERING AND RECURSIVE LEAST-SQUARES
31.A APPENDIX: EXTENDED RLS ALGORITHMS
CHAPTER 32: Order and Time-Update Relations
32.1 BACKWARD ORDER-UPDATE RELATIONS
32.2 FORWARD ORDER-UPDATE RELATIONS
32.3 TIME-UPDATE RELATION
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECTS
PART VIII: ARRAY ALGORITHMS
CHAPTER 33: Norm and Angle Preservation
33.1 SOME DIFFICULTIES
33.2 SQUARE-ROOT FACTORS
33.3 PRESERVATION PROPERTIES
33,4 MOTIVATION FOR ARRAY METHODS
CHAPTER 34: Unitary Transformations
34.1 GIVENS ROTATIONS
34.2 HOUSEHOLDER TRANSFORMATIONS
CHAPTER 35: QR and Inverse QR Algorithms
35.1 INVERSE QR ALGORITHM
35.2 QR ALGORITHM
35.3 EXTENDED QR ALGORITHM
35.A APPENDIX: ARRAY KALMAN FILTERS
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART IX: FAST RLS ALGORITHMS
CHAPTER 36: Hyperbolic Rotations
36.1 HYPERBOLIC GIVENS ROTATIONS
36.2 HYPERBOLIC HOUSEHOLDER TRANSFORMATIONS
36.3 HYPERBOLIC BASIS ROTATIONS
CHAPTER 37: Fast Array Algorithm
37.1 TIME-UPDATE OF THE GAIN VECTOR
37.2 TIME-UPDATE OF THE CONVERSION FACTOR
37.3 INITIAL CONDITIONS
37.4 ARRAY ALGORITHM
37.A APPENDIX: CHANDRASEKHAR FILTER
CHAPTER 38: Regularized Prediction Problems
38.1 REGULARIZED BACKWARD PREDICTION
38.2 REGULARIZED FORWARD PREDICTION
38.3 LOW-RANK FACTORIZATION
CHAPTER 39: Fast Fixed-Order Filters
39.1 FAST TRANSVERSAL FILTER
39.2 FAEST FILTER
39.3 FAST KALMAN FILTER
39.4 STABILITY ISSUES
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART X: LATTICE FILTERS
CHAPTER 40: Three Basic Estimation Problems
40.1 MOTIVATION FOR LATTICE FILTERS
40.2 JOINT PROCESS ESTIMATION
40.3 BACKWARD ESTIMATION PROBLEM
40.4 FORWARD ESTIMATION PROBLEM
40.5 TIME AND ORDER-UPDATE RELATIONS
CHAPTER 41: Lattice Filter Algorithms
41.1 SIGNIFICANCE OF DATA STRUCTURE
41.2 A POSTERIORI-BASED LATTICE FILTER
41.3 A PRIORI-BASED LATTICE FILTER
CHAPTER 42: Error-Feedback Lattice Filters
42.1 A PRIORI ERROR-FEEDBACK LATTICE FILTER
42.2 A POSTERIORI ERROR-FEEDBACK LATTICE FILTER
42.3 NORMALIZED LATTICE FILTER
CHAPTER 43: Array Lattice Filters
43.1 ORDER-UPDATE OF OUTPUT ESTIMATION ERRORS
43.2 ORDER-UPDATE OF BACKWARD ESTIMATION ERRORS
43.3 ORDER-UPDATE OF FORWARD ESTIMATION ERRORS
43.4 SIGNIFICANCE OF DATA STRUCTURE
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
PART XI: ROBUST FILTERS
CHAPTER 44: Indefinite Least-Squares
44.1 INDEFINITE LEAST-SQUARES FORMULATION
44.2 RECURSIVE MINIMIZATION ALGORITHM
44.3 TIME-UPDATE OF THE MINIMUM COST
44.4 SINGULAR WEIGHTING MATRICES
44.A APPENDIX: STATIONARY POINTS
44.B APPENDIX: INERTIA CONDITIONS
CHAPTER 45: Robust Adaptive Filters
45.1 A POSTERIORI-BASED ROBUST FILTERS
45.2 -NLMS ALGORITHM
45.3 A PRIORI-BASED ROBUST FILTERS
45.4 LMS ALGORITHM
45.A APPENDIX:
H
∞
FILTERS
CHAPTER 46: Robustness Properties
46.1 ROBUSTNESS OF LMS
46.2 ROBUSTNESS OF ∈-NLMS
46.3 ROBUSTNESS OF RLS
Summary and Notes
SUMMARY OF MAIN RESULTS
BIBLIOGRAPHIC NOTES
Problems and Computer Projects
PROBLEMS
COMPUTER PROJECT
REFERENCES AND INDICES
References
Author Index
Subject Index
End User License Agreement
Guide
Cover
Table of Contents
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e1
ADAPTIVE FILTERS
ALI H. SAYED
University of California at Los Angeles
Cover design by Michael Rutkowski.
Copyright © 2008 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750–8400, fax (978) 750–4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.
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Library of Congress Cataloging-in-Publication Data:
Sayed, Ali H.
Adaptive filters / Ali H. Sayed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-25388-5 (cloth)
1. Adaptive filters. I. Title.
TK7872.F5S285 2008
621.3815’324--dc22
2008003731
To my parents
