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Subband Adaptive Filtering Theory and Implementation.pdf

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    Subband Adaptive Filtering
    Contents
    About the authors
    Preface
    Acknowledgments
    List of symbols
    List of abbreviations
    1 Introduction to adaptive filters
    1.1 Adaptive filtering
    1.2 Adaptive transversal filters
    1.3 Performance surfaces
    1.4 Adaptive algorithms
    1.5 Spectral dynamic range and misadjustment
    1.6 Applications of adaptive filters
    1.6.1 Adaptive system identification
    1.6.2 Adaptive prediction
    1.6.3 Adaptive inverse modeling
    1.6.4 Adaptive array processing
    1.6.5 Summary of adaptive filtering applications
    1.7 Transform-domain and subband adaptive filters
    1.7.1 Transform-domain adaptive filters
    1.7.2 Subband adaptive filters
    1.8 Summary
    References
    2 Subband decomposition and multirate systems
    2.1 Multirate systems
    2.2 Filter banks
    2.2.1 Input–output relation
    2.2.2 Perfect reconstruction filter banks
    2.2.3 Polyphase representation
    2.3 Paraunitary filter banks
    2.4 Block transforms
    2.4.1 Filter bank as a block transform
    2.5 Cosine-modulated filter banks
    2.5.1 Design example
    2.6 DFT filter banks
    2.6.1 Design example
    2.7 A note on cosine modulation
    2.8 Summary
    References
    3 Second-order characterization of multirate filter banks
    3.1 Correlation-domain formulation
    3.1.1 Critical decimation
    3.2 Cross spectrum
    3.2.1 Subband spectrum
    3.3 Orthogonality at zero lag
    3.3.1 Paraunitary condition
    3.4 Case study: Subband orthogonality of cosine-modulated filter banks
    3.4.1 Correlation-domain analysis
    3.4.2 MATLAB simulations
    3.5 Summary
    References
    4 Subband adaptive filters
    4.1 Subband adaptive filtering
    4.1.1 Computational reduction
    4.1.2 Spectral dynamic range
    4.2 Subband adaptive filter structures
    4.2.1 Open-loop structures
    4.2.2 Closed-loop structures
    4.3 Aliasing, band-edge effects and solutions
    4.3.1 Aliasing and band-edge effects
    4.3.2 Adaptive cross filters
    4.3.3 Multiband-structured SAF
    4.3.4 Closed-loop delayless structures
    4.4 Delayless subband adaptive filters
    4.4.1 Closed-loop configuration
    4.4.2 Open-loop configuration
    4.4.3 Weight transformation
    4.4.4 Computational requirements
    4.5 MATLAB examples
    4.5.1 Aliasing and band-edge effects
    4.5.2 Delayless alias-free SAFs
    4.6 Summary
    References
    5 Critically sampled and oversampled subband structures
    5.1 Variants of critically sampled subband adaptive filters
    5.1.1 SAF with the affine projection algorithm
    5.1.2 SAF with variable step sizes
    5.1.3 SAF with selective coefficient update
    5.2 Oversampled and nonuniform subband adaptive filters
    5.2.1 Oversampled subband adaptive filtering
    5.2.2 Nonuniform subband adaptive filtering
    5.3 Filter bank design
    5.3.1 Generalized DFT filter banks
    5.3.2 Single-sideband modulation filter banks
    5.3.3 Filter design criteria for DFT filter banks
    5.3.4 Quadrature mirror filter banks
    5.3.5 Pseudo-quadrature mirror filter banks
    5.3.6 Conjugate quadrature filter banks
    5.4 Case study: Proportionate subband adaptive filtering
    5.4.1 Multiband structure with proportionate adaptation
    5.4.2 MATLAB simulations
    5.5 Summary
    References
    6 Multiband-structured subband adaptive filters
    6.1 Multiband structure
    6.1.1 Polyphase implementation
    6.2 Multiband adaptation
    6.2.1 Principle of minimal disturbance
    6.2.2 Constrained subband updates
    6.2.3 Computational complexity
    6.3 Underdetermined least-squares solutions
    6.3.1 NLMS equivalent
    6.3.2 Projection interpretation
    6.4 Stochastic interpretations
    6.4.1 Stochastic approximation to Newton’s method
    6.4.2 Weighted MSE criterion
    6.4.3 Decorrelating properties
    6.5 Filter bank design issues
    6.5.1 The diagonal assumption
    6.5.2 Power complementary filter bank
    6.5.3 The number of subbands
    6.6 Delayless MSAF
    6.6.1 Open-loop configuration
    6.6.2 Closed-loop configuration
    6.7 MATLAB examples
    6.7.1 Convergence of the MSAF algorithm
    6.7.2 Subband and time-domain constraints
    6.8 Summary
    References
    7 Stability and performance analysis
    7.1 Algorithm, data model and assumptions
    7.1.1 The MSAF algorithm
    7.1.2 Linear data model
    7.1.3 Paraunitary filter banks
    7.2 Multiband MSE function
    7.2.1 MSE functions
    7.2.2 Excess MSE
    7.3 Mean analysis
    7.3.1 Projection interpretation
    7.3.2 Mean behavior
    7.4 Mean-square analysis
    7.4.1 Energy conservation relation
    7.4.2 Variance relation
    7.4.3 Stability of the MSAF algorithm
    7.4.4 Steady-state excess MSE
    7.5 MATLAB examples
    7.5.1 Mean of the projection matrix
    7.5.2 Stability bounds
    7.5.3 Steady-state excess MSE
    7.6 Summary
    References
    8 New research directions
    8.1 Recent research on filter bank design
    8.2 New SAF structures and algorithms
    8.2.1 In-band aliasing cancellation
    8.2.2 Adaptive algorithms for the SAF
    8.2.3 Variable tap lengths for the SAF
    8.3 Theoretical analysis
    8.4 Applications of the SAF
    8.5 Further research on a multiband-structured SAF
    8.6 Concluding remarks
    References
    Appendix A Programming in MATLAB
    A.1 MATLAB fundamentals
    A.1.1 Starting MATLAB
    A.1.2 Constructing and manipulating matrices
    A.1.3 The colon operator
    A.1.4 Data types
    A.1.5 Working with strings
    A.1.6 Cell arrays and structures
    A.1.7 MATLAB scripting with M-files
    A.1.8 Plotting in MATLAB
    A.1.9 Other useful commands and tips
    A.2 Signal processing toolbox
    A.2.1 Quick fact about the signal processing toolbox
    A.2.2 Signal processing tool
    A.2.3 Window design and analysis tool
    A.3 Filter design toolbox
    A.3.1 Quick fact about the filter design toolbox
    A.3.2 Filter design and analysis tool
    A.3.3 MATLAB functions for adaptive filtering
    A.3.4 A case study: adaptive noise cancellation
    Appendix B Using MATLAB for adaptive filtering and subband adaptive filtering
    B.1 Digital signal processing
    B.1.1 Discrete-time signals and systems
    B.1.2 Signal representations in MATLAB
    B.2 Filtering and adaptive filtering in MATLAB
    B.2.1 FIR filtering
    B.2.2 The LMS adaptive algorithm
    B.2.3 Anatomy of the LMS code in MATLAB
    B.3 Multirate and subband adaptive filtering
    B.3.1 Implementation of multirate filter banks
    B.3.2 Implementation of a subband adaptive filter
    Appendix C Summary of MATLAB scripts, functions, examples and demos
    Appendix D Complexity analysis of adaptive algorithms
    Index
    Subband Adaptive Filtering
    Subband Adaptive Filtering Theory and Implementation Kong-Aik Lee Institute for Infocomm Research, Singapore Woon-Seng Gan Nanyang Technological University, Singapore Sen M. Kuo Northern Illinois University, USA A John Wiley and Sons, Ltd., Publication
    Disclaimer: This eBook does not include ancillary media that was packaged with the printed version of the book. This edition first published 2009  2009, John Wiley & Sons, Ltd. Registered office John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. 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 or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. MATLAB MATLAB and any associated trademarks used in this book are the registered trademarks of The MathWorks, Inc. For MATLAB product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA, 01760-2098 USA Tel: 508-647-7000 Fax: 508-647-7001 E-mail: info@mathworks.com Web: www.mathworks.com LabVIEWTM and National InstrumentsTM are trademarks and trade names of National Instruments Corporation. Interactive LabVIEW-based applications are available to support selected concepts and exercises from the textbook. The software is available on the companion website for this book: www3.ntu.edu.sg/home/ewsgan/saf_book.html or directly from the National Instruments website (go to http://www.ni.com/info and enter the code saftext). Library of Congress Cataloging-in-Publication Data Lee, Kong-Aik. Subband adaptive filtering : theory and implementation / by Kong-Aik Lee, Woon-Seng Gan, Sen M. Kuo. p. cm. Includes bibliographical references and index. ISBN 978-0-470-51694-2 (cloth) 1. Adaptive filters. 2. Adaptive signal processing. 3. Radio frequency modulation, Narrow-band. Title. I. Gan, Woon-Seng. II. Kuo, Sen M. (Sen-Maw) III. TK7872.F5L435 2009 621.3815 324–dc22 2009015205 A catalogue record for this book is available from the British Library. ISBN: 978-0-470-51694-2 Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India. Printed and bound in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire
    Contents About the authors Preface Acknowledgments List of symbols List of abbreviations 1 Introduction to adaptive filters 1.1 Adaptive filtering 1.2 Adaptive transversal filters 1.3 Performance surfaces 1.4 Adaptive algorithms 1.5 Spectral dynamic range and misadjustment 1.6 Applications of adaptive filters 1.6.1 Adaptive system identification 1.6.2 Adaptive prediction 1.6.3 Adaptive inverse modeling 1.6.4 Adaptive array processing 1.6.5 Summary of adaptive filtering applications 1.7 Transform-domain and subband adaptive filters 1.7.1 Transform-domain adaptive filters 1.7.2 Subband adaptive filters 1.8 Summary References 2 Subband decomposition and multirate systems 2.1 Multirate systems 2.2 Filter banks 2.2.1 Input–output relation xi xiii xv xvii xix 1 1 2 4 6 13 15 15 23 25 28 31 31 31 38 39 39 41 41 44 46
    vi CONTENTS 2.2.2 2.2.3 Perfect reconstruction filter banks Polyphase representation 2.3 Paraunitary filter banks 2.4 Block transforms 2.4.1 Filter bank as a block transform 2.5 Cosine-modulated filter banks 2.5.1 Design example 2.6 DFT filter banks 2.6.1 Design example 2.7 A note on cosine modulation 2.8 Summary References 3 Second-order characterization of multirate filter banks 3.1 Correlation-domain formulation 3.1.1 Critical decimation 3.2 Cross spectrum 3.2.1 Subband spectrum 3.3 Orthogonality at zero lag 3.3.1 Paraunitary condition 3.4 Case study: Subband orthogonality of cosine-modulated filter banks 3.4.1 Correlation-domain analysis 3.4.2 MATLAB simulations 3.5 Summary References 4 Subband adaptive filters 4.1 Subband adaptive filtering 4.1.1 Computational reduction 4.1.2 Spectral dynamic range 4.2 Subband adaptive filter structures 4.2.1 Open-loop structures 4.2.2 Closed-loop structures 4.3 Aliasing, band-edge effects and solutions 4.3.1 Aliasing and band-edge effects 4.3.2 Adaptive cross filters 4.3.3 Multiband-structured SAF 4.3.4 Closed-loop delayless structures 4.4 Delayless subband adaptive filters 4.4.1 Closed-loop configuration 4.4.2 Open-loop configuration 4.4.3 Weight transformation 4.4.4 Computational requirements 4.5 MATLAB examples 4.5.1 Aliasing and band-edge effects 47 48 54 55 55 59 63 65 66 67 68 69 73 73 77 79 82 85 86 89 89 92 96 97 99 99 100 101 104 104 104 106 107 108 110 113 114 114 115 116 123 124 125
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