Subband Adaptive Filtering : Theory and Implementation

Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap–weight adaptation, delayless architectures, and filter–bank design methods for reducing band–edge effects are included. Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. This book bridges the gaps between the mixed–domain natures of subband adaptive filtering techniques and provides enough depth to the material augmented by many MATLAB® functions and examples. Key Features: Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications. Bridges the gaps between two distinct domains: adaptive filter theory and multirate signal processing. Uses a practical approach through MATLAB®-based source programs on the accompanying CD. Includes more than 100 M-files, allowing readers to modify the code for different algorithms and applications and to gain more insight into the theory and concepts of subband adaptive filters. Subband Adaptive Filtering is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students. It will also be of interest to researchers, technical managers, and computer scientists. Wiley Subband Adaptive Filtering 5 Contents 7 About the authors 13 Preface 15 Acknowledgments 17 List of symbols 19 List of abbreviations 21 1 Introduction to adaptive filters 23 1.1 Adaptive filtering 23 1.2 Adaptive transversal filters 24 1.3 Performance surfaces 26 1.4 Adaptive algorithms 28 1.5 Spectral dynamic range and misadjustment 35 1.6 Applications of adaptive filters 37 1.6.1 Adaptive system identification 37 1.6.2 Adaptive prediction 45 1.6.3 Adaptive inverse modeling 47 1.6.4 Adaptive array processing 50 1.6.5 Summary of adaptive filtering applications 53 1.7 Transform-domain and subband adaptive filters 53 1.7.1 Transform-domain adaptive filters 53 1.7.2 Subband adaptive filters 60 1.8 Summary 61 References 61 2 Subband decomposition and multirate systems 63 2.1 Multirate systems 63 2.2 Filter banks 66 2.2.1 Input–output relation 68 2.2.2 Perfect reconstruction filter banks 69 2.2.3 Polyphase representation 70 2.3 Paraunitary filter banks 76 2.4 Block transforms 77 2.4.1 Filter bank as a block transform 77 2.5 Cosine-modulated filter banks 81 2.5.1 Design example 85 2.6 DFT filter banks 87 2.6.1 Design example 88 2.7 A note on cosine modulation 89 2.8 Summary 90 References 91 3 Second-order characterization of multirate filter banks 95 3.1 Correlation-domain formulation 95 3.1.1 Critical decimation 99 3.2 Cross spectrum 101 3.2.1 Subband spectrum 104 3.3 Orthogonality at zero lag 107 3.3.1 Paraunitary condition 108 3.4 Case study: Subband orthogonality of cosine-modulated filter banks 111 3.4.1 Correlation-domain analysis 111 3.4.2 MATLAB simulations 114 3.5 Summary 118 References 119 4 Subband adaptive filters 121 4.1 Subband adaptive filtering 121 4.1.1 Computational reduction 122 4.1.2 Spectral dynamic range 123 4.2 Subband adaptive filter structures 126 4.2.1 Open-loop structures 126 4.2.2 Closed-loop structures 126 4.3 Aliasing, band-edge effects and solutions 128 4.3.1 Aliasing and band-edge effects 129 4.3.2 Adaptive cross filters 130 4.3.3 Multiband-structured SAF 132 4.3.4 Closed-loop delayless structures 135 4.4 Delayless subband adaptive filters 136 4.4.1 Closed-loop configuration 136 4.4.2 Open-loop configuration 137 4.4.3 Weight transformation 138 4.4.4 Computational requirements 145 4.5 MATLAB examples 146 4.5.1 Aliasing and band-edge effects 147 4.5.2 Delayless alias-free SAFs 148 4.6 Summary 150 References 151 5 Critically sampled and oversampled subband structures 155 5.1 Variants of critically sampled subband adaptive filters 155 5.1.1 SAF with the affine projection algorithm 156 5.1.2 SAF with variable step sizes 158 5.1.3 SAF with selective coefficient update 159 5.2 Oversampled and nonuniform subband adaptive filters 160 5.2.1 Oversampled subband adaptive filtering 160 5.2.2 Nonuniform subband adaptive filtering 162 5.3 Filter bank design 163 5.3.1 Generalized DFT filter banks 163 5.3.2 Single-sideband modulation filter banks 164 5.3.3 Filter design criteria for DFT filter banks 166 5.3.4 Quadrature mirror filter banks 171 5.3.5 Pseudo-quadrature mirror filter banks 175 5.3.6 Conjugate quadrature filter banks 177 5.4 Case study: Proportionate subband adaptive filtering 178 5.4.1 Multiband structure with proportionate adaptation 178 5.4.2 MATLAB simulations 179 5.5 Summary 183 References 185 6 Multiband-structured subband adaptive filters 189 6.1 Multiband structure 189 6.1.1 Polyphase implementation 192 6.2 Multiband adaptation 195 6.2.1 Principle of minimal disturbance 195 6.2.2 Constrained subband updates 195 6.2.3 Computational complexity 197 6.3 Underdetermined least-squares solutions 199 6.3.1 NLMS equivalent 200 6.3.2 Projection interpretation 201 6.4 Stochastic interpretations 201 6.4.1 Stochastic approximation to Newton’s method 201 6.4.2 Weighted MSE criterion 203 6.4.3 Decorrelating properties 208 6.5 Filter bank design issues 209 6.5.1 The diagonal assumption 209 6.5.2 Power complementary filter bank 209 6.5.3 The number of subbands 210 6.6 Delayless MSAF 211 6.6.1 Open-loop configuration 211 6.6.2 Closed-loop configuration 213 6.7 MATLAB examples 214 6.7.1 Convergence of the MSAF algorithm 215 6.7.2 Subband and time-domain constraints 217 6.8 Summary 220 References 221 7 Stability and performance analysis 225 7.1 Algorithm, data model and assumptions 225 7.1.1 The MSAF algorithm 225 7.1.2 Linear data model 226 7.1.3 Paraunitary filter banks 228 7.2 Multiband MSE function 231 7.2.1 MSE functions 231 7.2.2 Excess MSE 232 7.3 Mean analysis 233 7.3.1 Projection interpretation 233 7.3.2 Mean behavior 235 7.4 Mean-square analysis 236 7.4.1 Energy conservation relation 236 7.4.2 Variance relation 238 7.4.3 Stability of the MSAF algorithm 238 7.4.4 Steady-state excess MSE 239 7.5 MATLAB examples 241 7.5.1 Mean of the projection matrix 241 7.5.2 Stability bounds 242 7.5.3 Steady-state excess MSE 244 7.6 Summary 245 References 246 8 New research directions 249 8.1 Recent research on filter bank design 249 8.2 New SAF structures and algorithms 250 8.2.1 In-band aliasing cancellation 250 8.2.2 Adaptive algorithms for the SAF 252 8.2.3 Variable tap lengths for the SAF 252 8.3 Theoretical analysis 254 8.4 Applications of the SAF 254 8.5 Further research on a multiband-structured SAF 255 8.6 Concluding remarks 256 References 257 Appendix A Programming in MATLAB 263 A.1 MATLAB fundamentals 263 A.1.1 Starting MATLAB 263 A.1.2 Constructing and manipulating matrices 266 A.1.3 The colon operator 266 A.1.4 Data types 270 A.1.5 Working with strings 270 A.1.6 Cell arrays and structures 271 A.1.7 MATLAB scripting with M-files 273 A.1.8 Plotting in MATLAB 274 A.1.9 Other useful commands and tips 277 A.2 Signal processing toolbox 280 A.2.1 Quick fact about the signal processing toolbox 280 A.2.2 Signal processing tool 284 A.2.3 Window design and analysis tool 289 A.3 Filter design toolbox 290 A.3.1 Quick fact about the filter design toolbox 290 A.3.2 Filter design and analysis tool 291 A.3.3 MATLAB functions for adaptive filtering 292 A.3.4 A case study: adaptive noise cancellation 294 Appendix B Using MATLAB for adaptive filtering and subband adaptive filtering 301 B.1 Digital signal processing 301 B.1.1 Discrete-time signals and systems 301 B.1.2 Signal representations in MATLAB 302 B.2 Filtering and adaptive filtering in MATLAB 304 B.2.1 FIR filtering 304 B.2.2 The LMS adaptive algorithm 306 B.2.3 Anatomy of the LMS code in MATLAB 307 B.3 Multirate and subband adaptive filtering 314 B.3.1 Implementation of multirate filter banks 314 B.3.2 Implementation of a subband adaptive filter 319 Appendix C Summary of MATLAB scripts, functions, examples and demos 323 Appendix D Complexity analysis of adaptive algorithms 329 Index 339 0470516941,9780470516942

subband Adaptive Filtering Is Rapidly Becoming One Of The Most Effective Techniques For Reducing Computational Complexity And Improving The Convergence Rate Of Algorithms In Adaptive Signal Processing Applications. This Book Provides An Introductory, Yet Extensive Guide On The Theory Of Various Subband Adaptive Filtering Techniques. For Beginners, The Authors Discuss The Basic Principles That Underlie The Design And Implementation Of Subband Adaptive Filters. For Advanced Readers, A Comprehensive Coverage Of Recent Developments, Such As Multiband Tap–weight Adaptation, Delayless Architectures, And Filter–bank Design Methods For Reducing Band–edge Effects Are Included. Several Analysis Techniques And Complexity Evaluation Are Also Introduced In This Book To Provide Better Understanding Of Subband Adaptive Filtering. This Book Bridges The Gaps Between The Mixed–domain Natures Of Subband Adaptive Filtering Techniques And Provides Enough Depth To The Material Augmented By Many Matlab® Functions And Examples.

key Features:

• acts As A Timely Introduction For Researchers, Graduate Students And Engineers Who Want To Design And Deploy Subband Adaptive Filters In Their Research And Applications.

• bridges The Gaps Between Two Distinct Domains: Adaptive Filter Theory And Multirate Signal Processing.

• takes practical Approach with Matlab®-based Source Programs On The Accompanying Cd.

• includes More Than 100 M-files, Allowing Readers To Modify The Code For Different Algorithms And Applications And To Gain More Insight Into The Theory And Concepts Of Subband Adaptive Filters.

subband Adaptive Filtering Is Aimed Primarily At Practicing Engineers, As Well As Senior Undergraduate And Graduate Students. It Will Also Be Of Interest To Researchers, Technical Managers, And Computer Scientists.

Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap–weight adaptation, delayless architectures, and filter–bank design methods for reducing band–edge effects are included. Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. This book bridges the gaps between the mixed–domain natures of subband adaptive filtering techniques and provides enough depth to the material augmented by many MATLAB® functions and examples.

Key Features:

• Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications.
• Bridges the gaps between two distinct domains: adaptive filter theory and multirate signal processing.
• Uses a practical approach through MATLAB®-based source programs on the accompanying CD.
• Includes more than 100 M-files, allowing readers to modify the code for different algorithms and applications and to gain more insight into the theory and concepts of subband adaptive filters.

Subband Adaptive Filtering is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students. It will also be of interest to researchers, technical managers, and computer scientists.

Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap–weight adaptation, delayless architectures, and filter–bank design methods for reducing band–edge effects are included. Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. This book bridges the gaps between the mixed–domain natures of subband adaptive filtering techniques and provides enough depth to the material augmented by many MATLAB® functions and examples. Key Features: * Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications. * Bridges the gaps between two distinct domains: adaptive filter theory and multirate signal processing. * Uses a practical approach through MATLAB®-based source programs on the accompanying CD. * Includes more than 100 M-files, allowing readers to modify the code for different algorithms and applications and to gain more insight into the theory and concepts of subband adaptive filters. __Subband Adaptive Filtering__ is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students. It will also be of interest to researchers, technical managers, and computer scientists. Content: Front Matter -- Introduction to Adaptive Filters -- Subband Decomposition and Multirate Systems -- Second-Order Characterization of Multirate Filter Banks -- Subband Adaptive Filters -- Critically Sampled and Oversampled Subband Structures -- Multiband-Structured Subband Adaptive Filters -- Stability and Performance Analysis -- New Research Directions -- Appendix A: Programming in MATLAB -- Appendix B: Using MATLAB for Adaptive Filtering and Subband Adaptive Filtering -- Appendix C: Summary of MATLAB Scripts, Functions, Examples and Demos -- Appendix D: Complexity Analysis of Adaptive Algorithms -- Index. Introduction to adaptive filters -- Subband decomposition and multirate systems -- Second-order characterization of multirate filter banks -- Subband adaptive filters -- Critically sampled and oversampled subband structures -- Multiband-structured subband adaptive filters -- Stability and performance analysis -- New research directions -- Appendix A : programming in MATLAB -- Appendix B : using MATLAB for adaptive filtering and subband adaptive filtering -- Appendix C : summary of MATLAB scripts, functions, examples, and demos -- Appendix D : complexity analysis of adaptive algorithms. "Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computation al complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap-weight adaptation, delayless architectures, and filter-bank design methods for reducing band-edge effects are included. Several analysis techniques and complexity evaluation are also introduced, to provide better understanding of subband adaptive filtering. This book brings together the mixed-domain natures of subband adaptive filtering techniques, supplemented by many MATLAB functions and examples."--Jacket