Preface
Acknowledgements
Table of Contents
List of Abbreviations
List of Symbols
Chapter 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
1.6.1.1 Acoustic echo cancellation
1.6.1.2 Active noise control
1.6.1.3 Adaptive noise cancellation
1.6.1.4 Acoustic feedback cancellation in hearing aids
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
1.7.1.1 Frequency-domain adaptive filters
1.7.1.2 Self-orthogonalizing adaptive filters
1.7.2 Subband adaptive filters
1.8 Summary
References
Chapter 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
2.3.3 Polyphase representation
2.3 Paraunitary Filter Banks
2.4 Block Transforms
2.4.1 Filter banks as 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
Chapter 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
Chapter 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 structure
4.2.2 Closed-loop structure
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
4.4.3.1 Frequency sampling method
4.4.3.2 DFT filter bank with fractional delays
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
Chapter 5 Critically-Sampled and Oversampled Subband Structures
5.1 Variants of Critically-Sampled Subband Adaptive Filters
5.1.1 SAF with 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
Chapter 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
Chapter 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
7.1.3.1 Paraunitary, lossless, and power complementary
7.1.3.2 Uncorrelated noise vectors
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
Chapter 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 SAF
8.2.3 Variable tap-lengths for SAF
8.3 Theoretical Analysis
8.4 Applications of SAF
8.5 Further Research on Multiband-Structured SAF
8.6 Concluding Remarks
References
Appendix A Programming in MATLAB
Appendix B Using MATLAB for Subband Adaptive Filtering
Appendix C Summary of MATLAB Scripts, Functions, Examples, and Demos
Appendix D Complexity Analysis of Adaptive Algorithms