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E-raamat: Adaptive Identification of Acoustic Multichannel Systems Using Sparse Representations

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This book treats the topic of extending the adaptive filtering theory in the context of massive multichannel systems by taking into account a priori knowledge of the underlying system or signal. The starting point is exploiting the sparseness in acoustic multichannel system in order to solve the non-uniqueness problem with an efficient algorithm for adaptive filtering that does not require any modification of the loudspeaker signals.
The book discusses in detail the derivation of general sparse representations of acoustic MIMO systems in signal or system dependent transform domains. Efficient adaptive filtering algorithms in the transform domains are presented and the relation between the signal- and the system-based sparse representations is emphasized. Furthermore, the book presents a novel approach to spatially preprocess the loudspeaker signals in a full-duplex communication system. The idea of the preprocessing is to prevent the echoes from being captured by the microphone array in order to support the AEC system. The preprocessing stage is given as an exemplarily application of a novel unified framework for the synthesis of sound figures. Finally, a multichannel system for the acoustic echo suppression is presented that can be used as a postprocessing stage for removing residual echoes. As first of its kind, it extracts the near-end signal from the microphone signal with a distortionless constraint and without requiring a double-talk detector.

1 Introduction
1(16)
1.1 Problem Statement
1(3)
1.2 State of the Art in High-Resolution Spatial Sound Reproduction
4(1)
1.3 State of the Art in High-Resolution Spatial Sound Analysis
5(1)
1.4 State of the Art in Adaptive Filtering
6(4)
1.4.1 Frequency-Domain Adaptive Filtering
7(1)
1.4.2 Proportionate Adaptive Filtering Algorithms
8(1)
1.4.3 Model-Based Adaptive Filtering and Post-Processing
8(1)
1.4.4 Convergence Enhancement for Stereo Acoustic Echo Cancellation by a Preprocessing Stage
9(1)
1.5 Overview of This Book
10(7)
References
11(6)
Part I Theoretical Multichannel System Identification
2 Fundamentals of Adaptive Filter Theory
17(6)
2.1 Signal and System Model
17(2)
2.1.1 Standard Representation
17(1)
2.1.2 Compact Representation
18(1)
2.2 Optimal System Identification in Least-Squares Sense
19(4)
2.2.1 The Wiener--Hopf Equation
19(1)
2.2.2 Derivation of Iterative Estimation Approaches
20(2)
References
22(1)
3 Spatio-Temporal Regularized Recursive Least Squares Algorithm
23(12)
3.1 Regularization from a Probabilistic Point of View
23(2)
3.2 Structured Regularization
25(1)
3.3 p,q-norm Constrained Adaptive Filtering
25(2)
3.4 Discussion of Special Cases
27(3)
3.4.1 Multichannel Sparse Adaptive Filtering
27(2)
3.4.2 Efficient Computation of the Regularized Inverse
29(1)
3.5 Ill-Conditioning in Multichannel Adaptive Filtering and Sparseness Constraint
30(1)
3.6 Experiments
31(4)
References
33(2)
4 Sparse Representation of Multichannel Acoustic Systems
35(20)
4.1 System Sparsity
35(13)
4.1.1 Prior Knowledge from Physics
35(8)
4.1.2 Incorporating the Prior Knowledge on Spatially Discrete Acoustic Systems
43(3)
4.1.3 Eigenspace Adaptive Filtering
46(2)
4.2 Signal Sparsity
48(1)
4.3 Source-Domain Estimation
48(3)
4.3.1 Permutation Problem
50(1)
4.4 Efficient System Identification in the Source Domain
51(1)
4.4.1 Algorithm
51(1)
4.4.2 Adaptation Control
52(1)
4.5 Experiments
52(3)
References
54(1)
5 Unique System Identification from Projections
55(12)
5.1 Generic Spatially Transformed Adaptive Filtering for Ill-Conditioned Problems
55(3)
5.2 System Eigenspace Estimation
58(3)
5.2.1 Validity of the Estimated Eigenspace
60(1)
5.2.2 Adaptation Control
61(1)
5.3 Experimental Results
61(6)
5.3.1 Performance Measures
61(1)
5.3.2 Simulation
62(1)
References
62(5)
Part II Practical Aspects
6 Geometrical Constraints
67(30)
6.1 Synthesis of Sound Fields
69(2)
6.2 Analytical Solution to the Synthesis of Sound Figures
71(6)
6.2.1 Mathematical Problem Formulation
71(1)
6.2.2 Conditions for the Synthesis of Sound Figures
72(5)
6.3 Synthesis of Closed Zones of Quiet
77(4)
6.3.1 Approximation of the Driving Functions Based on the Kirchhoff-Helmholtz Integral
79(1)
6.3.2 Analytical Derivation of the Driving Functions
79(2)
6.4 Linear Distribution of Secondary Sources as Limiting Case of a Closed Distribution
81(8)
6.4.1 Linear Secondary Source Distributions
81(2)
6.4.2 Arrays with Convex Geometries as Linear Arrays
83(1)
6.4.3 Example of the Synthesis of Sound Figures on a Line Using Linear Arrays
84(3)
6.4.4 Sound Figures as Functions on Two-Dimensional Manifolds
87(2)
6.5 Simulations and Discussion of Practical Aspects
89(8)
6.5.1 Limitations of the Synthesis of Sound Figures
91(1)
6.5.2 Robustness Due to Practical Aspects
91(2)
References
93(4)
7 Acoustic Echo Suppression
97(12)
7.1 Problem Formulation and the Proposed Approach
98(4)
7.1.1 Signal Model
98(1)
7.1.2 Initial Guess of the Near-End Signal
99(2)
7.1.3 Complexity Reduction for the Massive Multichannel Case
101(1)
7.2 MVDR Processing Stage
102(2)
7.2.1 Minimum Variance
103(1)
7.2.2 Distortionless Response
104(1)
7.3 Experimental Results
104(5)
7.3.1 Performance Measures
104(1)
7.3.2 Simulations
105(2)
References
107(2)
8 Conclusion and Outlook
109(2)
Appendix A Definitions and Useful Identities 111(2)
Appendix B Derivation of the Hessian Matrix for a Least-Squares Problem with Structured Regularization 113