Signals and Communication Technology

The Volterra and Wiener Model Approaches

By: Tokunbo Ogunfunmi

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Hardcover | 12 September 2007

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Hardcover
252 Pages

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23.39 x 15.6 x 1.6

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Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches introduces engineers and researchers to the field of nonlinear adaptive system identification. The book includes recent research results in the area of adaptive nonlinear system identification and presents simple, concise, easy-to-understand methods for identifying nonlinear systems. These methods use adaptive filter algorithms that are well known for linear systems identification. They are applicable for nonlinear systems that can be efficiently modeled by polynomials.

After a brief introduction to nonlinear systems and to adaptive system identification, the author presents the discrete Volterra model approach. This is followed by an explanation of the Wiener model approach. Adaptive algorithms using both models are developed. The performance of the two methods are then compared to determine which model performs better for system identification applications.

Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches is useful to graduates students, engineers and researchers in the areas of nonlinear systems, control, biomedical systems and in adaptive signal processing.

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"In this book, the author presents simple, concise, easy-to-understand methods for identifying nonlinear systems using adaptive filter algorithms well known for linear systems identification. The book focuses on the Volterra and Wiener models for nonlinear systems ... . It is another contribution to the current literature on the subject. The book will be useful for graduate students, engineers and researchers in the area of the nonlinear systems identification and adaptive signal processing." (George S. Stavrakakis, Zentralblatt MATH, Vol. 1130 (8), 2008)

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Preface	p. vii
Acknowledgements	p. xi
Introduction to Nonlinear Systems	p. 1
Linear Systems	p. 1
Nonlinear Systems	p. 11
Summary	p. 17
Polynomial Models of Nonlinear Systems	p. 19
Nonlinear Orthogonal and Nonorthogonal Models	p. 19
Nonorthogonal Models	p. 20
Orthogonal Models	p. 28
Summary	p. 35
Appendix 2A (Sturm-Liouville System)	p. 36
Volterra and Wiener Nonlinear Models	p. 39
Volterra Respresentation	p. 40
Discrete Nonlinear Wiener Representation	p. 45
Detailed Nonlinear Wiener Model Representation	p. 60
Delay Line Version of Nonlinear Wiener Model	p. 65
The Nonlinear Hammerstein Model Representation	p. 67
Summary	p. 67
Appendix 3A	p. 68
Appendix 3B	p. 70
Appendix 3C	p. 75
Nonlinear System Identification Methods	p. 77
Methods Based on Nonlinear Local Optimization	p. 77
Methods Based on Nonlinear Global Optimization	p. 80
The Need for Adaptive Methods	p. 81
Summary	p. 84
Introduction to Adaptive Signal Processing	p. 85
Weiner Filters for Optimum Linear Estimation	p. 85
Adaptive Filters (LMS-Based Algorithms)	p. 92
Applications of Adaptive Filters	p. 95
Least-Squares Method for Optimum Linear Estimation	p. 97
Adaptive Filters (RLS-Based Algorithms)	p. 107
Summary	p. 113
Appendix 5A	p. 113
Nonlinear Adaptive System Identification Based on Volterra Models	p. 115
LMS Algorithm for Truncated Volterra Series Model	p. 116
LMS Algorithm for Bilinear Model of Nonlinear Systems	p. 118
RLS Algorithm for Truncated Volterra Series Model	p. 121
RLS Algorithm for Bilinear Model	p. 122
Computer Simulation Examples	p. 123
Summary	p. 128
Nonlinear Adaptive System Identification Based on Wiener Models (Part 1)	p. 129
Second-Order System	p. 130
Computer Simulation Examples	p. 140
Summary	p. 148
Appendix 7A: Relation between Autocorrelation Matrix R[subscript xx], R[subscript xx] and Cross-Correlation Matrix R[subscript xx]	p. 148
Appendix 7B: General Order Moments of Joint Gaussian Random Variables	p. 150
Nonlinear Adaptive System Identification Based on Wiener Models (Part 2)	p. 159
Third-Order System	p. 159
Computer Simulation Examples	p. 170
Summary	p. 174
Appendix 8A: Relation Between Autocorrelation Matrix R[subscript xx], R[subscript xx] and Cross-Correlation Matrix R[subscript xx]	p. 174
Appendix 8B: Inverse Matrix of Cross-Correlation Matrix R[subscript xx]	p. 182
Appendix 8C: Verification of Equation 8.16	p. 183
Nonlinear Adaptive System Identification Based on Wiener Models (Part 3)	p. 187
Nonlinear LMF Adaptation Algorithm	p. 187
Transform Domain Nonlinear Wiener Adaptive Filter	p. 188
Computer Simulation Examples	p. 193
Summary	p. 197
Nonlinear Adaptive System Identification Based on Wiener Models (Part 4)	p. 199
Standard RLS Nonlinear Wiener Adaptive Algorithm	p. 200
Inverse QR Decomposition Nonlinear Wiener Filter Algorithm	p. 201
Recursive OLS Volterra Adaptive Filtering	p. 203
Computer Simulation Examples	p. 208
Summary	p. 212
Conclusions, Recent Results, and New Directions	p. 213
Conclusions	p. 214
Recent Results and New Directions	p. 214
References	p. 217
Index	p. 225
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Signals and Communication Technology

The Volterra and Wiener Model Approaches

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