Complex Valued Nonlinear Adaptive Filters ：Noncircularity, Widely Linear and Neural Models ( Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control )

Publication subTitle ：Noncircularity, Widely Linear and Neural Models

Publication series ：Adaptive and Cognitive Dynamic Systems: Signal Processing, Learning, Communications and Control

Author： Danilo P. Mandic  

Publisher： John Wiley & Sons Inc‎

Publication year： 2009

E-ISBN: 9780470742631

P-ISBN(Hardback):  9780470066355

Subject： TP183 Calculation with Artificial Neural Network

Language： ENG

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Description

This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general complex signals (circular and noncircular). It brings together adaptive filtering algorithms for feedforward (transversal) and feedback architectures and the recent developments in the statistics of complex variable, under the powerful frameworks of CR (Wirtinger) calculus and augmented complex statistics. This offers a number of theoretical performance gains, which is illustrated on both stochastic gradient algorithms, such as the augmented complex least mean square (ACLMS), and those based on Kalman filters. This work is supported by a number of simulations using synthetic and real world data, including the noncircular and intermittent radar and wind signals.

Chapter

Series Page

pp.：  9 – 10

Contents

pp.：  10 – 16

Preface

pp.：  16 – 20

Acknowledgements

pp.：  20 – 22

1 The Magic of Complex Numbers

pp.：  22 – 34

2 Why Signal Processing in the Complex Domain?

pp.：  34 – 54

3 Adaptive Filtering Architectures

pp.：  54 – 64

4 Complex Nonlinear Activation Functions

pp.：  64 – 76

5 Elements of CR Calculus

pp.：  76 – 90

6 Complex Valued Adaptive Filters

pp.：  90 – 112

7 Adaptive Filters with Feedback

pp.：  112 – 128

8 Filters with an Adaptive Stepsize

pp.：  128 – 140

9 Filters with an Adaptive Amplitude of Nonlinearity

pp.：  140 – 150

10 Data-reusing Algorithms for Complex Valued Adaptive Filters

pp.：  150 – 158

11 Complex Mappings and Möbius Transformations

pp.：  158 – 172

12 Augmented Complex Statistics

pp.：  172 – 190

13 Widely Linear Estimation and Augmented CLMS (ACLMS)

pp.：  190 – 204

14 Duality Between Complex Valued and Real Valued Filters

pp.：  204 – 212

15 Widely Linear Filters with Feedback

pp.：  212 – 228

16 Collaborative Adaptive Filtering

pp.：  228 – 242

17 Adaptive Filtering Based on EMD

pp.：  242 – 254

18 Validation of Complex Representations – Is This Worthwhile?

pp.：  254 – 266

Appendix A: Some Distinctive Properties of Calculus in C

pp.：  266 – 272

Appendix B: Liouville’s Theorem

pp.：  272 – 274

Appendix C: Hypercomplex and Clifford Algebras

pp.：  274 – 278

Appendix D: Real Valued Activation Functions

pp.：  278 – 280

Appendix E: Elementary Transcendental Functions (ETF)

pp.：  280 – 284

Appendix F: The O Notation and Standard Vector and Matrix Differentiation

pp.：  284 – 286

Appendix G: Notions From Learning Theory

pp.：  286 – 290

Appendix H: Notions from Approximation Theory

pp.：  290 – 294

Appendix I: Terminology Used in the Field of Neural Networks

pp.：  294 – 296

Appendix J: Complex Valued Pipelined Recurrent Neural Network (CPRNN)

pp.：  296 – 300

Appendix K: Gradient Adaptive Step Size (GASS) Algorithms in R

pp.：  300 – 304

Appendix L: Derivation of Partial Derivatives from Chapter 8

pp.：  304 – 308

Appendix M: A Posteriori Learning

pp.：  308 – 312

Appendix N: Notions from Stability Theory

pp.：  312 – 314

Appendix O: Linear Relaxation

pp.：  314 – 320

Appendix P: Contraction Mappings, Fixed Point Iteration and Fractals

pp.：  320 – 330

References

pp.：  330 – 342

Index

pp.：  342 – 345

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