Summary and Info
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.Content: Chapter 1 The Magic of Complex Numbers (pages 1–11): Chapter 2 Why Signal Processing in the Complex Domain? (pages 13–31): Chapter 3 Adaptive Filtering Architectures (pages 33–41): Chapter 4 Complex Nonlinear Activation Functions (pages 43–54): Chapter 5 Elements of CR Calculus (pages 55–67): Chapter 6 Complex Valued Adaptive Filters (pages 69–90): Chapter 7 Adaptive Filters with Feedback (pages 91–105): Chapter 8 Filters with an Adaptive Stepsize (pages 107–117): Chapter 9 Filters with an Adaptive Amplitude of Nonlinearity (pages 119–127): Chapter 10 Data?Reusing Algorithms for Complex Valued Adaptive Filters (pages 129–136): Chapter 11 Complex Mappings and Mobius Transformations (pages 137–149): Chapter 12 Augmented Complex Statistics (pages 151–168): Chapter 13 Widely Linear Estimation and Augmented CLMS (ACLMS) (pages 169–181): Chapter 14 Duality Between Complex Valued and Real Valued Filters (pages 183–190): Chapter 15 Widely Linear Filters with Feedback (pages 191–205): Chapter 16 Collaborative Adaptive Filtering (pages 207–220): Chapter 17 Adaptive Filtering Based on EMD (pages 221–232): Chapter 18 Validation of Complex Representations – Is This Worthwhile? (pages 233–244):
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