| Description |
1 online resource (xviii, 324 pages) : illustrations |
| Series |
Adaptive and learning systems for signal processing, communications, and control |
|
Adaptive and learning systems for signal processing, communications, and control.
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| Contents |
The magic of complex numbers -- Why signal processing in the complex domain? -- Adaptive filtering architectures -- Complex nonlinear activation functions -- Elements of CR calculus -- Complex valued adaptive filters -- Adaptive filters with feedback -- Filters with an adaptive stepsize -- Filters with an adaptive amplitude of nonlinearity -- Data-reusing algorithms for complex valued adaptive filters -- Complex mappings and Möbius transformations -- Augmented complex statistics -- Widely linear estimation and augmented CLMS (ACLMS) -- Duality between complex valued and real valued filters -- Widely linear filters with feedback -- Collaborative adaptive filtering -- Adaptive filtering based on EMD -- Validation of complex representations : is this worthwhile? -- Some distinctive properties of calculus in C -- Liouville's theorem -- Hypercomplex and Clifford algebras -- Real valued activation functions -- Elementary transcendental functions (ETF) -- The O notation and standard vector and matrix differentiation -- Notions from learning theory -- Notions from approximation theory -- Terminology used in the field of neural networks -- Complex valued pipelined recurrent neural network (CPRNN) -- Gradient adaptive step size (GASS) algorithms in R -- Derivation of partial derivatives from Chapter 8 -- A posteriori leraning -- Notions from stability theory -- Linear relaxation -- Contraction mappings, fixed point iteration, and fractals |
| Summary |
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 stochast |
| Bibliography |
Includes bibliographical references (pages 309-320) and index |
| Notes |
Print version record |
| Subject |
Functions of complex variables.
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Adaptive filters -- Mathematical models
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Filters (Mathematics)
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Nonlinear theories.
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Neural networks (Computer science)
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Neural Networks, Computer
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COMPUTERS -- Information Theory.
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TECHNOLOGY & ENGINEERING -- Signals & Signal Processing.
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Adaptive filters -- Mathematical models
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Filters (Mathematics)
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Functions of complex variables
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Neural networks (Computer science)
|
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Nonlinear theories
|
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Adaptives Filter
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Digitale Signalverarbeitung
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Funktionentheorie
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Mathematisches Modell
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Mehrere Variable
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Traitement adaptatif du signal.
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Filtres adaptatifs.
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| Form |
Electronic book
|
| Author |
Goh, Vanessa Su Lee
|
| LC no. |
2009001965 |
| ISBN |
9780470742631 |
|
0470742631 |
|
9780470742624 |
|
0470742623 |
|
1282123378 |
|
9781282123373 |
|
9786612123375 |
|
6612123370 |
|
0470066350 |
|
9780470066355 |
|
