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This article is part of the series Emerging Machine Learning Techniques in Signal Processing.

Open Access Open Badges Research Article

Complex-Valued Adaptive Signal Processing Using Nonlinear Functions

Hualiang Li and Tülay Adalı*

Author Affiliations

Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA

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EURASIP Journal on Advances in Signal Processing 2008, 2008:765615  doi:10.1155/2008/765615

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2008/1/765615

Received:16 October 2007
Accepted:14 February 2008
Published:25 February 2008

© 2008 The Author(s).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We describe a framework based on Wirtinger calculus for adaptive signal processing that enables efficient derivation of algorithms by directly working in the complex domain and taking full advantage of the power of complex-domain nonlinear processing. We establish the basic relationships for optimization in the complex domain and the real-domain equivalences for first- and second-order derivatives by extending the work of Brandwood and van den Bos. Examples in the derivation of first- and second-order update rules are given to demonstrate the versatility of the approach.

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