Skip to content


  • Research Article
  • Open Access

Complex-Valued Adaptive Signal Processing Using Nonlinear Functions

EURASIP Journal on Advances in Signal Processing20082008:765615

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


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.


  • Information Technology
  • Signal Processing
  • Quantum Information
  • Nonlinear Function
  • Full Advantage

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

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


© H. Li and T. Adalı 2008

This article is published under license to BioMed Central Ltd. 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.