Complex-Valued Adaptive Signal Processing Using Nonlinear Functions

  • Hualiang Li1 and

    Affiliated with

    • Tülay Adalı1Email author

      Affiliated with

      EURASIP Journal on Advances in Signal Processing20082008:765615

      DOI: 10.1155/2008/765615

      Received: 16 October 2007

      Accepted: 14 February 2008

      Published: 25 February 2008

      Abstract

      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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      Authors’ Affiliations

      (1)
      Department of Computer Science and Electrical Engineering, University of Maryland

      Copyright

      © 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.