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Complex-Valued Adaptive Signal Processing Using Nonlinear Functions


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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Correspondence to Tülay Adalı.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Li, H., Adalı, T. Complex-Valued Adaptive Signal Processing Using Nonlinear Functions. EURASIP J. Adv. Signal Process. 2008, 765615 (2008).

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