Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Complex-Valued Adaptive Signal Processing Using Nonlinear Functions | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 765615 9 pages doi 2008 765615 Research Article Complex-Valued Adaptive Signal Processing Using Nonlinear Functions Hualiang Li and Tulay Adali Department of Computer Science and Electrical Engineering University of Maryland Baltimore County Baltimore MD 21250 USA Correspondence should be addressed to Tulay Adali adali@ Received 16 October 2007 Accepted 14 February 2008 Recommended by Anibal Figueiras-Vidal 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. Copyright 2008 H. Li and T. Adali. 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. 1. INTRODUCTION Most of today s challenging signal processing applications require techniques that are nonlinear adaptive and with online processing capability. Also there is need for approaches to process complex-valued data as such data arises in a good number of scenarios for example when processing radar and magnetic resonance data as well as communications data and when working in a transform domain such as frequency. Even though complex signals play such an important role many engineering shortcuts have typically been taken in their treatment preventing full utilization of the power of complex domain processing as well as the .
