期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 59, 期 11, 页码 5101-5125出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2011.2162954
关键词
CR calculus; estimation; improper; independent component analysis; model selection; noncircular; widely linear; Wirtinger calculus
资金
- NSF [NSF-CCF 0635129, NSF-IIS 0612076, NSF-CCF 1018472]
- Australian Research Council (ARC) [DP0986391]
- AFOSR [FA 9550-10-1-0241]
- Australian Research Council [DP0986391] Funding Source: Australian Research Council
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [1017718, 1016619] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1116944, 1117056] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1018472] Funding Source: National Science Foundation
Complex-valued signals occur in many areas of science and engineering and are thus of fundamental interest. In the past, it has often been assumed, usually implicitly, that complex random signals are proper or circular. A proper complex random variable is uncorrelated with its complex conjugate, and a circular complex random variable has a probability distribution that is invariant under rotation in the complex plane. While these assumptions are convenient because they simplify computations, there are many cases where proper and circular random signals are very poor models of the underlying physics. When taking impropriety and noncircularity into account, the right type of processing can provide significant performance gains. There are two key ingredients in the statistical signal processing of complex-valued data: 1) utilizing the complete statistical characterization of complex-valued random signals; and 2) the optimization of real-valued cost functions with respect to complex parameters. In this overview article, we review the necessary tools, among which are widely linear transformations, augmented statistical descriptions, and Wirtinger calculus. We also present some selected recent developments in the field of complex-valued signal processing, addressing the topics of model selection, filtering, and source separation.
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