Statistics for complex random variables revisited

Authors:
Jan Eriksson;Esa Ollila;Visa Koivunen
Affiliations:
Helsinki University of Technology, SMARAD CoE, Signal Processing and Acoustics, P.O. Box 3000, FIN-02015 TKK, Finland;Helsinki University of Technology, SMARAD CoE, Signal Processing and Acoustics, P.O. Box 3000, FIN-02015 TKK, Finland;Helsinki University of Technology, SMARAD CoE, Signal Processing and Acoustics, P.O. Box 3000, FIN-02015 TKK, Finland
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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Abstract

Complex random signals play an increasingly important role in array, communications, and biomedical signal processing and related fields. However, the mathematical foundations of complex-valued signals and tools developed for handling them are scattered in literature. There appears to be a need for a concise, unified, and rigorous treatment of such topics. In this paper such a treatment is provided. Moreover, we establish connections between seemingly unrelated objects such as real differentiability and circularity. In addition, a novel complex-valued extension of Taylor series is presented and a measure for circularity is proposed.