期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 58, 期 10, 页码 5400-5408出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2054085
关键词
Circularity; complex moments and cumulants; complex random variables; Faa di Bruno's formula; Newton's method; properness; R-differentiability; Taylor's series
资金
- Academy of Finland
Complex random signals play an increasingly important role in array, communications, and biomedical signal processing and related fields. However, the fundamental properties of complex-valued signals and mathematical tools needed to process them are scattered in literature. We provide a concise, unified, and rigorous treatment of essential properties and tools of complex random variables, and apply these fundamentals to derive complex extensions of Leibniz rule, Faa di Bruno's formula, and Taylor's series. The extensions allow establishing relationships among complex moments and cumulants, and characterizing the circularity property. We propose measures for testing and quantifying circularity, and observe that non-circularity may be more common in practical applications than previously thought. All results are rigorously proved and supplemented with clarifying examples.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据