STATISTICAL ANALYSIS OF COMPLEX SIGNALS
is not very widespread in the scientific litterature.
The work by K.S.Miller, Stochastic Complex Variables, remains the main monography
on the subject.In this 1974 book, the author explains most of the usual techniques of
regression and statistical modeling, limiting himself to complex random variables
compatible with the circularity assumption. However, such an assumption, which bears
on second order statistical properties, is rarely verified in practical cases.Thus,
representations by complex wavelets leads to some signal noncircularity.
R. Picinbono's recent work has given a new look to the gaussian distribution of a complex variable by defining a relation matrix complementing the usual covariance matrix. The statistical description here proposed does probably not differ from multivariate analysis on cartesian components but it emphasizes the polar representation (amplitude, phase) of a normal law. This choice of variables precisely is one which allows a correct treatment of coefficients in complex wavelets.
