Statistical Analysis of Phase-Only Correlation Functions Between Two Signals with Stochastic Phase-Spectra Following Bivariate Circular Probability Distributions

Shunsuke YAMAKI  Ryo SUZUKI  Makoto YOSHIZAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.2   pp.478-485
Publication Date: 2020/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2018EAP1206
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
phase-only correlation functions,  bivariate probability distributions,  circular probability distributions,  directional statistics,  wrapped distributions,  

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Summary: 
This paper proposes statistical analysis of phase-only correlation functions between two signals with stochastic phase-spectra following bivariate circular probability distributions based on directional statistics. We give general expressions for the expectation and variance of phase-only correlation functions in terms of joint characteristic functions of the bivariate circular probability density function. In particular, if we assume bivariate wrapped distributions for the phase-spectra, we obtain exactly the same results between in case of a bivariate linear distribution and its corresponding bivariate wrapped distribution.