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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
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2020/02/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Digital Signal Processing
phase-only correlation functions, bivariate probability distributions, circular probability distributions, directional statistics, wrapped distributions,
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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.