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Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions
Shunsuke YAMAKI Masahide ABE Masayuki KAWAMATA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2016/10/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Digital Signal Processing
phase-only correlation functions, wrapped distributions, directional statistics, circular probability distributions,
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This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.