Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics

Shunsuke YAMAKI  Masahide ABE  Masayuki KAWAMATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.12   pp.2601-2610
Publication Date: 2014/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.2601
Type of Manuscript: PAPER
Category: Digital Signal Processing
phase-only correlation functions,  directional statistics,  circular probability distributions,  mean direction,  circular variance,  von-Mises distribution,  

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This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phase-spectrum differences. We next assume circular probability distributions for the phase-spectrum differences, considering phase-spectrum differences to be circular data. As a result, we can simply express the expectation and variance of phase-only correlation functions as linear and quadratic functions of circular variance of phase-spectrum differences, respectively.