Statistical analysis of phase-only correlation functions based on directional statistics

Shunsuke Yamaki; Masahide Abe; Masayuki Kawamata

doi:10.1587/transfun.E97.A.2601

Statistical analysis of phase-only correlation functions based on directional statistics

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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 phasespectrum 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.

Original language	English
Pages (from-to)	2601-2610
Number of pages	10
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E97A
Issue number	12
DOIs	https://doi.org/10.1587/transfun.E97.A.2601
Publication status	Published - 2014 Dec 1

Keywords

Circular probability distributions
Circular variance
Directional statistics
Mean direction
Phase-only correlation functions
Von-Mises distribution

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1587/transfun.E97.A.2601

Cite this

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title = "Statistical analysis of phase-only correlation functions based on directional statistics",

abstract = "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 phasespectrum 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.",

keywords = "Circular probability distributions, Circular variance, Directional statistics, Mean direction, Phase-only correlation functions, Von-Mises distribution",

author = "Shunsuke Yamaki and Masahide Abe and Masayuki Kawamata",

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T1 - Statistical analysis of phase-only correlation functions based on directional statistics

AU - Yamaki, Shunsuke

AU - Abe, Masahide

AU - Kawamata, Masayuki

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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 phasespectrum 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.

AB - 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 phasespectrum 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.

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KW - Circular variance

KW - Directional statistics

KW - Mean direction

KW - Phase-only correlation functions

KW - Von-Mises distribution

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Statistical analysis of phase-only correlation functions based on directional statistics

Abstract

Keywords

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