Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions

Shunsuke YAMAKI; Masahide ABE; Masayuki KAWAMATA

doi:10.1587/transfun.E99.A.1790

Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions

Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA

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Summary :

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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.10 pp.1790-1798

Publication Date: 2016/10/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.1790

Type of Manuscript: PAPER

Category: Digital Signal Processing

Authors

Shunsuke YAMAKI
  Tohoku University
Masahide ABE
  Tohoku University
Masayuki KAWAMATA
  Tohoku University

Keyword

phase-only correlation functions, wrapped distributions, directional statistics, circular probability distributions

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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 10, pp. 1790-1798, October 2016, doi: 10.1587/transfun.E99.A.1790.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1790/_p

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@ARTICLE{e99-a_10_1790,
author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions},
year={2016},
volume={E99-A},
number={10},
pages={1790-1798},
abstract={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.},
keywords={},
doi={10.1587/transfun.E99.A.1790},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1790
EP - 1798
AU - Shunsuke YAMAKI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2016
DO - 10.1587/transfun.E99.A.1790
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2016
AB - 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.
ER -