Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences

Shunsuke YAMAKI; Masahide ABE; Masayuki KAWAMATA

doi:10.1587/transfun.E100.A.1097

Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences

Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA

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This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.5 pp.1097-1108

Publication Date: 2017/05/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.1097

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, real signals, odd-symmetry, characteristic functions, trigonometric moments

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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 5, pp. 1097-1108, May 2017, doi: 10.1587/transfun.E100.A.1097.
Abstract: This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1097/_p

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@ARTICLE{e100-a_5_1097,
author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences},
year={2017},
volume={E100-A},
number={5},
pages={1097-1108},
abstract={This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.},
keywords={},
doi={10.1587/transfun.E100.A.1097},
ISSN={1745-1337},
month={May},}

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TY - JOUR
TI - Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1097
EP - 1108
AU - Shunsuke YAMAKI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2017
DO - 10.1587/transfun.E100.A.1097
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2017
AB - This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.
ER -