Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.12 pp.2601-2610
- Publication Date
- 2014/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.2601
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Shunsuke YAMAKI
Tohoku University
Masahide ABE
Tohoku University
Masayuki KAWAMATA
Tohoku University
Keyword
Latest Issue
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Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, "Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 12, pp. 2601-2610, December 2014, doi: 10.1587/transfun.E97.A.2601.
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 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.2601/_p
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@ARTICLE{e97-a_12_2601,
author={Shunsuke YAMAKI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics},
year={2014},
volume={E97-A},
number={12},
pages={2601-2610},
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 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.},
keywords={},
doi={10.1587/transfun.E97.A.2601},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2601
EP - 2610
AU - Shunsuke YAMAKI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2014
DO - 10.1587/transfun.E97.A.2601
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2014
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 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.
ER -
English
