Statistical Analysis of Phase-Only Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise
Summary :
This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.4 pp.671-679
- Publication Date
- 2021/04/01
- Publicized
- 2020/09/29
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2020EAP1024
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Shunsuke YAMAKI
Tohoku University
Kazuhiro FUKUI
Tohoku University
Masahide ABE
Tohoku University
Masayuki KAWAMATA
Tohoku University
Keyword
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Shunsuke YAMAKI, Kazuhiro FUKUI, Masahide ABE, Masayuki KAWAMATA, "Statistical Analysis of Phase-Only Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 4, pp. 671-679, April 2021, doi: 10.1587/transfun.2020EAP1024.
Abstract: This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1024/_p
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@ARTICLE{e104-a_4_671,
author={Shunsuke YAMAKI, Kazuhiro FUKUI, Masahide ABE, Masayuki KAWAMATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Analysis of Phase-Only Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise},
year={2021},
volume={E104-A},
number={4},
pages={671-679},
abstract={This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.},
keywords={},
doi={10.1587/transfun.2020EAP1024},
ISSN={1745-1337},
month={April},}
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TY - JOUR
TI - Statistical Analysis of Phase-Only Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 671
EP - 679
AU - Shunsuke YAMAKI
AU - Kazuhiro FUKUI
AU - Masahide ABE
AU - Masayuki KAWAMATA
PY - 2021
DO - 10.1587/transfun.2020EAP1024
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2021
AB - This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.
ER -
English
