Statistical Analysis of Phase-Only Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise

Shunsuke YAMAKI  Kazuhiro FUKUI  Masahide ABE  Masayuki KAWAMATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   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
phase-only correlation functions,  phase fluctuation,  additive Gaussian noise,  probability density functions,  

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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.