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Statistical Analysis of PhaseOnly Correlation Functions under the Phase Fluctuation of Signals due to Additive Gaussian Noise
Shunsuke YAMAKI Kazuhiro FUKUI Masahide ABE Masayuki KAWAMATA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E104A
No.4
pp.671679 Publication Date: 2021/04/01 Publicized: 2020/09/29 Online ISSN: 17451337
DOI: 10.1587/transfun.2020EAP1024 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: phaseonly correlation functions, phase fluctuation, additive Gaussian noise, probability density functions,
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Summary:
This paper proposes statistical analysis of phaseonly correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phasespectrum differences between original signal and its noisecorrupted 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.

