Statistical analysis of the quasi-harmonic signal’s phase by method of moments as a tool of signal’s parameters estimation

Yakovleva T.V.
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The paper presents the results of theoretical investigation of the peculiarities of the quasi-harmonic signal’s phase statistical distribution, while the quasi-harmonic signal is formed as a result of the Gaussian noise impact on the initially harmonic signal. The revealed features of the phase distribution became a basis for the original technique elaborated for estimating the parameters of the initial, undistorted signal. It has been shown that the task of estimation of the initial phase value can be efficiently solved by calculating the magnitude of the mathematical expectation of the results of the phase sampled measurements, while for solving the task of estimation of the second parameter — the signal level respectively to the noise level — the dependence of the phase sampled measurements variance upon the sough-for parameter is proposed to be used. For solving this task the analytical formulas having been obtained in explicit form for the moments of lower orders of the phase distribution, are applied. A new approach to quasi-harmonic signal’s parameters estimation based on the method of moments has been developed and substantiated. In particular, the application of this method ensures a high-precision measuring the amplitude characteristics of a signal by means of the phase measurements only. The numerical results obtained by means of conducted computer simulation of the elaborated technique confirm both the theoretical conclusions and the method’s efficiency. The existence and the uniqueness of the task solution by the method of moments is substantiated. It is shown that the function that describes the dependence of the phase second central moment on the sough-for parameter, is a monotonically decreasing and thus the single-valued function. The developed method may be of interest for solving a wide range of scientific and applied tasks, connected with the necessity of estimation of both the signal level and the phase value, in such areas as data processing in systems of medical diagnostic visualization, radio-signals processing, radio-physics, optics, radio-navigation and metrology.

Keywords: quasi-harmonic signal, Gaussian noise, signal-to-noise ratio, method of moments, dispersion, second central moment, cumulative distribution function, probability density function
Citation in English: Yakovleva T.V. Statistical analysis of the quasi-harmonic signal’s phase by method of moments as a tool of signal’s parameters estimation // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1037-1049
Citation in English: Yakovleva T.V. Statistical analysis of the quasi-harmonic signal’s phase by method of moments as a tool of signal’s parameters estimation // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1037-1049
DOI: 10.20537/2076-7633-2025-17-6-1037-1049
URL: http://crm-en.ics.org.ru/journal/article/3665/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Yakovleva T.V.

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