Frequency estimate for symmetric and asymmetric structure of spectral components of sampled harmonic signal

DOI: 10.34759/trd-2023-129-15

Аuthors

Alrubei M. A.^*, Pozdnyakov A. D.^**

State University named after Alexander and Nikolay Stoletovs, 87, Gorky str. Vladimir, 600000, Russia

*e-mail: inj.moh3@atu.edu.iq
**e-mail: 11alexpozd@mail.ru

Abstract

A sampled harmonic signal frequency estimating is an important task while signal processing in many applications such as radio communications, monitoring and control systems and others. Discrete spectra may be employed to measure frequencies of the sine signal components. The said measurement consists in digitizing the composite signal, performing window processing of the signal samples and cpmputing their discrete amplitude spectrum, usually using a fast Fourier transform algorithm. However, the frequency of a sine component can be determined with improved resolution using the moment method of the largest consecutive element of the spectrum corresponding to this component. The abscissa of its maximum represents the best frequency approximation.

An algorithm for the frequency estimating of a sampled harmonic signal of limited duration by the method of moments is proposed, which allows obtaining a weighted average estimate of the energy spectrum peak position. The methodological component of the error depends on the degree of closeness of the frequency true value and the energy center position, due to the type of window function. The error is being determined by the step of the fast Fourier transform (FFT) frequency grid, the type of the window function used, and duration of the signal sampling interval. The article shows a noticeable effect of the even and odd structure of the spectral lines being accounted for. In the symmetry region of the even spectrum structure, when the levels of the principal components change, a jump in the methodological error is formed, which can be eliminated by introducing correction or limiting the operating frequency range to the region of odd symmetry. The authors propose introducing an estimate of the spectrum structure into the algorithm and automatically select an even number of spectral lines for the spectrum close to even symmetry and an odd number for odd symmetry to compute frequency. The maximum methodological error can be reduced herewith by an order of magnitude or more. Some windows allow increasing the frequency measurement resolution by more than an order of magnitude. The purpose of this article is to show as well that even better results are achieved using the Chebyshev window. This method has been employed to set up measurement systems in control and management systems.

Keywords:

frequency, harmonic signal, frequency estimation methods, reading, error, spectrum, asymmetric structure, fast Fourier transform, moment method

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