P.А. Моrоzоv1, R.А. Аniкin2, V.А. Pеtrov3

1–3 Yaroslavl Higher Military School of Air Defense (Yaroslavl, Russia)

1 mpa24@mail.ru, 2 anik-roman@mail.ru, 3 Peter.viacheslav@yandex.ru

This article discusses the choice of sampling frequency of an analog periodic signal with a limited spectrum at which there is no error when restoring from the received samples. As is known, the choice of sampling frequency is established by Kotelnikov's theorem, but its formulation in choosing the lowest sampling frequency does not indicate whether it refers to periodic or non-periodic signals. The relevance of the article is due to insufficient attention in this theoretical issue, since for periodic signals, the choice of the minimum sampling frequency is critically important due to the discrete nature of the signal spectrum.

The authors of this article have established a criterion for choosing the minimum sampling frequency for periodic signals with a limited spectrum at which there is no error when restoring an analog signal from the received samples.

In this paper, the authors used mathematical models of periodic discrete signals, Fourier transforms, integral calculus and the properties of the delta function.

In the course of the study, for a periodic signal, the process of its recovery from samples obtained by sampling with a sampling frequency equal to twice the upper frequency in the signal spectrum is analyzed. The original signal and the reconstructed one from the samples are presented in harmonic decomposition. A comparison of the received signals unambiguously gives an answer to the questions raised about the magnitude of the recovery error and ways to eliminate it. As a result of the calculations, the conditions imposed on the initial phase of the upper frequency harmonic are found at which there is no recovery error, and the maximum recovery error value is also found. The obtained calculation results show that the maximum recovery error does not exceed the amplitude of the upper frequency harmonic.

Thus, the resulting decomposition of the restored signal by harmonics allows you to specify the conditions under which there is no recovery error. Based on this, the authors propose the choice of the minimum sampling frequency, taking into account the minimum of samples on the signal period, at which there is no recovery error at an arbitrary initial phase of the upper frequency harmonic.

Morozov P.A., Anikin R.I., Petrov V.A. Features of sampling frequency selection according to Kotelnikov's theorem for periodic signals with a limited spectrum. Information-measuring and Control Systems. 2024. V. 22. № 1. P. 65−71. DOI: https://doi.org/10.18127/j20700814-202401-07 (in Russian)

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