A METHOD OF ANALYSIS OF DEPENDENCE BETWEEN SAMPLING RATE OF SIGNAL AND ITS APPROXIMATION USING INTERPOLATION ANALOGUES

DOI: 10.31673/2409-7292.2026.010962

Abstract

Modern digital signal processing is very useful and productive field of IT. Nowadays methods of this field are
used in solving of a number of problems in data science, artificial intelligence, economics and other spheres of human
activity. As research of last years shows, special interest is concentrated on some groups of methods of digital signal
processing, one of which is a group of methods, what are based on Fourier analysis. Especially last research demonstrate
an interest to operators, generated by linear summation methods of Fourier series, and its interpolation analogues. This
class of methods in context of digital signal processing allows to solve tasks, related with signals approximation, signal
filtering and some other aspects of signals analysis. In other hand, some of these methods are well studied in context of
Fourier analysis and approximation theory, what allows to make general understanding of possibilities and specifics if its
usage in context of digital signal processing. Despite it, there is a number of aspects, specific for digital signal processing,
what must be studied but are usually ignored by researchers. One of these aspects is dependence between a sampling rate
of considered signal and accuracy of approximation of this signal using interpolation analogue of some operator, generated
by linear summation method of Fourier series. This work demonstrates a method of studying this dependence and shows
an its usage for interpolation analogues of Fejer operators and Abel-Poisson operators. As experiments show, described
method of analysis of dependence between sampling rate of considered signal and interpolation analogues have hidden
relation with convergence of operators, which interpolation analogue is used, what allows to predict a sampling rate, what
is sufficient to guarantee needed accuracy of approximation of a signal.
Keywords: Fourier analysis, DSP, approximation, linear summation, signals analysis.

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