PHYSICS AND MATHEMATICS

Approximation and interpolation of wave signals in the basis of bordering functions in the study of mechanical and other physical fields

A. V. Sedov<sup>ab

a</sup> South-Russian State Polytechnic University named M. I. Platov
^b Southern Research Center of the Russian Academy of Sciences, Rostov-on-Don

Abstract: A formula for trigonometric approximation and interpolation of signals based on the bordering functions is proposed, which simplifies the process of modeling and reconstructing changes of wave signals from measured samples. Proposed modifications of the formula for simultaneous parallel filtering of signals based on the use of families of new bordering and filtering functions. The advantages of using the proposed approach and formulas over the known ones are shown. The interrelation of the formula with the known sampling theorem of is shown.

Keywords: trigonometric approximation, bordering functions, parallel filtering, sampling theorem, wave signals.

Received: 19.12.2018

DOI: 10.23670/IRJ.2018.78.12.008

 English version: DOI: 10.23670/IRJ.2018.78.12.008