Open AccessINVESTIGATION OF THE KOLMOGOROV-WIENER FILTER FOR CONTINUOUS FRACTAL PROCESSES ON THE BASIS OF THE CHEBYSHEV POLYNOMIALS OF THE FIRST KIND
Author(s) -
В. Н. Горев,
Alexander Gusev,
В. І. Корнієнко
Publication year - 2020
Publication title -
informatyka, automatyka, pomiary w gospodarce i ochronie środowiska
Language(s) - English
Resource type - Journals
eISSN - 2391-6761
pISSN - 2083-0157
DOI - 10.35784/iapgos.912
Subject(s) - mathematics , chebyshev polynomials , polynomial , weight function , basis (linear algebra) , fractal , chebyshev nodes , chebyshev equation , chebyshev filter , mathematical analysis , pure mathematics , orthogonal polynomials , classical orthogonal polynomials , geometry
This paper is devoted to the investigation of the Kolmogorov-Wiener filter weight function for continuous fractal processes with a power-law structure function. The corresponding weight function is sought as an approximate solution to the Wiener-Hopf integral equation. The truncated polynomial expansion method is used. The solution is obtained on the basis of the Chebyshev polynomials of the first kind. The results are compared with the results of the authors’ previous investigations devoted to the same problem where other polynomial sets were used. It is shown that different polynomial sets present almost the same behaviour of the solution convergence.