INVESTIGATION OF THE KOLMOGOROV-WIENER FILTER FOR CONTINUOUS FRACTAL PROCESSES ON THE BASIS OF THE CHEBYSHEV POLYNOMIALS OF THE FIRST KIND


Abstract

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.


Keywords

continuous fractal processes; Kolmogorov–Wiener filter weight function; Chebyshev polynomials of the first kind

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Published : 2020-03-30


Gorev, V., Gusev, A., & Korniienko, V. (2020). INVESTIGATION OF THE KOLMOGOROV-WIENER FILTER FOR CONTINUOUS FRACTAL PROCESSES ON THE BASIS OF THE CHEBYSHEV POLYNOMIALS OF THE FIRST KIND. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 10(1), 58-61. https://doi.org/10.35784/iapgos.912

Vyacheslav Gorev  lordjainor@gmail.com
Dnipro University of Technology, Department of Information Security and Telecommunications  Ukraine
http://orcid.org/0000-0002-9528-9497
Alexander Gusev 
Dnipro University of Technology, Department of Information Security and Telecommunications  Ukraine
http://orcid.org/0000-0002-0548-728X
Valerii Korniienko 
Dnipro University of Technology, Department of Information Security and Telecommunications  Ukraine
http://orcid.org/0000-0002-0800-3359