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

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

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

Cited by

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

Authors

Vyacheslav Gorev 
lordjainor@gmail.com
Dnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-9528-9497

Authors

Alexander Gusev 

Dnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-0548-728X

Authors

Valerii Korniienko 

Dnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-0800-3359

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