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.comDnipro 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 kindReferences
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Authors
Vyacheslav Gorevlordjainor@gmail.com
Dnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-9528-9497
Authors
Alexander GusevDnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-0548-728X
Authors
Valerii KorniienkoDnipro University of Technology, Department of Information Security and Telecommunications Ukraine
http://orcid.org/0000-0002-0800-3359
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