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

В. Н. Горев | Zendy; Alexander Gusev | Zendy; В. І. Корнієнко | Zendy

Open Access

INVESTIGATION 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 , basis (linear algebra) , chebyshev nodes , weight function , fractal , chebyshev equation , mathematical analysis , chebyshev filter , orthogonal polynomials , pure mathematics , 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.

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