Investigation of the Kolmogorov–Wiener filter for treatment of fractal processes on the basis of the Chebyshev polynomials of the second kind
Vyacheslav N. Gorev, Alexander Gusev, В. І. Корнієнко · 2019
We consider the Kolmorogov-Wiener filter for continuous fractal processes with a power-law structure function.The corresponding filter is used for data forecast; the noiseless case is considered.The aim of the paper is to obtain the weight function for the corresponding filter based on the integral Wiener-Hopf equation.The problem under consideration is important, for example, for traffic forecast in telecommunication systems and for the forecast of the chemical composition of cast iron.An exact analytical solution for the corresponding equation meets difficulties, so an approximate solution is sought in the form of a truncated Chebyshev polynomial expansion.The Chebyshev polynomials of the second kind are used.The behavior of the polynomial solutions for different numbers of polynomials is investigated.The results are compared with the corresponding results of our previous paper where another polynomial set is used.It is found that the corresponding behavior is almost identical for different polynomial sets.