METHOD FOR SIGNAL PROCESSING BASED ON KOLMOGOROVWIENER PREDICTION OF MFSD PROCESS

Context. We investigate a method to signal processing based on the Kolmogorov-Wiener filter weight function calculation for the prediction of a continuous stationary heavy-tail process in the MFSD (multifractal fractional sum-difference) model. Such a process may describe telecommunication traffic in some systems with data packet transfer, the consideration of the continuous filter may be reliable in the case of the large amount of data. Objective. The aim of the work is to obtain an approximate solution for the Kolmogorov-Wiener filter weight function and to show the applicability of the method to signal processing used in the paper. Method. The Galerkin method based on the orthogonal Chebyshev polynomials of the first kind is used for the calculation of the weight function under consideration. The approximations up to the thirteen-polynomial one are investigated. The corresponding integrals are calculated numerically on the basis of the Wolfram Mathematica package. The higher is the packet rate, the higher accuracy of the integral calculation is needed. Results. It is shown that for rather large number of polynomials the misalignment between the left-hand side and the right-hand side of the Wiener-Hopf integral equation under consideration is rather small for the obtained solutions. The corresponding mean absolute percentage errors of misalignment for different packet rates are calculated. The method to signal processing used in the paper leads to reliable results for the Kolmogorov-Wiener filter weight function for the prediction of a process in the MFSD model. Conclusions. The theoretical fundamentals of the continuous Kolmogorov-Wiener filter construction for the prediction of a random process in the MFSD model are investigated. The filter weight function is obtained as an approximate solution of the Wiener-Hopf integral equation with the help of the Galerkin method based on the Chebyshev polynomials of the first kind. It is shown that the obtained results for the filter weight function are reliable. The obtained results may be useful for the practical telecommunication traffic prediction. The paper results may also be applied to the treatment of heavy-tail random processes in different fields of knowledge, for example, in agriculture.