General Approach to Building the Methods of Filtering Based on the Minimum Duration Principle

摘要

A new general approach to building the filtering methods has been created on the basis of minimum duration principle. A class of filtering methods for noisy fixed signals was developed within the framework of this approach. The specified class depends on three freely adjustable parameters and includes the known methods of averaging, median, myriad, and meridian filtering. The efficiency of the proposed approach is achieved by the adjustment of free parameters to their optimal values that depend on the noise scale (dispersion), magnitude of the weight of tails and distribution law waveforms. The general statement and partial statements of the problem of filtering the noisy fixed signal were formulated for a discrete case. The above statements were presented in the form of appropriate optimization problems. Numerical simulation results for the filtering problem of fixed signal distorted by the Gaussian, Laplace, Cauchy noises and mixtures of these noises were also presented.