The Methods of Choice the Wavelets for One Dimensional Signals Processing

Abstract

The paper describes the problems of the effectiveness increasing in the selection of base functions for the processing of different types of one-dimensional signals in the wavelet domain. The efficiency of representing signals in the wavelet domain has been shown; their analysis and processing are related to the choice of base functions. The basic methods and algorithms for selecting base functions are defined, in which the choice of optimal wavelets has been carried out according to a particular criterion for certain types of signals. Methods have been presented for assessing the efficiency of the choice of base wavelets by the criterion for the ratio of the energy of the wavelet coefficients to the entropy of energy distribution of wavelet coefficients, the criterion for estimating the correlation coefficient, and the information criterion. The universal index of quality of the signal has been proposed and substantiated for the first time as a new criterion for choosing a wavelet and the method has been improved for the choice of base wavelets using a genetic algorithm according to the universal signal quality index criterion. The method of multi-criteria optimization of the choice of base wavelet for the processing one-dimensional nonperiodic signals based on the tools of fuzzy logic has been proposed and developed, which made it possible to improve the efficiency of signal processing.