Lagun I. Methods of effective selection of base functions for time-frequency transformation of signals

The thesis addresses the problems of the effectiveness increasing of the selection of base functions for the processing of different types of one-dimensional signals in the time-frequency (wavelet) domain. In that thesis, it is shown that the efficiency of representing signals in the wavelet domain, their analysis and processing are related to the selection of base functions. The basic methods and algorithms for selecting base functions are defined, in which the selection of optimal wavelets is carried out according to a certain criterion for definite types of signals. Further development methods for assessing the efficiency of the wavelet selection by the criterion for the ratio of the energy of the wavelet coefficients to the entropy of energy distribution of wavelet coefficients, by the criterion for estimating the correlation coefficient and by the information criterion, have been obtained. The universal index of quality of the signal was proposed and substantiated for the first time as a new criterion for selecting a wavelet and the method for selecting base wavelets using a genetic algorithm according to the universal signal quality index criterion was improved. The method of multi-criteria optimization of the selection of base wavelet for the processing of one-dimensional non-periodic signals based on the tools of fuzzy logic has been proposed and developed, which made it possible to improve the efficiency of selection of optimal wavelets. The research of the methods of selecting base wavelet using test signals of the Matlab package has been carried out. The efficiency of the methods for selecting base wavelet was evaluated based on the results of the algorithm denoising signal.