Ocena wp?ywu metodyki doboru falki bazowej na analiz? falkow? zarysów nierówno?ci powierzchni

摘要

The paper deals with one of the most important problems of the wavelet analysis - the methodology of selection of basic wavelets. Correct selection of the basic wavelet (so-called the mother wavelet) allows distinguishing the main signal and removal of signal disturbances. This problem is fundamental because the basic function form influences significantly the spectrum components. In metrological practice, there are no criteria that could be used for selection of the mother wavelet. Such decision is usually taken on a basis of the fundamental of visual evaluation of an analyzed signal. In the paper there are described three criteria that can be used for selection of the basic wavelets: the statistical test of autocorrelation of the coefficients of the decomposition details [3, 4], values of the normalized cross-correlation function [5, 6] and minimisation of the Shannon entropy [1,7]. The calculations were performed with use of Wavelet toolbox - the component of the Matlab environment, for a selected roughness profile. The investigations were carried out for the roughness profile consisting of N=1024 sampling points using following wavelet types: Haar, Daubechies, Coiflets, Symlet and biorthogonal ones. The calculation results are given in Table 1. The authors draw a conclusion from them that the most promising criterion is investigation of the entropy values (however, other methods should not be neglected). The reason is that the method of entropy minimisation is not limited to one decomposition only, but it allows searching an optimum decomposition tree, applying multilevel analysis by the wavelet packets.%W referacie przedstawiono jedno z wa?niejszych zagadnień analizy lalkowej, a mianowicie metodyk? doboru postaci falki bazowej. W tre?ci zaprezentowano metodyk? i wyniki obliczeń dla sygna?u reprezentuj?cego zarys nierówno?ci powierzchni z wykorzystaniem trzech kryteriów doboru falki: testu autokorelacji, funkcji korelacji wzajemnej i procedury z wykorzystaniem wska?ników entropii. Obliczenia i wykresy wykonano z wykorzystaniem pakietu Wavelet toolbox ?rodowiska MATLAB dla wybranego profilu chropowato?ci powierzchni.