Investigating Advantages and Disadvantages of the Analysis of a Geometrical Surface Structure with the Use of Fourier and Wavelet Transform

Abstract

Nowadays a geometrical surface structure is usually e valuated with the use of Fourier transform. This type of transform allows for accurate analysis of harmonic components of surface profiles. Due to its funda mentals, Fourier transform is particularly efficient when eval uating periodic signals. Wavelets are the small waves that are oscillatory and limited in the range. Wavelets ar e special type of sets of basis functions that are useful in the description of function spaces. They are particularly useful for the description of non-continuous and irregular functions that appear most often as responses of real physical systems. Bases of wavelet functions are usually well located in the frequency and in the time domain. In the case of periodic signals, the Fourier transform is still extremely useful. It allows to obtain accurate inform ation on the analyzed surface. Wavelet analysis does not provide as accurate information about the measured surface as the Fourier tra nsform, but it is a useful tool for detection of irregularities of the profile. Therefore , wavelet analysis is the better way to detect scratches or cracks that sometimes occur on the surface. The pape r presents the fundamentals of both types of transform. It presents also the comparison of an evaluation of the roundness profile by Fourier and wavelet transforms.