Signal analysis performed during surface texture measurement frequently involves applying the Fourier transform. The method is particularly useful for assessing roundness and cylindrical profiles. Since the wavelet transform is becoming a common tool for signal analysis in many metrological applications, it is vital to evaluate its suitability for surface texture profiles. The research presented in this paper focused on signal decomposition and reconstruction during roundness profile measurement and the effect of these processes on the changes in selected roundness profile parameters. The calculations were carried out on a sample of 100 roundness profiles for 12 different forms of mother wavelets using MATLAB. The use of Spearman's rank correlation coefficients allowed us to evaluate the relationship between the two chosen criteria for selecting the optimal mother wavelet.

Nowadays a geometrical surface structure is usually evaluated with the use of Fourier transform. This type of transform allows for accurate analysis of harmonic components of surface profiles. Due to its fundamentals, Fourier transform is particularly efficient when evaluating periodic signals. Wavelets are the small waves that are oscillatory and limited in the range. Wavelets are 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 information on the analyzed surface. Wavelet analysis does not provide as accurate information about the measured surface as the Fourier transform, 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 paper 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.