Comparison of various methods of digital signal processing based on atomic functions.

The paper considers various methods of digital signal processing. The article contains several sections that consistently reveal the stated task. Each section contains a description of the completed subtask and conclusions on this part of the work. The first part of the work contains the generation of test signals consisting of sums of elementary harmonics, jumps and other nonlinear effects. After that, these signals are processed using a window Fourier transform and spectrograms are constructed to evaluate the time–frequency and phase representation of the signal. In the second part, the Meyer wavelet is constructed based on a class of atomic functions, the main stages are supported by illustrations. The obtained atomic wavelet is compared with known analogues by calculating uncertainty constants. With the help of the received wavelet, a continuous wavelet transform (CWT) of the test signals is performed, after which the obtained waveletograms are compared with the spectrograms from the previous section. The third part of the work is devoted to Synchrosqueezed Wavelet Transforms (SSQ CWT), which provides the best time–frequency localization, as well as comparisons with the results from the previous parts of the work. In the final part of the article, the application of these methods for processing various real signals of a mechanical nature obtained experimentally from a sensor is considered. The analysis of the obtained results is carried out, on the basis of which a method of signal processing of this type is proposed. Based on the results of signal processing, conclusions are drawn about the course of the physical processes of the mechanical system corresponding to the signals. Calculations are performed in python using standard libraries. [ABSTRACT FROM AUTHOR]