What is it about?
In this work, a comparative analysis between Gaussian and Golden wavelets is presented. These wavelets are generated by the derivative of specific base functions. In this case, the order of the derivative also indicates the number of vanishing moments of the wavelet. Although these wavelets have a similar waveform, they have several distinct characteristics in time and frequency domains. These distinctions are explored here in the scale space. In order to compare the results provided by these wavelets for a real signal, they are used in the decomposition of a signal inserted in the context of structural health monitoring.
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Why is it important?
Wavelet analysis is a powerfull mathematical tool for several areas of science and engineering. There are several problems in different areas that can be explored and solved using this theory. Defined in a simple way, wavelets are analysis functions that satisfy certain conditions, mostly used in the Wavelet Transform (WT)
Perspectives
Since Gaussian and Golden wavelets have very similar waveforms, the differences from the results obtained in the application show that not only the wavelet waveform should be taken into account, but also its time-frequency resolution. It is clear from the application shown in this paper, since the difference in results between gausN and goldN is quite evident, although they have very similar waveforms. Preliminary results show that the detection of transients or singularities present in the signals can be performed more efficiently with Golden wavelets. It can also be explained by the fact that Golden wavelets have good resolution in time domain.
Bruno Rodrigues de Oliveira
Pantanal Editora
Read the Original
This page is a summary of: Gaussian and Golden Wavelets: A Comparative Study and their Applications in Structural Health Monitoring, Trends in Computational and Applied Mathematics, March 2021, Brazilian Society for Computational and Applied Mathematics (SBMAC),
DOI: 10.5540/tcam.2021.022.01.00139.
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