Gaussian and Golden Wavelets: A Comparative Study and their Applications in Structural Health Monitoring

F. E. Gossler, B. R. Oliveira, M. A. Q. Duarte, J. Vieira Filho, F. Villarreal, R. L. Lamblém

Abstract


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.


Keywords


Gaussian wavelets; Golden wavelets; Vanishing moments; Structural Health Monitoring

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DOI: https://doi.org/10.5540/tcam.2021.022.01.00139

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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