A Theoretical Explanation for the Efficiency of Generalized Harmonic Wavelets in Engineering and Seismic Spectral Analysis

Authors

Michael Beer, Leibniz University HannoverFollow
Afshin Gholamy, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2019

Comments

Technical Report: UTEP-CS-19-26

Abstract

Wavelets of different shapes are known to be very efficient in many data processing problems. In many engineering applications, the most efficient shapes are shapes of a generalized harmonic wavelet, i.e., a wavelet of the shape w(t) = t^a * exp(b * t) for complex b. Similar functions are empirically the most successful in the seismic analysis -- namely, in simulating the earthquake-related high-frequency ground motion. In this paper, we provide a theoretical explanation for the empirical success of these models.