Why Daubechies wavelets are so successful

Authors

Solymar Ayala Cortez, The University of Texas at El PasoFollow
Laxman Bokati, The University of Texas at El PasoFollow
Aaron Velasco, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-1-2021

Comments

Technical Report: UTEP-CS-21-62a

To appear in Journal of Intelligent and Fuzzy Systems

Abstract

In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families of wavelets. In this paper, we provide a possible theoretical explanation for the empirical success of Daubechies wavelets. Specifically, we show that these wavelets are optimal with respect to any optimality criterion that satisfies the natural properties of scale- and shift-invariance.