Why Daubechies wavelets are so successful

Author:

Cortez Solymar Ayala1,Bokati Laxman2,Velasco Aaron1,Kreinovich Vladik3

Affiliation:

1. Department of Geological Sciences, University of Texas at El Paso, 500 W. University, El Paso, TX, USA

2. Computational Science Program, University of Texasat El Paso, 500 W. University, El Paso, TX, USA

3. Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, USA

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.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

Reference13 articles.

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3. A real-time earthquake detector with prefiltering bywavelets;Botella;Computers & Geosciences,2003

4. Daubechies wavelets inquality of electrical power, Athens,Greece;Brito;Proceedings of the 8thInternational Conference on Harmonics and Quality of Power,1998

5. Burrus C. , Gopinath R. , Guo H. Introduction toWavelets and Wavelet Transforms: A Primer, Prentice Hall, Upper Saddle Rover, New Jersey (1997).

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