Journal of Physical Mathematics

On the Exact Values of Daubechies Wavelets

Hajji MA

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Abstract

In this paper we propose an algorithm for the calculation of the exact values of compactly-supported Daubechies wavelet functions. The algorithm is iterative, performing a single convolution operation at each step. It requires solving, at the first step only, a linear system of a relatively small size. The novelty of the algorithm is that once the values at dyadic points at a certain level j are calculated they do not need to be updated at the next step. We find that this algorithm is superior to the well-known cascade algorithm proposed by Ingrid Daubechies. This algorithm can serve well in wavelet based methods for the numerical solutions of differential equations. The algorithm is tested on Daubechies scaling functions as well as Daubechies coiflets. Comparison with the values obtained using the cascade algorithm is made. We found that the cascade algorithm results converge to ours.

Article information

Source
J. Phys. Math., Volume 7, Number 1 (2016), 6 pages.

Dates
First available in Project Euclid: 31 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.jpm/1504144875

Digital Object Identifier
doi:10.4172/2090-0902.1000157

Keywords
Daubechies wavelets Daubechies coiflets multiresolution analysis the cascade algorithm convolution

Citation

MA, Hajji. On the Exact Values of Daubechies Wavelets. J. Phys. Math. 7 (2016), no. 1, 6 pages. doi:10.4172/2090-0902.1000157. https://projecteuclid.org/euclid.jpm/1504144875


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