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Symbolic Computation for Parametrized Wavelets in SAGE
Wang Le * #
Beihang University
*Correspondence author
#Submitted by
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Funding: none
Opened online:17 December 2009
Accepted by: none
Citation: Wang Le.Symbolic Computation for Parametrized Wavelets in SAGE[OL]. [17 December 2009] http://en.paper.edu.cn/en_releasepaper/content/37659
 
 
In this paper, author mainly discusses parametrizing filter coefficients for wavelets in the open-source computer algebra system SAGE. We first recall the general ideas of wavelets construction and then we discuss how to solve wavelet design problems by using symbolic methods, in particular Groebner bases, for compactly supported orthonormal wavelets. Second, We make a brief review of the ideas of Regensburger and Scherzer for parametrizing compactly supported orthonormal wavelets by discrete moments and introduce the parametrization procedures for orthonormal wavelets with the corresponding functions defined in SAGE and analyze the solutions by using different reduction order during the symbolic computation. Complete solutions and analysis for parametrized filter coefficients of length eight in the orthonormal case are presented.
Keywords:Compactly supported orthonormal wavelets;Parametrized filter coefficients;Moments;Groebner bases;SAGE
 
 
 

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