The complete length sixteen parametrized wavelets

In this paper, a complete parametrization of the length sixteen wavelets is given for the dilation coefficients of the trigonometric polynomials, , that satisfy the necessary conditions for orthogonality, that is, and . This parametrization has seven free parameters and has a simple compatibility wi...

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Bibliographic Details
Published inSampling theory, signal processing, and data analysis Vol. 23; no. 2
Main Author Roach, David
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Subjects
Abstract Harmonic Analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Paper
Signal,Image and Speech Processing
Dilation equation coefficients
Wavelets
Parametrization
C30
Discrete
Finite length
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Summary:In this paper, a complete parametrization of the length sixteen wavelets is given for the dilation coefficients of the trigonometric polynomials, , that satisfy the necessary conditions for orthogonality, that is, and . This parametrization has seven free parameters and has a simple compatibility with the shorter length parametrizations for some specific choices of the free parameters. This construction is a more efficient representation than the work of Schneid and Pittner who were the first to give a general technique for the construction of any finite length orthogonal wavelet parametrization in [Schneid, Computing 51 , 1993]. These wavelets have varying numbers of vanishing moments and regularity, and continuously transform from one to the other with the perturbation of the free parameters.    
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-025-00109-0