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Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness Read chapter Read first chapter

2017 | OriginalPaper | Chapter

The Complete Length Twelve Parametrized Wavelets

Author : David W. Roach

Published in: Approximation Theory XV: San Antonio 2016

Publisher: Springer International Publishing

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Abstract

In this paper, a complete parametrization of the length twelve wavelets is given for the dilation coefficients of the trigonometric polynomials, \(m(\omega )\), that satisfy the necessary conditions for orthogonality, that is \(m(0)=\sqrt{2}\) and \(|m(\omega )|^2+|m(\omega +\pi )|^2=2\). This parametrization has five free parameters and has a simple compatibility with the shorter length parametrizations for some specific choices of the free parameters. These wavelets have varying numbers of vanishing moments and regularity, but continuously transform from one to the other with the perturbation of the free parameters. Finally, we graph some example scaling functions from the parametrization which includes the standard Daubechies wavelets and some new wavelets that perform better than the CDF biorthogonal 9/7 wavelet in an image compression experiment on some fingerprint images.

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previous chapter A Fractional Spline Collocation Method for the Fractional-order Logistic Equation
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Metadata
Title
The Complete Length Twelve Parametrized Wavelets
Author
David W. Roach
Copyright Year
2017
Book
Approximation Theory XV: San Antonio 2016

Print ISBN: 978-3-319-59911-3

Electronic ISBN: 978-3-319-59912-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-59912-0_16

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