Displaying similar documents to “Approximation properties of wavelets and relations among scaling moments II”

On the computation of scaling coefficients of Daubechies' wavelets

Dana Černá, Václav Finěk (2004)

Open Mathematics

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In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.

On the exact values of coefficients of coiflets

Dana Černá, Václav Finěk, Karel Najzar (2008)

Open Mathematics

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In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling...

Wavelets generated by the Rudin-Shapiro polynomials

Abdolaziz Abdollahi, Jahangir Cheshmavar, Mohsen Taghavi (2011)

Open Mathematics

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In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

Quadrature formulas based on the scaling function

Václav Finěk (2005)

Applications of Mathematics

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The scaling function corresponding to the Daubechies wavelet with two vanishing moments is used to derive new quadrature formulas. This scaling function has the smallest support among all orthonormal scaling functions with the properties M 2 = M 1 2 and M 0 = 1 . So, in this sense, its choice is optimal. Numerical examples are given.