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On the exact values of coefficients of coiflets

  • Research Article
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Central European Journal of Mathematics

Abstract

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 coefficients of coiflets up to length 8 and two further with length 12. Furthermore for scaling coefficients of coiflets up to length 14 we obtain two quadratic equations, which can be transformed into a polynomial of degree 4 for which there is an algebraic formula to solve them.

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Authors and Affiliations

  1. Department of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, Liberec 1, 461 17, Czech Republic

    Dana Černá & Václav Finěk

  2. Department of Numerical Mathematics, Charles University, Prague Ke Karlovu 3, Prague 2, 121 16, Czech Republic

    Karel Najzar

Authors
  1. Dana Černá
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  2. Václav Finěk
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  3. Karel Najzar
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Correspondence to Dana Černá.

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Černá, D., Finěk, V. & Najzar, K. On the exact values of coefficients of coiflets. centr.eur.j.math. 6, 159–169 (2008). https://doi.org/10.2478/s11533-008-0011-2

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  • DOI: https://doi.org/10.2478/s11533-008-0011-2

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