Central European Journal of Mathematics

, Volume 6, Issue 1, pp 159–169

# On the exact values of coefficients of coiflets

• Dana Černá
• Václav Finěk
• Karel Najzar
Research Article

## 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.

## Keywords

orthonormal wavelet coiflet exact value of filter coefficients

65T60

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