# On the exact values of coefficients of coiflets

Open Mathematics (2008)

• Volume: 6, Issue: 1, page 159-169
• ISSN: 2391-5455

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## Abstract

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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 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.

## How to cite

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Dana Černá, Václav Finěk, and Karel Najzar. "On the exact values of coefficients of coiflets." Open Mathematics 6.1 (2008): 159-169. <http://eudml.org/doc/269141>.

@article{DanaČerná2008,
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.},
author = {Dana Černá, Václav Finěk, Karel Najzar},
journal = {Open Mathematics},
keywords = {orthonormal wavelet; coiflet; exact value of filter coefficients; numerical examples},
language = {eng},
number = {1},
pages = {159-169},
title = {On the exact values of coefficients of coiflets},
url = {http://eudml.org/doc/269141},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Dana Černá
AU - Václav Finěk
AU - Karel Najzar
TI - On the exact values of coefficients of coiflets
JO - Open Mathematics
PY - 2008
VL - 6
IS - 1
SP - 159
EP - 169
AB - 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.
LA - eng
KW - orthonormal wavelet; coiflet; exact value of filter coefficients; numerical examples
UR - http://eudml.org/doc/269141
ER -

## References

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