On the exact values of coefficients of coiflets
- 155 Downloads
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.
Keywordsorthonormal wavelet coiflet exact value of filter coefficients
Unable to display preview. Download preview PDF.
- Adams W.W., Loustaunau P., An Introduction to Gröbner Bases, American Mathematical Society, 1994Google Scholar
- Bittner K., Urban K., Adaptive wavelet methods using semiorthogonal spline wavelets: Sparse evaluation of nonlinear functions, preprintGoogle Scholar
- Buchberger B., An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal, PhD thesis, University of Inssbruck, Austria, 1965 (in German)Google Scholar
- Burrus C.S., Gopinath R.A., On the moments of the scaling function ψ 0, Proceedings of the ISCAS-92, 1992, 963–966Google Scholar
- Tian J., The mathematical theory and applications of biorthogonal Coifman wavelet systems, Ph.D. thesis, Rice University, Houston, TX, 1996Google Scholar
- Tian J., Wells R.O. Jr., Vanishing moments and biorthogonal Coifman wavelet systems, Proceedings of 4th International Conference on Mathematics in Signal Processing, University of Warwick, England, 1997Google Scholar
- Tian J., Wells R.O. Jr., Vanishing moments and wavelet approximation, Technical Report, CML TR95-01, Rice University, January 1995Google Scholar