On the computation of scaling coefficients of Daubechies' wavelets

• Autorzy: Dana Černá , Václav Finěk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Daubechies' wavelets; computation of scaling coefficients; 65T60

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 3
• Strony: 399-419

Daty

wydano

2004-06-01

online

2004-06-01

Twórcy

autor

Dana Černá

• Technical University of Liberec

autor

Václav Finěk

• Dresden University of Technology

Bibliografia

• [1] B. Han: “Analysis and construction of optimal multivariate biortogonal wavelets with compact support”,SIAM J. Math. Anal., Vol. 31, (2000), pp. 274–304. http://dx.doi.org/10.1137/S0036141098336418
• [2] B. Han: “Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets”,J. Approx. Theory,Vol. 110, (2001),pp. 18–53. http://dx.doi.org/10.1006/jath.2000.3545
• [3] B. Han: “Symmetric multivariate orthogonal refinable functions”,Appl. Comput. Harmon. Anal., to appear.
• [4] A. Cohen and R.D. Ryan:Wavelets and Multiscale Signal Processing, Chapman & Hall, London, 1995.
• [5] A. Cohen: “Wavelet methods in numerical analysis”, In: P.G. Ciarlet et al. (Eds.):Handbook of numerical analysis, Vol. VII, Amsterdam: North-Holland/Elsevier, 2000, pp. 417–711.
• [6] I. Daubechies:Ten Lectures on Wavelets. Society for industrial and applied mathematics, Philadelphia, 1992.
• [7] V. Finěk:Approximation properties of wavelets and relations among scaling moments II, Preprint, TU Dresden, 2003.
• [8] W. Lawton: “Necessary and sufficient conditions for constructing orthonormal wavelet bases”,J. Math. Phys., Vol. 32, (1991), pp. 57–61. http://dx.doi.org/10.1063/1.529093
• [9] A.K. Louis, P. Maass and A. Rieder:Wavelets: Theorie und Anwendungen, B.G. Teubner, Stuttgart, 1994.
• [10] G. Polya and G. Szegö:Aufgaben und Lehrsätze aus der Analysis, Vol. II, Springer-Verlag, Berlin, 1971.
• [11] W.C. Shann and C.C. Yen: “On the exampleact values of the orthogonal scaling coefficients of lenghts 8 and 10”,Appl. Comput. Harmon. Anal., Vol. 6, (1999), pp 109–112. http://dx.doi.org/10.1006/acha.1997.0240
• [12] G. Strang and T. Nguyen:Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996.
• [13] P. Wojtaszczyk:A Mathematical introduction to wavelets, Cambridge University Press, 1997.

Identyfikatory

DOI

10.2478/BF02475237