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2004 | 2 | 3 | 399-419
Tytuł artykułu

On the computation of scaling coefficients of Daubechies' wavelets

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
3
Strony
399-419
Opis fizyczny
Daty
wydano
2004-06-01
online
2004-06-01
Twórcy
autor
  • Technical University of Liberec
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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475237
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