Comptes Rendus
Wavelet packets with uniform time-frequency localization
[Paquets d'ondelettes avec localisation temps-fréquentielle uniforme]
Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 793-796.

Nous construisons des paquets d'ondelettes de base uniformément bien localisés en temps et en fréquences. Les bases orthonormées correspondantes de paquets d'ondelettes sons parametrisées par des partitions dyadiques obeissants une condition de variation locale.

We construct basic wavelet packets with uniformly bounded localization in both time and frequency. The corresponding orthonormal bases of wavelet packets are parametrized by dyadic segmentations obeying a local variation condition.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02570-0

Lars F. Villemoes 1

1 Coding Technologies, Döbelnsgatan 64, 11352 Stockholm, Sweden
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Lars F. Villemoes. Wavelet packets with uniform time-frequency localization. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 793-796. doi : 10.1016/S1631-073X(02)02570-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02570-0/

[1] L. Borup, M. Nielsen, Approximation with brushlet systems, J. Approx. Theory, to appear

[2] A. Cohen; E. Séré Time-frequency localization with non-stationary wavelet packets (M.T. Smith; A. Akansu, eds.), Subband and Wavelet Transforms — Theory and Design, Kluwer Academic, 1996, pp. 189-211

[3] R.R. Coifman; Y. Meyer; V. Wickerhauser Size properties of wavelet-packets, Wavelets and Their Applications, Jones and Bartlett, Boston, MA, 1992, pp. 453-470

[4] I. Daubechies; S. Jaffard; J.-L. Journé A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal, Volume 22 (1991), pp. 554-573

[5] T.N.T. Goodman; S.L. Lee; W.S. Tang Wavelets in wandering subspaces, Trans. Amer. Math. Soc, Volume 338 (1993), pp. 639-654

[6] N. Hess-Nielsen Control of frequency spreading of wavelet packets, Appl. Comput. Harmon. Anal, Volume 1 (1994) no. 2, pp. 157-168

[7] E. Laeng Une base orthonormale de L 2 () dont les éléments sont bien localisés dans l'espace de phase et leurs supports adaptés à toute partition symétrique de l'espace des fréquences, C. R. Acad. Sci. Paris, Série I, Volume 31 (1990) no. 11, pp. 677-680

[8] Y. Meyer Wavelets: Algorithms and Applications, SIAM, 1993

[9] F.G. Meyer; R.R. Coifman Brushlets: a tool for directional image analysis and image compression, Appl. Comput. Harmon. Anal, Volume 4 (1997), pp. 147-187

[10] M. Nielsen; D.-X. Zhou Mean size of wavelet packets, Appl. Comput. Harmon. Anal, Volume 13 (2002), pp. 22-34

[11] E. Séré Localisation fréquentielle des paquets d'ondelettes, Rev. Mat. Iberoamericana, Volume 11 (1995) no. 2, pp. 334-354

[12] L.F. Villemoes Adapted bases of time-frequency local cosines, Appl. Comput. Harmon. Anal, Volume 10 (2001), pp. 139-162

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