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Wavelet packets with uniform time-frequency localization. (English) Zbl 1015.42026
Summary: 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.

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
Full Text: DOI
[1] L. Borup, M. Nielsen, Approximation with brushlet systems, J. Approx. Theory, to appear · Zbl 1038.42032
[2] Cohen, A.; Séré, E., Time-frequency localization with non-stationary wavelet packets, (), 189-211
[3] Coifman, R.R.; Meyer, Y.; Wickerhauser, V., Size properties of wavelet-packets, (), 453-470 · Zbl 0822.42019
[4] Daubechies, I.; Jaffard, S.; Journé, J.-L., A simple Wilson orthonormal basis with exponential decay, SIAM J. math. anal, 22, 554-573, (1991) · Zbl 0754.46016
[5] Goodman, T.N.T.; Lee, S.L.; Tang, W.S., Wavelets in wandering subspaces, Trans. amer. math. soc, 338, 639-654, (1993) · Zbl 0777.41011
[6] Hess-Nielsen, N., Control of frequency spreading of wavelet packets, Appl. comput. harmon. anal, 1, 2, 157-168, (1994) · Zbl 0798.42019
[7] Laeng, E., Une base orthonormale de \( L\^{}\{2\}(R)\) 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, 31, 11, 677-680, (1990) · Zbl 0711.42033
[8] Meyer, Y., Wavelets: algorithms and applications, (1993), SIAM
[9] Meyer, F.G.; Coifman, R.R., Brushlets: a tool for directional image analysis and image compression, Appl. comput. harmon. anal, 4, 147-187, (1997) · Zbl 0879.68117
[10] Nielsen, M.; Zhou, D.-X., Mean size of wavelet packets, Appl. comput. harmon. anal, 13, 22-34, (2002) · Zbl 1011.42020
[11] Séré, E., Localisation fréquentielle des paquets d’ondelettes, Rev. mat. iberoamericana, 11, 2, 334-354, (1995) · Zbl 0829.42024
[12] Villemoes, L.F., Adapted bases of time-frequency local cosines, Appl. comput. harmon. anal, 10, 139-162, (2001) · Zbl 1161.94319
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