Time-frequency representations : wavelet packets and optimal decomposition

B. Torresani

Annales de l'I.H.P. Physique théorique (1992)

  • Volume: 56, Issue: 2, page 215-234
  • ISSN: 0246-0211

How to cite

top

Torresani, B.. "Time-frequency representations : wavelet packets and optimal decomposition." Annales de l'I.H.P. Physique théorique 56.2 (1992): 215-234. <http://eudml.org/doc/76566>.

@article{Torresani1992,
author = {Torresani, B.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {time-frequency analysis; information entropy; signal analysis; coherent states systems; wavelets; Gabor functions; minimal-entropy criteria; optimal decomposition},
language = {eng},
number = {2},
pages = {215-234},
publisher = {Gauthier-Villars},
title = {Time-frequency representations : wavelet packets and optimal decomposition},
url = {http://eudml.org/doc/76566},
volume = {56},
year = {1992},
}

TY - JOUR
AU - Torresani, B.
TI - Time-frequency representations : wavelet packets and optimal decomposition
JO - Annales de l'I.H.P. Physique théorique
PY - 1992
PB - Gauthier-Villars
VL - 56
IS - 2
SP - 215
EP - 234
LA - eng
KW - time-frequency analysis; information entropy; signal analysis; coherent states systems; wavelets; Gabor functions; minimal-entropy criteria; optimal decomposition
UR - http://eudml.org/doc/76566
ER -

References

top
  1. [Al-An-Ga] S.T. Ali, J.P. Antoine and J.P. Gazeau, Square Integrable Group Representations on Homogeneous Spaces, I, Preprint UCL-IPT-89-18; II, Preprint UCL-IPT-89-19, Louvain-la-Neuve. 
  2. [Be-Be] J. Bertrand and P. Bertrand, Classification of Affine Wigner Functions via an Extended Covariance Principle, Proc. of the 17th International Colloquium on Group Theoretical Methods in Physics, Sainte ADÈLE, Y. SAINT-AUBIN and L. VINET Ed., World Scientific (1989), pp. 380-383. MR1134841
  3. [Bo] G. Bohnké, Treillis d'ondelettes sur le groupe de Lorentz, Ann. Inst. H. Poincaré, Physique Théorique, Vol. 54, 1991, pp. 245-260. Zbl0743.43005MR1122655
  4. [Ca] A.L. Carey, Square Integrable Representations of Non Unimodular Groups, Bull. Austr. Math. Soc., Vol. 15, 1976, pp. 1-12. Zbl0327.22008MR430146
  5. [Ca] A.P. Calderon, Intermediate Spaces and Interpolation, the Complex Method, Studia Math., Vol. 24, 1964, pp. 113-190 Zbl0204.13703MR167830
  6. [Coh] A. Cohen, Ondelettes, analyses multirésolution et traitement numérique du signal, PhD Thesis, CEREMADE, Université de Paris-Dauphine, 1990. 
  7. [Co-Me] R.R. Coifman and Y.R. Meyer, Nouvelles bases orthomormées de L2 (R) ayant la structure du système de Walsh, Preprint, Yale University, New Haven, 1990. 
  8. [Co-Me-Qu-Wi] R.R. Coifman, Y.R. Meyer, S. Quake and M.V. Wickerhauser, Signal processing and compression with wavelet packets, Preprint, Yale University, New Haven1990. Zbl0818.94005
  9. [Co-Wi] R.R. Coifman and M.V. Wickerhauser, Best Adapted Wave Packet Bases, Preprint, Yale University, NewHaven, 1990. 
  10. [Com-Gr-Tc] J. M. COMBES, A. GROSSMANN and Ph. TCHAMITCHIAN Ed., Wavelets, Time-Frequency Methods and Phase Space, Springer, 1989. MR1010895
  11. [Cor-Fef] A. Cordoba and Fefferman, Wave Packets and Fourier Integral Operators, Comm. Part. Diff. Eq., 3, Vol. 3, 1978, pp. 979-1005. Zbl0389.35046MR507783
  12. [d'A-Bea] C. D'Alessandro and D. Beautemps, Représentation et modification du signal de parole par transformée en ondelettes utilisant des contraintes auditives, Preprint, LIMSI 90-10, Orsay, October 1990. 
  13. [Da 1] I. Daudechies, The Wavelet Transform, Time-Frequency Localisation and Signal Analysis, IEEE Trans, on Information Theory, Vol. 36, 1991, pp. 961-1005. Zbl0738.94004MR1066587
  14. [Da 2] I. Daubechies, Orthonormal Bases of Compactly Supported Wavelets, Comm. Pure Appl. Math., Vol. XLI, 1988, pp. 909-996. Zbl0644.42026MR951745
  15. [Di] J. Dixmier, Les C*-algèbres et leurs représentations, Cahiers Scientifiques, Vol. 29, Gauthier-Villars, 1957. MR171173
  16. [Du-Mo] M. Duflo and C.C. Moore, On the Regular Representation of a Non Unimodular Locally Compact Group, J. Funct. An., Vol. 21, 1976, p. 209. Zbl0317.43013MR393335
  17. [Fe-Grö] H.G. Feichtinger and K.H. Gröchenig, Banach Spaces Related to Integrable Group Representations and their Atomic Decompositions, I, J. Funct. An., Vol. 86, 1989, pp. 307-340; II, Mh. Math., Vol. 108, 1989, pp. 129-148. Zbl0691.46011MR1021139
  18. [Ga] D. Gabor, Theory of Communication, J. Inst. Elec. Eng., Vol. 903, 1946, pp. 429-457. 
  19. [Gr-KM-Mo] A. Grossmann, R. Kronland-Martinet and J. Morlet, Reading and Understanding Continuous Wavelet Transform, in [Com-Gr-Tc]. Zbl0850.42006
  20. [Gr-Mo] A. Grossmann and J. Morlet, Decomposition of Hardy Functions Into Wavelets of Constant Shape, S.LA.M. J. Math. An., Vol. 15, 1984, pp. 723-736. Zbl0578.42007MR747432
  21. [Gr-Mo-Pa 1] A. Grossmann, J. Morlet and T. Paul, Transforms Associated with Square Integrable Group Representations, I, J. Math. Phys., Vol. 27, 1985, pp. 2473-2479; II. Ann. Inst. H. Poincaré, Vol. 45, 1986, pp. 293- 309. Zbl0571.22021MR868528
  22. [Gr-Mo-Pa2] A. Grossmann, J. Morlet and T. Paul, Transforms Associated with Square Integrable Group Representations, II, Ann. Inst. H. Poincaré, Vol. 45, 1986, pp. 293-309. Zbl0601.22001MR868528
  23. [He-Wa] C.E. Heil and D.F. Walnut, Continuous and Discrete Wavelet Transform, S.I.A.M. Rev., Vol. 31, 1989, pp. 628-666. Zbl0683.42031MR1025485
  24. [Ho-Tc] M. Holschneider and Ph. Tchamitchian, Pointwise analysis of Riemann's Nowhere Differentiable Function, Preprint CPT89/P.2274, Invent. Math. (to appear). MR1109624
  25. [Kl-Sk] J.R. Klauder and B.S. Skagerstam, Coherent States, World Scientific, 1985, Singapore. MR826247
  26. [Li] E. Lieb, Some Convexity and Subadditivity Properties of Entropy, Bull. Am. Math. Soc., Vol. 81, 1975, pp. 1-13. Zbl0308.94020MR356797
  27. [Me 1] Y. Meyer, Ondelettes et opérateurs I : Ondelettes, Hermann, Paris, 1989. Zbl0694.41037MR1085487
  28. [Me 2] Y. Meyer, Ondelettes et opérateurs II : Opérateurs de Caldeŕon-Zygmund, Hermann, 1990. Zbl0745.42011MR1085488
  29. [Mu] R. Murenzi, Ondelettes multidimensionnelles et applications à l'analyse d'images, Ph-D Thesis, IPT-UCLLouvain-La-Neuve, 1990 
  30. [Pe] A. Perelomov, Generalized Coherent States and their Applications, Springer Verlag, Berlin, 1986. Zbl0605.22013MR899736
  31. [Sc] W. Schempp, Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory, Longman, 1986. Zbl0632.43001MR872095
  32. [Sh-We] C.E. Shannon and W. Weaver, The Mathematical Theory of Communication, The University of Illinois Press, 1964. Zbl0126.35701MR32134
  33. [Tc-To] Ph. Tchamitchian and B. Torrésani, Ridge and Skeleton Extraction from the Wavelet Transform, in Wavelets and their applications, B. RUSKAI et al. Eds, Jones & Bartlett Publ. Comp., Boston, 1992. Zbl0798.94006
  34. [To 1] B. Torrésani, Wavelets Associated with Representations of the Affine Weyl-Heisenberg Group, J. Math. Phys., Vol. 32, 1991, pp. 1273-1279. Zbl0748.46046MR1103481
  35. [To 2] B. Torrésani, Wavelet Analysis of Asymptotic Signals: Ridge and Skeleton of the Transform, (to appear) in the Proceedings of the 2nd Conference on Wavelet and Applications, 1989, Y. MEYER Ed., Masson, Paris1991. 
  36. [Ve] M. Vetterli, Private communication, 1990. 
  37. [Wi 1] M.V. Wickerhauser, Applications of Wavelets to Signal Compression, Yale University Preprint, Mathematics department, 1990. 
  38. [Wi 2] M.V. Wickerhauser, Picture Compression by Best Basis Sub-Band Coding, Yale University Preprint, Mathematics department, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.