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Représentations Temps-Fréquence et Temps-Echelle Bilinéaires: Synthèse et Contributions

Paulo Gonçalves 1
1 RESO - Protocols and softwares for very high-performance network
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : In the first part of this thesis, we present a unified approach to time-frequency and to time-scale analysis. Time-frequency and time-scale representations are multidimensional transformations that indicate the joint time-frequency and joint time-scale content of a signal. Although different in their goals, both the time-frequency and the time-scale tools can be expressed in terms of unitary groups representations based on particular covariance operators on the time-frequency plane. Thus, the time-frequency distributions of the Cohen's class, which correspond to the Weyl-Heisenberg group, are naturally covariant to time and frequency shifts, whereas the time-scale distributions of the affine class, which correspond to the affine algebraic group, are covariant to time shifts and to scale changes. Moreover, by means of unitary equivalence, it is possible to generate classes of distributions that are covariant to other displacement operators of the time-frequency plane. In the second part, we present a new approach for generating bilinear signal representations based on the geometry of cross-terms that arise from the quadratic structure of the distributions. Using geometrical rules and parity operators, we derive a class of affine-localized distributions. Finally, we emphasize the role of time-scale analysis in several applications, including Doppler radar and sonar processing, 1/f spectral estimation, and characterization of processes exhibiting scaling law organization. In particular, signal singularities, described by Hölder exponents, can be easily revealed and estimated by affine distributions when the scale dependence of these tools matches the self-similarity properties of the processes.
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https://tel.archives-ouvertes.fr/tel-00572335
Contributor : Paulo Gonçalves <>
Submitted on : Tuesday, March 1, 2011 - 11:33:07 AM
Last modification on : Friday, September 11, 2020 - 6:10:04 PM
Long-term archiving on: : Monday, May 30, 2011 - 2:55:15 AM

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Paulo Gonçalves. Représentations Temps-Fréquence et Temps-Echelle Bilinéaires: Synthèse et Contributions. Traitement du signal et de l'image [eess.SP]. Institut National Polytechnique de Grenoble - INPG, 1993. Français. ⟨tel-00572335⟩

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