Quelques représentations d'un polynôme et leurs applications en traitement du signal
Some polynomial representations and the associated applications
OPEN ACCESS
Three representations associated with a polynomial are presented, giving algorithms that allow us to determine them as well as the main associated applications. The first ones have a direct link with the study of the stability of linear filters and the third one with the time-frequency analysis of polynomial phase signals.
Résumé
Nous exposons dans cet article trois représentations associées à un polynôme en donnant des algorithmes qui permettent de les déterminer ainsi que les principales applications associées . Les deux premières, sont en rapport direct avec l'étude de la stabilité des filtres dynamiques et la troisième avec l'analyse temps-fréquence des signaux à phase polynômiale.
Polynomial, filter, stability, continued fraction, lattice representation, time-frequency analysis, generalized ambiguity function, generalized Wigner-Ville distribution
Mots clés
Polynôme, filtre dynamique, stabilité, fraction continue, représentation en treillis, analyse temps-fréquence, fonction ambiguïté généralisée, Distribution de Wigner-Ville généralisée
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