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Décomposition d'un processus stationnaire du second ordre . Propriétés statistiques d'ordre 2 des coefficients d'ondelettes et localisation fréquentielle des paquets d'ondelettes

Abstract : This paper deals with wide-sense stationnary processes analysis through wavelet and wavelet packets decomposition. This study is based on the theory of Stochastic Integral. In the case of band-limited processes (which are those encountered a t most from a praticai point of view), we show that the wavelet packets coefficients are asymptotically uncorrelated random variables, taking into account the wavele t packets regularity and the decomposition level. The relation between this convergence toward uncorrelated random variables and the subspaces frequency local-ization is analysed.
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Dominique Pastor, Roger Gay. Décomposition d'un processus stationnaire du second ordre . Propriétés statistiques d'ordre 2 des coefficients d'ondelettes et localisation fréquentielle des paquets d'ondelettes. Traitement du Signal, Lavoisier, 1995. ⟨hal-02194999⟩

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