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            <title xml:lang="en">*Wide-sense Stationnary Random Processe s Analysis through Wavelet Packets Decomposition. Statistical Properties of Wavelet Coefficients.</title>
            <title xml:lang="fr">Décomposition d'un processus stationnaire du second ordre . Propriétés statistiques d'ordre 2 des coefficients d'ondelettes et localisation fréquentielle des paquets d'ondelettes</title>
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                <forename type="first">Dominique</forename>
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                <title xml:lang="en">*Wide-sense Stationnary Random Processe s Analysis through Wavelet Packets Decomposition. Statistical Properties of Wavelet Coefficients.</title>
                <title xml:lang="fr">Décomposition d'un processus stationnaire du second ordre . Propriétés statistiques d'ordre 2 des coefficients d'ondelettes et localisation fréquentielle des paquets d'ondelettes</title>
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                <term xml:lang="en">intégrale stochastique</term>
                <term xml:lang="en">localisation fréquentielle des paquets d'ondelettes</term>
                <term xml:lang="en">propriétés statistiques des coefficients d'ondelettes</term>
                <term xml:lang="en">processus aléatoires stationnaires au sens large</term>
                <term xml:lang="en">processus aléatoires</term>
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              <p>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.</p>
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              <p>Dans cet article, nous étudions la décomposition en ondelettes et en paquet s d'ondelettes des processus aléatoires stationnaires au sens large. Le cadre choisi pour l'exposition est celui de l'intégrale stochastique. Dans le cas des processus à bande limitée, qui sont ceux rencontrés dans la pratique, nous étudions le comportement asymptotique des moments d'ordre 1 et 2 des suites des coefficient s d'ondelettes, en donnant les conditions de convergence de ces suites vers de s séquences blanches en fonction de la régularité et du niveau de décomposition. Le lien étroit entre ces résultats et la localisation fréquentielle des paquets d'ondelettes est analysée.</p>
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