Wide-sense stationnary random processes analysis through wavelet packets decomposition. Statistical properties of wavelet coefficients

摘要

This paper deals with wide—sense stationnary processes analysis through waveletudand wavelet packets decomposition. This study is based on the theory of StochasticudIntegral. In the case of band—limited processes (which are those encountered a tudmost from a praticai point of view), we show that the wavelet packets coefficien tudara asymptotically uncorrelated random variables, taking into account the wavele tudpackets regularity and the decomposition level . The relation between this convergenceudtoward uncorrelated random variables and the subspaces frequency localizationudis analysed.