Wavelet Transforms of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation
Résumé
The paper presents some statistical properties of the wavelet transforms, in the framework of nonstationary random processes. It investigates the factors that make wavelet subband coefficients behave as stationary discrete sequences. Conditions are given under which stationarization, decorrelation and higher order dependency reduction occur among the wavelet coefficients of a large class of nonstationary random processes. The paper also highlights the presence of singular paths, i.e. the paths such that no stationarization occurs and those for which no dependency reduction are expected through successive decompositions. The overall presentation focuses on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet domain. This is performed with respect to semi-analytical expansions of cumulants for modeling different types of correlation structures that characterize many random processes.
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