Wavelet Packets of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation

The paper addresses the analysis and interpretation of second order random processes by using the wavelet packet transform. It is shown that statistical properties of the wavelet packet coefficients are specific to the filtering sequences characterizing wavelet packet paths. These statistical properties also depend on the wavelet order and the form of the cumulants of the input random process. The analysis performed points out the wavelet packet paths for which stationarization, decorrelation and higher order dependency reduction are effective among the coefficients associated with these paths. This analysis also highlights the presence of singular wavelet packet paths: the paths such that stationarization does not occur and those for which dependency reduction is not expected through successive decompositions. The focus of the paper is on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet packet domain. This is addressed with respect to semi-analytical cumulant expansions for modeling different types of nonstatonarity and correlation structures. The characterization obtained eases the interpretation of random signals and time series with respect to the statistical properties of their coefficients on the different wavelet packet paths.