%0 Journal Article
%T Some Results on the Wavelet Packet Decomposition of Nonstationary Processes
%A Jean-Christophe Pesquet
%A Sami Touati
%J EURASIP Journal on Advances in Signal Processing
%D 2002
%I Springer
%R 10.1155/s1687617202207040
%X Wavelet/wavelet packet decomposition has become a very useful tool in describing nonstationary processes. Important examples of nonstationary processes encountered in practice are cyclostationary processes or almost-cyclostationary processes. In this paper, we study the statistical properties of the wavelet packet decomposition of a large class of nonstationary processes, including in particular cyclostationary and almost-cyclostationary processes. We first investigate in a general framework, the existence and some properties of the cumulants of wavelet packet coefficients. We then study more precisely the almost-cyclostationary case, and determine the asymptotic distributions of wavelet packet coefficients. Finally, we particularize some of our results in the cyclostationary case before providing some illustrative simulations.
%K wavelets
%K wavelet packets
%K cyclostationary processes
%K non- stationarity
%K higher order statistics
%K central limit
%K asymptotic statistics.
%U http://dx.doi.org/10.1155/S1110865702207040