Open Access

Some Results on the Wavelet Packet Decomposition of Nonstationary Processes

EURASIP Journal on Advances in Signal Processing20022002:214797

Received: 20 July 2001

Published: 28 November 2002


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.


waveletswavelet packetscyclostationary processesnon- stationarityhigher order statisticscentral limitasymptotic statistics

Authors’ Affiliations

Equipe Signal pour les Communication, Institut d'électronique et d'informatique Gaspard-Monge and URA 820, Université de Marne-la-Vallée, Marne la Vallée Cédex 2, France


© Touati and Pesquet 2002