Open Access

Some Results on the Wavelet Packet Decomposition of Nonstationary Processes

EURASIP Journal on Advances in Signal Processing20022002:214797

https://doi.org/10.1155/S1110865702207040

Received: 20 July 2001

Published: 28 November 2002

Abstract

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.

Keywords

wavelets wavelet packets cyclostationary processes non- stationarity higher order statistics central limit asymptotic statistics

Authors’ Affiliations

(1)
Equipe Signal pour les Communication, Institut d'électronique et d'informatique Gaspard-Monge and URA 820, Université de Marne-la-Vallée

Copyright

© Touati and Pesquet 2002