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  • Research Article
  • 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:


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.


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

Authors’ Affiliations

Equipe Signal pour les Communication, Institut d'électronique et d'informatique Gaspard-Monge and URA 820, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs sur Marne, Marne la Vallée Cédex 2, 77 454, France


© Touati and Pesquet 2002