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Some Results on the Wavelet Packet Decomposition of Nonstationary Processes

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.

Author information

Correspondence to Sami Touati.

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Keywords

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