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hal-00241849, version 2

Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

Abdourrahmane Atto () 1, Dominique Pastor () 1

IEEE Transactions on Signal Processing (2008) 1-12

Abstract: This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the $M$-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency.

  • 1:  Traitement Algorithmique et Matériel de la Communication, de l'Information et de la Connaissance (TAMCIC)
  • CNRS : UMR2872 – Ecole Nationale Supérieure des Télécommunications de Bretagne
  • Domain : Mathematics/Information Theory
    Computer Science/Information Theory and Coding
  • Keywords : Wavelet transforms – Band-limited stochastic processes – Spectral analysis
  • Comment : Submitted to the IEEE Transactions on Signal Processing – October~2008
  • Available versions :  v1 (2008-02-06) v2 (2008-02-12) v3 (2009-04-17)
 
  • hal-00241849, version 2
  • http://hal.archives-ouvertes.fr/hal-00241849
  • oai:hal.archives-ouvertes.fr:hal-00241849
  • From: Abdourrahmane Mahamane Atto <>
  • Submitted on: Tuesday, 12 February 2008 11:28:40
  • Updated on: Friday, 17 April 2009 09:45:47