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Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2009

Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

Résumé

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.
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Dates et versions

hal-00241849 , version 1 (06-02-2008)
hal-00241849 , version 2 (12-02-2008)
hal-00241849 , version 3 (17-04-2009)

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Citer

Abdourrahmane Atto, Dominique Pastor. Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes. IEEE Transactions on Signal Processing, 2009, 58 (2), pp.896-901. ⟨10.1109/TSP.2009.2031726⟩. ⟨hal-00241849v3⟩
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