Central Limit theorems for wavelet packet decompositions of stationary random processes

Authors:
Abdourrahmane M. Atto;Dominique Pastor
Affiliations:
Institut TELECOM-TELECOM Bretagne, Université Européenne de Bretagne, Brest Cedex 3, France;Institut TELECOM-TELECOM Bretagne, Université Européenne de Bretagne, Brest Cedex 3, France
Venue:
IEEE Transactions on Signal Processing
Year:
2010

Citing 6
Cited 1

Ten lectures on wavelets

Ten lectures on wavelets
Cardinal spline filters: stability and convergence to the ideal sinc interpolator

Signal Processing
Review: On the statistical decorrelation of the wavelet packet coefficients of a band-limited wide-sense stationary random process

Signal Processing
Some results on the wavelet packet decomposition of nonstationary processes

EURASIP Journal on Applied Signal Processing
High-order wavelet packets and cumulant field analysis

IEEE Transactions on Information Theory
Noise Covariance Properties in Dual-Tree Wavelet Decompositions

IEEE Transactions on Information Theory

Wavelet packets of fractional Brownian motion: asymptotic analysis and spectrum estimation

IEEE Transactions on Information Theory

Quantified Score

Hi-index	35.74

Visualization

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 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.