Ten lectures on wavelets
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
On the Use of Wavelet Packets in Ultra Wideband Pulse Shape Modulation Systems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Some results on the wavelet packet decomposition of nonstationary processes
EURASIP Journal on Applied Signal Processing
Exploiting the synergies of circular simplex turbo block coding and wavelet packet modulation
MILCOM'03 Proceedings of the 2003 IEEE conference on Military communications - Volume II
A wavelet-based KL-like expansion for wide-sense stationary randomprocesses
IEEE Transactions on Signal Processing
Multiresolution representations using the autocorrelation functionsof compactly supported wavelets
IEEE Transactions on Signal Processing
Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets
IEEE Transactions on Signal Processing
High-order wavelet packets and cumulant field analysis
IEEE Transactions on Information Theory
Asymptotic decorrelation of between-Scale Wavelet coefficients
IEEE Transactions on Information Theory
Entropy-based algorithms for best basis selection
IEEE Transactions on Information Theory - Part 2
Correlation structure of the discrete wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Wavelet analysis and synthesis of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
On the correlation structure of the wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Central Limit theorems for wavelet packet decompositions of stationary random processes
IEEE Transactions on Signal Processing
Wavelet packets of fractional Brownian motion: asymptotic analysis and spectrum estimation
IEEE Transactions on Information Theory
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This paper is a contribution to the analysis of the statistical correlation of the wavelet packet coefficients resulting from the decomposition of a random process, stationary in the wide-sense, whose power spectral density (PSD) is bounded with support in [-@p,@p]. Consider two quadrature mirror filters (QMF) that depend on a parameter r, such that these filters tend almost everywhere to the Shannon QMF when r increases. The parameter r is called the order of the QMF under consideration. The order of the Daubechies filters (resp. the Battle-Lemarie filters) is the number of vanishing moments of the wavelet function (resp. the spline order of the scaling function). Given any decomposition path in the wavelet packet tree, the wavelet packet coefficients are proved to decorrelate for every packet associated with a large enough resolution level, provided that the QMF order is large enough and above a value that depends on this wavelet packet. Another consequence of our derivation is that, when the coefficients associated with a given wavelet packet are approximately decorrelated, the value of the autocorrelation function of these coefficients at lag 0 is close to the value taken by the PSD of the decomposed process at a specific point. This specific point depends on the path followed in the wavelet packet tree to attain the wavelet packet under consideration. Some simulations highlight the good quality of the ''whitening'' effect that can be obtained in practical cases.