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

Domenii publicaţii > Stiinte ingineresti + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Atto, A, Pastor, D and Isar, A

Editorial: Elsevier, Signal Processing, Elsevier, vol. 87, Issue 10, p.2320-2335, 2007.


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 [-pi, pi].
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.

Cuvinte cheie: prelucrarea semnalelor // signal processing