On the Asymptotic Decorrelation of the Wavelet Packet Coefcients of a Wide-Sense Stationary Random Process

Abstract Consider the wavelet packet coefcients issued from the decomposition of a random process stationary in the wide-sense. We address the asymptotic behaviour of the autocorre-lation of these wavelet packet coefcients. In a rst step, we explain why this analysis is more intricate than that already achieved by several authors in the case of the standard discrete orthonormal wavelet decomposition. In a second step, it is shown that the autocorrelation of the wavelet packet coefcients can be rendered arbitrarily small provided that both the decomposition level and the regularity of the quadrature mirror lters are large enough. I