Some results on the wavelet packet decomposition of nonstationary processes
EURASIP Journal on Applied Signal Processing
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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In many applications it is necessary to characterize the statistical properties of the wavelet/wavelet packet coefficients of a stationary random signal. In particular, in a stationary non-Gaussian noise scenario it may be useful to determine the high-order statistics of the wavelet packet coefficients. In this work we prove that this task may be performed through multidimensional filter banks. In particular, we show how the cumulants of the M-band wavelet packet coefficients of a strictly stationary signal are derived from those of the signal and we provide scale-recursive decomposition and reconstruction formulae to compute these cumulants. High-order wavelet packets, associated with these multidimensional filter banks, are presented along with some of their properties. It is proved that under some conditions these high-order wavelet packets allow us to define frame multiresolution analyses. Finally, the asymptotic normality of the coefficients is studied by showing the geometric decay of their polyspectra/cumulants (of order greater than two) with respect to the resolution level