In many applications it is necessary to characterize the statistical proper
ties of the wavelet/wavelet packet coefficients of a stationary random sign
al. In particular, in a stationary non-Gaussian noise scenario it may be us
eful to determine the high-order statistics of the wavelet packet coefficie
nts. In this work we prove that this task may be performed through multidim
ensional filter banks, In particular, we show how the cumulants of the M-ba
nd wavelet packet coefficients of a strictly stationary signal are derived
from those of the signal and we provide scale-recursive decomposition and r
econstruction formulae to compute these cumulants, High-order wavelet packe
ts, associated with these multidimensional filter banks, are presented alon
g with some of their properties. It is proved that under some conditions th
ese high-order wavelet packets allow us to define frame multiresolution ana
lyses, Finally, the asymptotic normality of the coefficients is studied by
showing the geometric decay of their polyspectra/cumulants (of order greate
r than two) with respect to the resolution level.