High-order wavelet packets and cumulant field analysis

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.