Digital filtering and higher order statistics

This paper addresses a new problem in higher order statistics (HOS), that of low pass filtering in the two dimensional cumulant domain which exploits third order statistical based algorithms operating on data where the assumption of additive Gaussian noise to a signal does not hold. The filters presented in this paper concentrate the filter energy into a desired region in the bispectral domain which leads to an impulse response and magnitude squared function for these filters, that represent a new form of two dimensional discrete prolate spheroidal sequence (DPSS) and discrete prolate spheroidal wave function (DPSWF) respectively. The fundamental properties of one dimensional DPSS can be found and their application to one dimensional finite impulse response (FIR) filters in [3,4]. The extension of these techniques to one dimensional infinite impulse response(IIR) filtering was presented by the author and extended to two dimensional filters with circularly symmetric passband.