Optimal cumulant domain filtering

This paper presents a new technique which exploits constrained optimization methods to derive optimal two dimensional filters in the cumulant domain for processing signals in non Gaussian noise, or signals with corrupting interferences which have non symmetrical probability density functions. The approach proposed here for enhancing signals in such noise is important, as increasingly practical engineering application areas are identifying occasions where the perceived wisdom of modelling signals in additive Gaussian noise simply does not hold. Since the bispectrum of non Gaussian noise and interference is not zero, it corrupts the bispectrum of the signal. Thus filters that suppress the bispectral component of the noise and enhance the signal bispectrum, are required. The two dimensional filters proposed in this paper have the property of concentrating the filter energy into a hexagonal region in the bispectral domain. This leads to an impulse response for these filters which represents a new form of two dimensional discrete prolate spheroidal sequence. The sensitivity of cumulant determination to non Gaussian noise has been noted in the area of array processing [10]. However this paper presents one of the first attempts to remove non Gaussian noise by cumulant filtering. .