Bussgang Gaussianity test for stationary series

In this contribution we develop a procedure for deciding whether a finite segment of a signal can be considered as a realization of a Gaussian process or not. We first present the theoretical bases leading to the formulation of the Bussgang test. A novel test based on the sign nonlinearity is introduced and its performance analysed in comparison with two simple Gaussianity tests presented in the literature. The results have shown a very promising behaviour of the suggested method in the presence of small amount of available data in both the cases of white and correlated samples.