Efficient nonlinear system identification

System identification of a second order truncated Volterra series with correlated and Gaussian input is investigated. This problem has been treated by Schetzen using Wiener nonlinear theory. In this paper we show how this nonlinear system can be efficient|y identified using Gaussian properties of the input. In a second order Volterra representation there are unknowns elements for the linear kernel and an additional N²unknowns elements representing the second order Volterra kernel. The identification of the system by standard least squares technique require to solve a set of linear equations, or equivalently to invert a matrix of dimension . Using the fact that for Gaussian signals all the higher moments are determined by the first two, we show that the identification of the second order truncated Volterra series can be reduced to an inversion of a matrix of dimension . An additional advantage of the proposed method is that is is applicable to any correlated Gaussian signals; Schetzen method is limited to correlated Gaussian process generated by invertible filters.