The response of a non-linear system to random noise

A formula for the auto-correlation function of the output of a nonlinear system, the input being random Gaussian noise, has been given in the literature for the case where the non-linear output/input relation is expressed as a power series. This formula can be simplified; the new version emphasizes the fact that intermodulation products of different orders are uncorrelated, but that contributions to the intermodulation product of a given order from different terms of the power series are completely correlated. If the output is expressed as a series of Hermite polynomial functions of the input, rather than as a power series, each term of the series gives rise to intermodulation products of one order only.