The Equivalent Gain Matrix of a Multivariable Non-Linearity

Abstract

The equivalent gain concept of a mono-variable non-linear stochastic process is used to evaluate the linear matrix equivalent of a multi-variable non-linearity having n independent inputs and m outputs. It is shown that if the n inputs are restricted to separable class of processes (which includes Gaussian random signals and also sinusoidal wave forms but is much wider), then the distortion terms produced by the non-linearity and by cross modulation have zero cross-correlation with any of the input signals.