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.
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