Bussgang theorem

In mathematics, the Bussgang theorem is a theorem of . The theorem states that the crosscorrelation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the Massachusetts Institute of Technology.

Let ${\displaystyle \left\{X(t)\right\}}$ be a zero-mean stationary Gaussian random process and ${\displaystyle \left\{Y(t)\right\}=g(X(t))}$ where ${\displaystyle g(\cdot )}$ is a nonlinear amplitude distortion.

...
Wikipedia