Gaussianization of random inputs by filtering plants: The case of poisson white and telegraph processes

It is well known that low-pass filtering plants “harmonize” periodic inputs in the sense that the steady state response in close to harmonic. It has been observed, both experimentally and analytically, that low-pass filters “Gaussianize” some random inputs in the sense that the steady state response is close to being Gaussian. This Technical Note is intended to formalize the notion of Gaussianization and prove that it takes place for two types of input signals: Poisson white noise and telegraph processes. The general case is a subject of future work.