On Defining White Noise

Abstract

The mathematical background necessary to rigorously define white noise is detailed. It is shown that it is necessary to accept an arbitrarily small correlation time, and a flat power spectral density approximation over a finite, but arbitrarily large, frequency range, to adequately define a white noise random process consistent with the Wiener-Khintchine relationships. Dichotomous random processes are used to illustrate appropriate principles and problems. The results are generalized to Gaussian white noise.