Some Results on Noise Through Circuits

The object of this paper is to give some novel analyses of noise statistics. Specifically, the zero crossing problem is analyzed for non-stationary noise, and some features of the envelope of noise are established. The theory underlying the formulation of the average number of times a noise, possibly not stationary, attains some specified value is given in some detail. The crossing rate for the non-stationary noise consisting of the sum of a stationary Gaussian noise and a determinate signal is found in terms of a rather simple integral. The integral is evaluated and approximated for such determinate signals as video pulse trains and sine waves. The following two properties of the envelope of noise are proved: (1) the mean square output of an envelope detector is twice the mean square input (independent of the statistics of the input), and (2) the derivative of the envelope of Gaussian noise has a Gaussian first probability distribution.