Statistics of1fNoise

Abstract

Probability amplitude distributions of $\frac{1}{f}$ noise and Nyquist noise in a 8 Hz-to-10 kHz band are examined using a multichannel plus-heigh analyzer. Both types of noise obey a normal distribution law in all sample lengths investigated, 100, 10, and 1.0 sec. In the case of $\frac{1}{f}$ noise, the variance of the distribution itself fluctuates in identical sample intervals. The distribution of variances appears to be from an exponential population. The difference between Nyquist-noise and $\frac{1}{f}$-noise data suggests that the latter is not stationary in the statistical sense, but rather possesses a weaker form of stationarity.