Amplitude truncation of Gaussian 1/f(alpha) noises: Results and problems

An interesting property of Gaussian 1/f noise was found experimentally a fe w years ago: The amplitude truncation does not change the power spectral de nsity of the noise under rather general conditions. Here we present a brief theoretical derivation of this invariant property of band-limited Gaussian 1/f noise and include 1/f(alpha) noises also with 0 less than or equal to alpha <2. It is shown that when alpha less than or equal to1, a transformat ion of keeping only the sign of the zero-mean 1/f(alpha) noise does not alt er the shape of the spectral density. The theoretical results are extended to truncation levels differing significantly from the mean value. Numerical simulation results are also presented to draw attention to unsolved proble ms of amplitude truncation using asymmetric levels. (C) 2001 American Insti tute of Physics.