Amplitude truncation of Gaussian 1/f(alpha) noises

An interesting experimental fact concerning Gaussian 1/f noise was reported a few years ago: when the noise amplitude is truncated at two levels under rather general conditions, the power spectral density remains the same. In this Letter, we present a theoretical derivation of this invariant propert y of 1/f noise, together with a generalization for Gaussian 1/f(alpha) nois es with 0 < alpha < 2. More specifically, it is proved that when 0 < alpha less than or equal to 1, a transformation of keeping only the sign of 1/f(a lpha) noise, i.e. y(t)= sgn[ x(t>)], leads to the same 1/f(alpha) spectrum. When 1 < alpha < 2, the transformation yields 1/f((alpha+1)/2) noise. Our theoretical results are confirmed by numerical simulations. (C) 2000 Elsevi er Science B.V. All rights reserved.