Generalized amplitude truncation of gaussian 1/f(alpha) noise

We study a kind of filtering, an amplitude truncation with upper and lower truncation levels sm, and x(min). This is a generalization of the simple tr ansformation y(t) = sgn[x(t)], for which a rigorous result was obtained rec ently. So far numerical experiments have shown that a power law spectrum 1/ f(alpha) appears to be transformed again into a power law spectrum 1/f(beta ) under rather general condition for the truncation levels. We examine the above numerical results analytically. When 1 < <alpha> < 2 and x(max) = -x( min) = a, the transformed spectrum is shown to be characterized by a certai n corner frequency Sc which divides the spectrum into two parts with differ ent exponents. We derive f(c) depending on a as f(c) <similar to> a(-2/(alp ha -1)). It turns out that the output signal should deviate from the power law spectrum when the truncation is asymmetric. We present a numerical exam ple such that 1/f(2) noise converges to 1/f noise by applying the transform ation y(t) = sgn[x(t)] repeatedly.