Generalized Amplitude Truncation of Gaussian 1/f^α Noise : Cross-Disciplinary Physics

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We study a kind of filtering, an amplitude truncation with upper and lower truncate,ion levels x_<max> and x~i*<mix>. This is a generalization of the simple transformation y(t) = sgn[x(t)], for which a rigorous result was obtained recently. So far numerical experiments have shown that a power law spectrum 1/f^α appears to be transformed again into a power law spectrum 1/f^β under rather general condition for the truncation levels. We examine the above numerical results analytically. When 1 <α< 2 and x_<max> = -x_<mix> = a, the transformed spectrum is shown to be characterized by a certain corner frequency f_c which divides the spectrum into two parts with different exponents. We derive f_c depending on a as f_c ~ a^<-2/('α-1)>. It turns out that the output signal should deviate from the power law spectrum when the truncation is asymmetric. We present a numerical example such that 1/f^2 noise converges to 1/f noise by applying the transformation y(t) = sgn[x(t)] repeatedly.
社団法人日本物理学会の論文
2001-01-15