On the Amplitude and Time‐structure Properties of 1/fα Noises

An interesting invariant property of 1/f noises was found experimentally a few years ago: amplitude truncation does not change the shape of the power spectral density (PSD) under rather general conditions. Later the phenomenon was explained theoretically including extensions to 1/fα noises with 0<α<2 and associated unsolved problems were also presented [1–7]. In this work we present a brief review of our recent results and also report investigations of the amplitude‐truncation and level‐crossing properties of 1/fα noises in more detail. Particularly, we analyze the dependence of the spectral density and successive level‐crossing interval statistics on the level of truncation. From the results of our numerical simulation, it turns out that the case α≈1 is unique in the range from 0 to 2 in two respects. First, 1/f noise is the most sensitive to the level of amplitude truncation when close levels are used. Second, the successive level‐crossing intervals exhibit a correlation maximum for α≈1. These amplitude...