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Level-crossing time statistics of Gaussian 1/fα noises

It has been recently shown that the amplitude truncation of Gaussian 1/f noise does not change the shape of the power spectral density under rather general conditions, including the case when a Heaviside transformation results in a dichotomous noise. This invariance of 1/f noise seems to be an important addition to the knowledge about this kind of noise and may be promising in understanding dichotomous 1/f noise, noise-driven switching and stepping. Probably the most important application is the explanation of ion channel currents in biomembranes. In this work we have extended our investigations, especially concerning the level crossing properties of 1/f noises. We determined the level crossing time statistics for 1/fα noises (0<α<2) and found an empirical formula for the level-crossing time distribution. The correlation properties of successive level crossing intervals are also explored by measurements and numerical simulations and it is shown that the case α=1 is unique in the range from 0 to 2. These time structure related additions to the knowledge about 1/f noise further emphasize the uniqueness of this kind of noise. These results may help to understand 1/f noises better and are strongly relevant to 1/f noise driven switching, dichotomous noises such as the case of ion channel current fluctuations.