Level-crossing time statistics of Gaussian 1/f~α noises

摘要

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/f~α 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.