Level-crossing time statistics of Gaussian 1/fª noises

Robert Mingesz; Zoltan Gingl; Peter Makra

doi:10.1117/12.496960

30 April 2003 Level-crossing time statistics of Gaussian 1/f^α noises

Robert Mingesz, Zoltan Gingl, Peter Makra

Proceedings Volume 5110, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems; (2003) https://doi.org/10.1117/12.496960
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

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.

Citation Download Citation

Robert Mingesz, Zoltan Gingl, and Peter Makra "Level-crossing time statistics of Gaussian 1/f^α noises", Proc. SPIE 5110, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems, (30 April 2003); https://doi.org/10.1117/12.496960

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