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arXiv · 1512.04298

1/f noise from the nonlinear transformations of the variables

B. Kaulakys·M. Alaburda·J. Ruseckas
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Abstract

The origin of the low-frequency noise with power spectrum $1/f^β$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^β$ noise have been proposed and analyzed. Here we use the self-similarity properties of this model with respect to the nonlinear transformations of the variable of these equations and show that $1/f^β$ noise of the observable may yield from the power-law transformations of well-known standard processes, like the Brownian motion, Bessel and similar stochastic processes. Analytical and numerical investigations of such techniques for modeling processes with $1/f^β$ fluctuations is presented.

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B. Kaulakys, M. Alaburda, J. Ruseckas. 2015-12-14. 1/f noise from the nonlinear transformations of the variables. https://doi.org/10.1142/s0217984915502231

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