1/f noise from the nonlinear transformations of the variables

Abstract

The origin of the low-frequency noise with power spectrum $1/f^{\beta }$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^{\beta }$ 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 $1/f^{\beta }$ 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 $1/f^{\beta }$ fluctuations is presented.

5 pages, 11 figures

References in corpus (3)

• Review of the Low-Frequency 1/f Noise in Graphene Devices
• 1/f noise: implications for solid-state quantum information
• Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations

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