1/f noise from the nonlinear transformations of the variables

TL;DR

This paper demonstrates that 1/f^β noise can originate from nonlinear transformations of standard stochastic processes like Brownian motion, providing analytical and numerical insights into modeling flicker noise.

Contribution

It reveals that 1/f^β noise can be generated through power-law transformations of well-known stochastic processes, expanding understanding of flicker noise origins.

Findings

1/f^β noise can result from nonlinear transformations of standard processes.

Analytical and numerical methods confirm the generation of flicker noise.

Self-similarity properties are key to understanding the noise's origin.

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.