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1/f noise from the nonlinear transformations of the variables (1512.04298v1)
Published 14 Dec 2015 in physics.data-an
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.