1/f noise from nonlinear stochastic differential equations

TL;DR

This paper derives 1/f^b noise power spectra directly from nonlinear stochastic differential equations, expanding understanding of their origin and providing a broader class of models that generate such noise.

Contribution

It presents a direct derivation of 1/f^b noise spectra from stochastic differential equations, avoiding point process models and expanding the theoretical framework.

Findings

Power spectrum can be represented as a sum of Lorentzian spectra

Derivation provides justification for equations generating 1/f^b noise

Expands class of equations capable of producing 1/f^b noise

Abstract

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f^b noise, and provides further insights into the origin of 1/f^b noise.