A general mechanism for the `$1/f$' noise

Abstract

We consider the response of a memoryless nonlinear device that converts an input signal $\xi (t)$ into an output $\eta (t)$ that only depends on the value of the input at the same time, $t$. For input Gaussian noise with power spectrum $1/f^{\alpha }$, the nonlinearity modifies the spectral index of the output to give a spectrum that varies as $1/f^{{\alpha }^{\prime }}$ with ${\alpha }^{\prime }\ne \alpha$. We show that the value of ${\alpha }^{\prime }$ depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous `$1/f$' noise found in nature.

5 pages, 3 figures + 2 page supplementary information