Memoryless nonlinear response: A simple mechanism for the 1/f noise

Abstract

Discovering the mechanism underlying the ubiquity of “” noise has been a long-standing problem. The wide range of systems in which the fluctuations show the implied long-time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a memoryless nonlinear response suffices to explain the observed nontrivial values of α: a random input noisy signal S(t) with a power spectrum varying as , when fed to an element with such a response function R, gives an output that can have a power spectrum with . As an illustrative example, we show that an input Brownian noise acting on a device with a sigmoidal response function , with x < 1, produces an output with , for . Our discussion is easily extended to more general types of input noise as well as more general response functions.