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

Author： Chand Yadav Avinash Ramaswamy Ramakrishna Dhar Deepak

E-ISSN： 1286-4854|103|6|60004-60004

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.103, Iss.6, 2013-10, pp. : 60004-60004

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Abstract

Discovering the mechanism underlying the ubiquity of “$1/f^{\alpha}$ ” 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 $1/f^{\alpha'}$ , when fed to an element with such a response function R, gives an output $R(S(t))$ that can have a power spectrum $1/f^{\alpha}$ with $\alpha < \alpha$ '. As an illustrative example, we show that an input Brownian noise $(\alpha'=2)$ acting on a device with a sigmoidal response function $R(S)= \text{sgn}(S)|S|^x$ , with x < 1, produces an output with $\alpha = 3/2 +x$ , for $0 \leq x \leq 1/2$ . Our discussion is easily extended to more general types of input noise as well as more general response functions.