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

Chand Yadav, Avinash ; Ramaswamy, Ramakrishna ; Dhar, Deepak (2013) Memoryless nonlinear response: a simple mechanism for the 1/f noise EPL (Europhysics Letters), 103 (6). p. 60004. ISSN 0295-5075

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

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Deposited On:04 Jun 2015 09:13
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