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

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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 non--trivial 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)= (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.