Volume 103, Number 6, September 2013
|Number of page(s)||5|
|Published online||22 October 2013|
Memoryless nonlinear response: A simple mechanism for the 1/f noise
1 School of Physical Sciences, Jawaharlal Nehru University - New Delhi 110 067, India
2 University of Hyderabad - Hyderabad 500 046, India
3 Department of Theoretical Physics, Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 400 005, India
Received: 31 July 2013
Accepted: 16 September 2013
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Ca – Noise / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2013
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