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  • Title: Relation between optimal nonlinearity and non-Gaussian noise: enhancing a weak signal in a nonlinear system.
    Author: Ichiki A, Tadokoro Y.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2013 Jan; 87(1):012124. PubMed ID: 23410300.
    Abstract:
    In the study of stochastic resonance, it is often mentioned that nonlinearity can enhance a weak signal embedded in noise. In order to give a systematic proof of the signal enhancement in nonlinear systems, we derive an optimal nonlinearity that maximizes a signal-to-noise ratio (SNR). The obtained optimal nonlinearity yields the maximum unbiased signal estimation performance, which is known in the context of information theory. It is found that a linear system is optimal for a Gaussian noise, but for a non-Gaussian noise, there exist nonlinear systems that can achieve an SNR higher than that obtained from linear systems. This analysis refers to a system subjected to an additive non-Gaussian noise with a small signal input.
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