title: Relation between optimal nonlinearity and non-Gaussian noise: enhancing a weak signal in a nonlinear system.
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.
authors: Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan. aichiki@mosk.tytlabs.co.jp
authors: Akihisa
authors: A
authors: Ichiki
authors: Yukihiro
authors: Y
authors: Tadokoro
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution