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.
- Received 22 May 2012
DOI:https://doi.org/10.1103/PhysRevE.87.012124
©2013 American Physical Society