Abstract
The optimal nonlinearity for readout a weak signal embedded in strong noise is investigated. In practical devices, a high signal-to-noise ratio (SNR) is preferred more than the Bayesian estimation, which generally requires complicated calculations. The optimal nonlinearity is determined by the noise statistics including its temporal correlations, and provides the highest SNR. According to the result, the existence of nonlinear devices that exhibit SNR higher than linear devices is shown under non-Gaussian noise. In contrast, linear devices exhibit the highest SNR in the presence of Gaussian noise. Using the resultant nonlinearity, the Cramér–Rao lower bound is realized by an easy linear estimator. Our derivation of the optimal characteristics of the filter gives the criterion to designed practical devices in the presence of noise.
