NONLINEAR SIGNAL DETECTION IN THE TIME DOMAIN: LEVEL CROSSING STATISTICS AND NOISE-MEDIATED MINIMIZATION OF THE MEASUREMENT ERROR

We study the problem of detecting a small de signal by quantifying its effect on the mean difference AT in residence times in the stable steady states of a bistable dynamical measurement device, in the presence of a noise-floor and a known time-sinusoidal bias signal. Errors in the measurement process occur due to a finite observation time that is present in most practical scenarios; in turn, noise degrades the measurement. Adjusting the bias signal amplitude to a slightly subthreshold operating regime, leads to a nonmonotonic dependence of the (suitably defined) error on the noise intensity; at a critical noise intensity, the error is minimized. This phenomenon, reminiscent of the well-known Stochastic Resonance effect [1-4], appears to be most pronounced for subthreshold bias signals in the strongly nonlinear response regime. The results can be applied to a variety of nonlinear systems, including neurons, that operate in the time-domain.