Signal-to-noise ratio gain in non-dynamical and dynamical bistable stochastic resonators

it has recently been reported that in some systems showing stochastic resonance, the signal-to-noise ratio (SNR) at the output can significantly exceed that at the input; in other words, SNR gain is possible. We took two such systems, the non-dynamical Schmitt trigger and the dynamical double well potential, and using numerical and mixed-signal simulation techniques, we examined what SNR gains these systems can provide. In the non-linear response limit, we obtained SNR gains much greater than unity for both systems. In addition to the classical narrow-band SNR definition, we also measured the ratio of the total power of the signal to the power of the noise part, and it showed even better signal improvement. Here we present a brief review of our results, and scrutinise, for both the Schmitt-trigger and the double well potential, the behaviour of the SNR gain by stochastic resonance for different signal amplitudes and duty cycles. We also discuss the mechanism of providing gains greater than unity.