A dynamical system exhibits high signal-to-noise ratio gain by stochastic resonance

On the basis of mixed-signal simulations, we demonstrate that signal-to-noise ratio (SNR) gains much greater than unity can be obtained in the double-well potential through stochastic resonance (SR) with a symmetric periodic pulse train as deterministic and Gaussian white noise as random excitation. We also show that significant SNR improvement is possible in this system even for a sub-threshold sinusoid input if, instead of the commonly used narrowband SNR, we apply an equally simple but much more realistic wide-band SNR definition. Using the latter result as an argument, we draw attention to the fact that the choice of the measure to reflect signal quality is critical with regard to the extent of signal improvement observed, and urge reconsideration of the practice prevalent in SR studies that most often the narrow-band SNR is used to characterise SR. Finally, we pose some questions concerning the possibilities of applying SNR improvement in practical set-ups.