Signal-to-noise ratio gain in stochastic resonators driven by coloured noises

摘要

We studied two non-dynamical stochastic resonators, the level-crossing detector (LCD) and the Schmitt trigger, driven by a periodic pulse train plus 1/f~κ-type coloured noises, and we have examined the dependence of the SNR gain maxima on the spectral exponent κ of the random excitation. We have found, in accordance with what previous studies predict for the output SNR in non-dynamical systems, that the correlation only degrades the SNR gain: greater noise amplitudes are required for the gain to peak if we increase the spectral exponent. We have observed that the two different kinds of SNR gains we used, the narrow-band and the wide-band gain, describe the behaviour of these systems rather differently: while the maximum of the wide-band gain decreases monotonically with the spectral exponent κ, the narrow-band gain is optimal at a certain κ. We have also surveyed how the value of the optimal κ depends on the frequency conditions.