We studied two non-dynamical stochastic resonators, the level-crossing detector (LCD) and the Schmitt trigger, driven by a periodic pulse train plus 1/fκ-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.
In the last few years, several papers have been published that reported high signal-to-noise ratio (SNR) gains in systems showing stochastic resonance. In the present work, we consider a level-crossing detector driven by a periodic pulse train plus Gaussian band-limited white noise, and provide analytical formulae for the dependence of the SNR gain on the relevant parameters of the input (the amplitude and the cut-off frequency of noise, the duty cycle of the deterministic signal and the distance between the threshold and the amplitude of the signal). Our results are valid in the input parameter range wherein high gains are expected, that is, wherein the probabilities of missing and, especially, extra output peaks are very low. We also include numerical simulation results that support the theory, along with illustrations of cases which are outside the validity of our theory.