QUANTIFYING STOCHASTIC RESONANCE IN A SINGLE THRESHOLD DETECTOR FOR RANDOM APERIODIC SIGNALS

Abstract

We explore stochastic resonance (SR) effects in a single comparator (threshold detector) driven by either a Gaussian or exponentially distributed aperiodic signal. The behaviour of different performance measures, namely the cross-correlation coefficient (CCC), signal-to-noise ratio (SNR) and mutual information, I, has been investigated. The signals were added to Gaussian noise before being passed through the threshold detector. For the two signals tested, we observe the perhaps surprising result that the SNR never displays SR. However, SR is displayed by both the CCC and I for Gaussian signals. For exponential signals SR is not displayed by any of the measures. By generating signals whose probability distributions have the generalized Gaussian form Ae-|βx|n it is possible to demonstrate that SR ceases to occur if n<1.7. We conclude that SR is only observable in threshold based systems for certain types of aperiodic signal. Specifically, SR is not expected to occur for signals whose probability density functions have long, slowly decaying, tails. We discuss the implication of these results for the role of SR in biological sensory systems.