Simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic-resonance or SR effect. Input-output mutual information measures the performance of such threshold systems that use subthreshold signals. The SR result holds for all possible noise probability density functions with finite variance. The only constraint is that the noise mean must fall outside a “forbidden” threshold-related interval that the user can control—a new theorem shows that this condition is also necessary. A corollary and simulations show that the SR effect occurs for right-sided beta and Weibull noise as well. These SR results further hold for the entire uncountably infinite class of alpha-stable probability density functions. Alpha-stable noise densities have infinite variance and infinite higher-order moments and often model impulsive noise environments. The stable noise densities include the special case of symmetric bell-curve densities with thick tails such as the Cauchy probability density. The SR result for alpha-stable noise densities shows that the SR effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise. Regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell-curve tail thickness and an approximate linear relationship for the SR-maximal mutual information as a function of the alpha bell-curve tail thickness.

• Received 27 January 2003

DOI:https://doi.org/10.1103/PhysRevE.70.031911