Input-output gains for signal in noise in stochastic resonance

A theoretical model for the transmission of a periodic signal added to a noise through a static nonlinearity is considered. Expressions are derived for the gains experienced by the signal, the noise and the signal-to-noise ratio in the input-output nonlinear transmission. The gains are obtained in the presence of a periodic input, a noise distribution and a static nonlinearity, all three being arbitrary. These gains are studied as measures of the phenomenon of stochastic resonance whereby the transmission of the periodic signal can be improved by means of noise addition. As the noise level is raised, resonant evolutions for the signal and signal-to-noise gains or antiresonant evolutions for the noise gain, are demonstrated. At the same time, conditions are exhibited where the signal-to-noise gain is larger than unity, demonstrating several realizations of a signal-to-noise ratio larger at the output than at the input in stochastic resonance. (C) 1997 Elsevier Science B.V.