Theory of stochastic resonance in signal transmission by static nonlinear systems

A deterministic periodic signal plus a stationary random noise is applied to a static nonlinearity taking the form of a monovariable arbitrary function on real numbers. The property of noise-enhanced signal transmission through stochastic resonance is studied for this class of static nonlinear systems. A theory is developed that provides expressions for the output autocorrelation function, power spectral density, signal-to-noise ratio, and input-output phase shift, in the presence of a periodic input, a noise distribution, and a static nonlinearity, all three being arbitrary. Both white and colored input noises are successively considered. For white input noise, exact expressions are derived in a discrete-time framework directly confrontable to simulations or experiments. The theory is applied to describe stochastic resonance in various examples of static nonlinear systems, for instance, a diode nonlinearity. In addition, confrontations with experiments and simulations are given that support the theory. In particular, interesting effects are reported such as a signal-to-noise ratio larger at the output than at the input or stochastic resonance at zero frequency. Finally, the validity of the theory is extended to dynamic nonlinear systems that can be decomposed into a static nonlinearity followed by an arbitrary dynamic linear system. @S1063-651X~97!12002-5#