On the theory of signal filtration in a bistable moderately dissipating oscillatory system

The interaction of a weak periodic signal with noise is studied theoretically in bistable systems. Based on the generalised Smoluhowski equation, it is shown that, depending on the relation between the friction coefficient and the oscillation eigenfrequency, the solution of this equation has the aperiodic or oscillatory character. Within the framework of the linear response theory, the stochastic resonance effect is explained and the optimum value of the friction coefficient is found at which the output signal-to-noise ratio of a bistable system exceeds the input signal-to-noise ratio.