Periodic and aperiodic stochastic resonance with output signal-to-noise ratio exceeding that at the input

Stochastic resonance (SR) is a nonlinear effect whereby a system is able to improve, via noise addition, the detectability of a signal in noise. SR has been demonstrated with different types of systems and signals where in each case, an appropriate detectability measure is shown improvable at the output of the stochastic resonator when noise is added at its input. A complementary issue, important for practical applications of SR, is the possibility of making the signal detectability at the ouput exceed that at the input when noise is added. We demonstrate this possibility, for both periodic and aperiodic SR, with a simple nonlinear system that we show exactly tractable analytically.