A periodic signal superposed to a white noise are input onto a nonlinear two-state threshold comparator. The output signal contains, embedded in random fluctuations originating in the input noise, a part of correlation with the periodic input. We show that a regime exists where this part of correlation can be enhanced by means of an increase of the input noise level. This is the phenomenon of stochastic resonance, whereby the noise becomes beneficial to the transmission of a coherent signal, and where an increase of the noise can result in improved performances. We experimentally demonstrate this property in an electronic circuit. We then develop a complete theoretical analysis of this effect of noise-assisted signal transmission. This simple electronic implementation of a stochastic resonator, together with its theoretical analysis, constitute a unique framework for further investigations on the nonlinear phenomenon of stochastic resonance and its implications for signal processing.