Noise-assisted signal transmission in discrete-time systems

This paper discusses noise-assisted signal transmission in discrete-time systems based on an average signal-to-noise ratio (ASNR) for three representative noises. We find, by numerical simulation, when the periodic input is subthreshold, noise can assist signal transmission, stochastic resonance (SR) exists. There is a range of the noise intensity, where the output ASNR is greater than the input ANSR, i.e., the output-input ASNR gain is greater than one. The efficacy of SR decreases as the system threshold increases, or as the impulsion of the noise probability density function (PDF) around zero mean becomes thinner and the tail in PDF becomes heavier. These results show also the complexity of SR in a discrete-time system, the existence and the efficacy of SR depends on the system measure and noise, too. These results extend further SR to be applied in digital signal processing.