A characterization of suprathreshold stochastic resonance in an array of comparators by correlation coefficient

Suprathreshold Stochastic Resonance (SSR), as described recently by Stocks, is a new form of Stochastic Resonance (SR) which occurs in arrays of nonlinear elements subject to aperiodic input signals and noise. These array elements can be threshold devices or FitzHugh-Nagurno neuron models for example. The distinguishing feature of SSR is that the output measure of interest is not maximized simply for nonzero values of input noise, but is maximized for nonzero values of the input noise to signal intensity ratio, and the effect occurs for signals of arbitrary magnitude and not just subthreshold signals. The original papers described SSR in terms of information theory. Previous work on SR has used correlation based measures to quantify SR for aperiodic input signals. Here, we argue the validity of correlation based measures and derive exact expressions for the cross-correlation coefficient in the same system as the original work, and show that the SSR effect also occurs in this alternative measure. If the output signal is thought of as a digital estimate of the input signal, then the output noise can be considered simply as quantization noise. We therefore derive an expression for the output signal to quantization noise ratio, and show that SSR also occurs in this measure.