Coherence resonance: On the use and abuse of the Fano factor

Coherence resonance describes a phenomenon in excitable systems in which a suitable dose of noise generates excitation-events that maximizes its periodicity or coherence. The Fano-factor, defined as the ratio of the standard deviation of the time-intervals between successive events and the average time interval, exhibits a minimum at this optimal noise level. It is shown here that a decreasing Fano factor is a necessary but not a sufficient criterion to indicate enhanced coherence of a signal.