Noise suppression and spectral decomposition for state-dependent noise in the presence of a stationary fluctuating input

It recently has been shown that the observed noise amplitude of an intrinsically noisy system may be reduced by causing the underlying state to fluctuate [Phys. Rev. Lett. 86, 950 (2001)]]. This paper extends the previous theory by considering the full power spectrum of the output signal, interpreting noise reduction in terms of the low-frequency end of the spectrum as well as the integrated spectrum. Our treatment accounts for arbitrarily sized fluctuations and deals with both continuous and discretely sampled observations. We show that noise suppression is possible if and only if the stationary average of the intensity of state-dependent noise decreases. We apply our analysis to an example involving saturable electrical conduction discussed in the original paper by Vilar and Rubí.