High-frequency power spectra for systems subject to noise

Abstract

We examine the falloff of power spectra at high frequencies as a possible means of distinguishing systems exhibiting deterministic chaos from systems subject to noise. To this end, we derive the asymptotic series describing the high-frequency falloff of the power spectrum for systems subject to noise. Our analysis applies to systems with an arbitrary finite number of degrees of freedom and includes the cases of additive and multiplicative white noise and the case of continuous nonwhite noise appearing with a general parametric dependence. In the case of colored noise, we show that the frequency at which crossover to the asymptotic behavior occurs is the effective bandwidth of the noise, i.e., the inverse of the correlation time. This result should be particularly useful in cases where the noise is not directly observable.