Signal/noise ratio stochastic resonance

It is intuitively obvious that this phenomenon should also exist in systems having steady states (e.g., in a system described by quartic potential that has been intensively studied in the context of stochastic resonance), but it is more natural to investigate the resonant properties of signal-to-noise ratio (SNR) in those cases [113]. 

According to several studies [12,13,19,96], the two principal features of stochastic resonance phenomena are that the signal and/or the signal-to-noise ratio R... 

Stochastic resonance is a kinetic effect universally inherent to bi- or multistable dynamic systems exposed to either white or color noise. Its main manifestation is the appearance of a maximum on the noise intensity dependencies of the signal-to-noise ratio in a system subject to a weak driving force. Essentially, this behavior is due to the presence of an exponential Kramers time x cx exp(AU/3>) of the system switching between energy minima here AU is the effective height of the energy barrier separating the potential wells and 3> is the noise intensity. 

In Section IV.B.4 we have shown that the quadratic dynamic susceptibilities of a superparamagnetic system display temperature maxima that are sharper than those of the linear ones. If the maximum occurs as well at the temperature dependence of the signal-to-noise ratio, this should be called the nonlinear stochastic resonance. However, before discussing this phenomenon, one has to define what should be taken as the signal-to-noise ratio in a nonlinear case. 

At last, it should be mentioned that, as always applies to Fourier methods , the major advantage of FTNMR is the multiplex advantage (see also (Chapter 1). Ernst and Anderson have shown that the gain in the signal-to-noise ratio between FTNMR and conventional NMR is proportional to the square root of the number of spectral elementsS . This result is the same as that obtained for infrared Fourier spectroscopy. In this context, it should be noted that a complete analogon to infrared Fourier spectroscopy is the nuclear magnetic Fourier-transfoim resonance with an incoherent rf-field (stochastic resonance) . Of course, Fourier methods depend on electronic computers to perform the Fourier transform of the measured data and were widely used when sufficiently cheap computers became available. The use of the compute- and of the mathematical treatment of the experimental... 

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