Abstract
Some nonlinear systems possess innate capabilities of enhancing weak signal transmissions through a unique process called Stochastic Resonance (SR). However, existing SR mechanism suffers limited signal enhancement from inappropriate entraining signals. Here we propose a new and effective implementation, resulting in a new type of spectral resonance similar to SR but capable of achieving orders of magnitude higher signal enhancement than previously reported. By employing entraining frequency in the range of the weak signal, strong spectral resonances can be induced to facilitate nonlinear modulations and intermodulations, thereby strengthening the weak signal. The underlying physical mechanism governing the behavior of spectral resonances is examined, revealing the inherent advantages of the proposed spectral resonances over the existing implementation of SR. Wide range of parameters have been found for the optimal enhancement of any given weak signal and an analytical method is established to estimate these required parameters. A reliable algorithm is also developed for the identifications of weak signals using signal processing techniques. The present work can significantly improve existing SR performances and can have profound practical applications where SR is currently employed for its inherent technological advantages.
Highlights
Stochastic Resonance (SR) is a unique phenomenon of certain nonlinear systems whereby a generally feeble input such as a weak signal is amplified and optimized by the assistance of an entraining white Gaussian noise, or other entraining signals such as sinusoids
Current stochastic resonance is often considered for the simplest possible nonlinear system representing an over damped bistable oscillator described by, x where U(x), Asin(ωt + α) and F(t) are the potential function of the system, the weak periodic input signal to be identified and the entraining signal
The fundamental mechanism of SR, together with the subsequent signal extraction, can be schematically illustrated in Fig. 1 in which theapplied entraining signal is supposed to lift the system just out of its potential wells by overcoming the potential barrier so that the embedded weak signal becomes capable to assist the crossings between the two competing stable equilibriums, thereby enhancing the strength and the sensibility of the weak signal before it is identified
Summary
Some nonlinear systems possess innate capabilities of enhancing weak signal transmissions through a unique process called Stochastic Resonance (SR). We propose a new and much more effective strategy for driving a system into strong spectral resonances and we report that orders of magnitude better signal enhancement which has been achieved by employing sinusoidal entraining signals with frequencies in the same range as that of the weak signal. By allowing the entraining frequency to be tuned in the range of the weak signal, the underlying mechanism of spectral resonances tend to facilitate greatly increased nonlinear modulations and intermodulations, and their associated energy transfers, thereby strengthening the weak signals. Such underlying physical mechanism governing the behavior of spectral resonances is examined, revealing the inherent advantages of the proposed spectral resonances over the existing implementation of SR. The work provides significantly improved SR performances, as well as effective methods for weak signal identifications, and can have profound practical applications where SR mechanisms are currently employed for its potential technological advantages
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