A novel parameter-induced stochastic resonance phenomena in fractional Fourier domain

The parameter-induced stochastic resonance (SR) phenomenon in a novel self-adaptive dynamical system driven by linear frequency modulated (LFM) signal and additive noise is considered from the view of the signal-to-noise ratio (SNR). It is found that the dynamical system can be perfectly analyzed by equivalently transforming it into a traditional first-order linear dynamical system driven by periodic signal and additive noise in fractional Fourier transform (FrFT) domain with an optimal rotated angle, and the theoretical analysis and simulation results show that output SNR exhibits the SR behavior when it is plotted as a function of the system parameter. Furthermore, the optimal value of adjusted parameter is obtained, and the possible area of SNR gain is theoretically determined only by center-frequency and modulated frequency of the driving LFM signal.