Adaptive piecewise re-scaled stochastic resonance excited by the LFM signal

The piecewise re-scaled stochastic resonance method is proposed and thoroughly investigated in a bistable system, which is induced by the linear frequency-modulated (LFM) signal. At first, the theoretical formulation for piecewise re-scaled stochastic resonance is explained in detail. Then, several numerical simulations are carried out and the effects of some related parameters are discussed, in which the moment of the signal segmentation and the re-scaled coefficient are key factors. Meanwhile, the numerical results indicate that the proposed method manages to process the LFM signal submerged in the noise. After that, adaptive piecewise re-scaled SR is proposed to solve the problem of the parameter selection. At last, the comparison between fractional Fourier transform (FRFT) and the proposed method is present. Compared to the traditional FRFT, the method has a better performance, especially in amplification effect. The method in this paper may provide reference for processing other kinds of frequency-modulated signals besides the LFM signal.