Theory and method for weak signal detection in engineering practice based on stochastic resonance

Abstract

In this paper, the Kramers rate was derived using the Fokker–Planck (FP) equation with the condition of adiabatic approximation (the amplitude and frequency of signal detected are small [Formula: see text]) and the signal-to-noise ratio (SNR) was proved by means of Fourier transform and the power spectrum in bistable system. This is a concise and superior method to demonstrate the Kramers rate and SNR compared to the past methods. It is convenient for readers to understand. The SNR of the bistable system obtained shows that stochastic resonance (SR) can be used to realize energy transition from noise to a periodic signal under the adiabatic approximation condition. Therefore, SR could enhance the SNR of the output signal. The signal modulation technique was employed to transform the large frequency components into a small parameter signal to meet the adiabatic approximation requirement. Furthermore, we have designed the model of modulator. The simulation results show that the modulation method can generate SR in a bistable system and detect weak signals with large parameters from strong noise background.