基于随机共振原理的分段线性模型的理论分析与实验研究

Theory and experiment research on a Piecewise-linear model based on stochastic resonance

提出了一种分段线性双稳态模型,推导了模型的解析关系及其输出信噪比,通过对该模型与连续双稳态模型的对比分析和仿真实验,证明了该模型的优越性.该模型具有参数之间相互独立、易于调节的特点.在对模型分析与数值仿真的基础上,通过电路对强噪声背景下的微弱周期信号检测进行了实验研究.结果表明分段线性随机共振模型能够有效实现对微弱周期信号的检测,并能显著增强输出信噪比.

We propose a new piecewise-linear model. The principle of stochastic resonance in the new piecewise-linear model is introduced, and the formula of the signal-to-noise ratio （SNR） is deduced. It is proved that stochastic resonance characteristics can be utilized to realize the conversion of noise energy into periodic signal energy. The results clearly show the enhancement of the SNR of the output signal. The model characteristic that the weak periodic signal can be detected from noise background is investigated by the numerical simulation. The stochastic resonance system based on the model is built by using a circuit. The behaviors of stochastic resonance are studied when the circuit is driven by noise and period signal. The simulation and experimental results show that the model can effectively detect weak periodic signal, and enhance the SNR prominently.