线性调频信号激励过阻尼双稳系统的随机共振现象研究

Stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise

线性调频信号是工程中常见的一种信号,由于其为非周期信号,无法以频域信噪比作为衡量其是否产生随机共振的测量手段,故鲜有文献研究以线性调频信号为激励信号的随机共振现象.本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性,首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段,研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象,且发现了以线性调频信号为激励信号时产生的新现象,即随着信号频率的增大,随机共振将逐渐减弱,并给出了合理的解释.仿真的结果与理论分析一致,验证了本文所提出方法的有效性.

It is improper to use frequency domain signal-to-noise ratio as a measure to judge whether stochastic resonance happens with chirp signal which is common in engineering. As a result, there is little literature on this subject. Using the energy aggregation in an optimal fractional Fourier transform domain of chirp signal, in this paper we propose a new signal-to-noise ratio defined in an optimal fractional domain to study the stochastic resonance of over-damped bistable system driven by chirp signal and Gaussian white noise. A new phenomenon is found, that is, the stochastic resonance phenomenon weakens gradually as the frequency of chirp signal increases. And it is reasonably explained in this paper. The consistency of simulation results with theoretical analysis verifies the effectiveness of the method proposed in this paper.