双稳系统噪声特性的分析与弱信号检测的研究

研究了噪声通过双稳系统其能量向低频区集中的频谱特性，并根据绝热近似理论，得出只有在噪声能量集中的低频区域才能产生随机共振(SR)主谱峰的结论。提出频率压缩变换的SR方法，分析了绝热近似SR技术在大参数条件下从强噪声中检测弱信号的应用。仿真结果表明，只要双稳系统输入端的信噪比不低于-30 dB，且实测采样频率不小于弱周期信号频率的50倍，就可由双稳系统的响应谱得到弱周期信号频率处的SR谱峰值特征。达到识别弱信号的目的。

Analysis of Bistable System Noise and Study for Weak Signal Detection

It is investigated that the noise energy in the power spectrum is concentrated in the low frequency region when a bistable system responds to the noise. In terms of the adiabatic elimination theory, the viewpoint is deduced that the main stochastic resonance (SR) peak is only produced in the low frequency region. With the new method of frequency compression transformation stochastic resonance (FCTSR) proposed here, the application of the adiabatic elimination principle for detecting a weak signal embedded in noise is analyzed under the condition of large parameters. The numerical simulation shows that, so long as the input signal-to-noise ratio of the bistable system is larger than -30 dB and the real practical frequency is not smaller than 50 times of the value of the weak periodic signal frequency, the SR spike at the signal frequency can be obtained from the response spectrum of the bistable system, and hence the weak signal submerged in strong noise is able to be extracted.