高频随机共振在信号检测中的研究

【作者】 孙静静；

【导师】 王辅忠；

【作者基本信息】 天津工业大学 ， 物理电子学， 2007， 硕士

【摘要】 随机共振机理表明，对于小参数信号(幅度、频率和噪声强度均小于1)，根据绝热近似或线性响应理论，双稳态系统的输出在时域和频域中有着明显的随机共振表现形式。合适的噪声强度可以使得弱周期信号驱动下的非线性系统的输出信噪比达到某一最佳值。在一定噪声强度范围内，输出信噪比随噪声强度的增强而增大。其本质是部分噪声能量转化为信号能量的结果，是输入信号与噪声的协作效应。然而频谱能量均匀分布的白噪声，经过非线性双稳态系统，其谱结构发生变化，不再是均匀分布，能量向低频区域集中。因此，在高频段，没有足够的噪声能量使布朗粒子越过势垒以在双稳态系统的两势阱之间以信号频率跃迁，也就不能观察到随机共振现象。即对于大频率输入信号，双稳态系统的输出在时域和频域中没有明显的随机共振表现形式。本文针对高频率输入信号的随机共振现象不明显的问题，提出了频移随机共振。即利用傅立叶变换的频移特性，先将信号的频率搬移到一个较小的值，再利用随机共振系统中噪声和信号的协同作用，实现强噪声背景下大频率周期信号的检测。仿真结果表明，经频移后产生的小频率信号通过双稳态系统的协同作用形成的输出信号，其信号频率处的功率谱谱峰有很大的提高。此方法实现了在较宽的频率范围内检测弱信号，提高了强噪声背景下弱信号检测的能力。更多还原

【Abstract】 The principle of Stochastic Resonance (SR) shows that obvious SR phenomenon can be observed at the output for signals with small parameters according to adiabatic approximation theory. Small parameters mean that the amplitude and frequency of period signal and noise intensity are all far less than 1. Stochastic resonance is a nonlinear effect that accounts for the optimum response of a dynamical system to an external forcing at a precise value of the noise intensity. The output signal-to-noise ratio (SNR) increases as the input noise intensity is increased over a certain range. The essence of the improvement of SNR is that the energy of noise is transformed into the signal energy. And the power spectrum of white noise changes in the structure after passing through the nonlinear bistable system. It is not the uniform distribution of energy any more, its energy focuses on the low frequency region in the form of Lorentzian. Therefore there is not enough energy for the Brown particle to get across the double-well potential at the high frequency region, and it’s impossible to observe the phenomenon of SR. In other words, the detecting effect of stochastic resonance system is not obvious when the frequency of the weak signal is high.In order to deal with this problem, we take wide parameter input signal into consideration .This paper presents frequency shifting stochastic resonance. First, we shift the frequency of the input signal to a small one using the frequency shifting characteristic of Fourier transform, and then take advantage of the nonlinear cooperative effect of the bistable system to get the small frequency weak signal.The simulation results show that after shifting the input frequency to a small one, the output power spectrum peaks of the bistable system are strongly enhanced at this frequency. The ability of detecting weak signal overwhelmed in strong noise within a rather broad frequency range is improved in this way.更多还原