【作者】 张文英；

【导师】 张卫东；

【作者基本信息】 上海交通大学 ， 控制理论与控制工程， 2009， 硕士

【摘要】 传统的检测方法,例如取样积分、相关检测、谱分析等方法,它们采用的是抑制噪声技术。本文采用一种新的信号处理方法来检测信号,基于随机共振原理来提取淹没在强噪声中的有用信号,该方法的本质是利用噪声来增强信号。目前为止,随机共振在信号处理中的研究还只是局限在高斯白噪声,对Lévy噪声的研究还比较少。高斯噪声是Lévy噪声的一种特例。相对高斯分布来说,Lévy分布中包含了更多的参数,克服了高斯分布的不足,能更准确地描述实际情况,因此研究基于随机共振原理来提取淹没在Lévy噪声中的有用信号信息是具有重要意义。本文的主要工作和研究内容如下:1.分析了高斯噪声激励下的双稳态系统中,系统参数对随机共振的影响。并分析了产生随机共振的几种方法。2.证明了Lévy分布的两个重要性质,并分析了Lévy噪声的产生方法。3.研究了Lévy噪声激励下,非线性双稳态系统的输出以及输出信噪比的求解方法。仿真表明,对共振后信息进行处理的方法可以对Lévy噪声激励下双稳态随机共振系统中的弱周期信号进行有效提取。4.对高斯噪声和Lévy噪声分别激励下的随机共振进行了比较,说明Lévy噪声激励下的随机共振更为复杂。更多还原

【Abstract】 The conventional detection methods, such as sampling integral, correlation detection, spectrum analysis, are based on the restraining noise technologies. In this paper, a new method is proposed based on the stochastic resonance to detect weak signals from high intensity noises. In this method, noise is utilized to enhance the signal.Up to now, the researches of stochastic resonance are restricted to the use of Gauss noise. There are only a few researches on Lévy noise. Gauss noise is a special case of Lévy noise. Compared to Gauss distribution, more parameters are contained in Lévy distribution, the insufficiency of Gauss distribution can be compensated by Lévy distribution, and the actual situation can be described much more exactly by Lévy distribution. So the research of detecting weak periodic signal from Lévy noise based on stochastic resonance is of significance.The following part introduces main work and contribution: 1. The impact of parameters on stochastic resonance for bistable system with the stimulus of Gauss noise, and several methods for stochastic resonance generation are analyzed.2. Two important properties of Lévy distribution are proved, and the methods to produce Lévy noise are analyzed.3. The method to solve output and Signal-to-Noise of nonlinear bistable stochastic resonance system with the stimulus of Lévy noise are researched. Simulation example shows that the proposed post-processing to the output of bistable system with the stimulus of Levy noise is very effective to the detection of weak periodic signal.4. The nonlinear stochastic resonance system with the stimulus of Gauss noise and Lévy noise respectively are compared, which shows that the nonlinear stochastic resonance system with the stimulus of Lévy noise is much more complicated.更多还原