【作者】 李华锋；

【导师】 徐博候；

【作者基本信息】 浙江大学 ， 固体力学， 2003， 博士

【摘要】 随机共振现象是非线性动力学系统中的一种反直观的现象，当一个非线性动力学系统受到一个随机力(噪声)的激励，也就是系统输入具有一个连续的频谱，系统和输入的随机激励之间会产生一种协同作用，使得系统输出的性能有所提高，这一现象被称为随机共振。在过去的二十多年里，随机共振现象受到广泛的关注，这一现象也在最初的双稳态动力学系统之外的其他许多系统中被发现。随着研究的深入，在被用来解释许多不同领域的自然现象之外，随机共振现象开始获得了一些应用，而随机共振在信号处理中的应用则是其中倍受关注的一个。 但是到目前为止，随机共振在信号处理中的应用的研究还只是局限在很小的范围内，主要原因是以前大量的研究工作都从调节噪声强度出发。随着参数调节随机共振(PSR)概念的提出，随机共振在信号处理中的应用有着很大拓展的空间，本文就主要研究几个目前随机共振在信号处理中应用时经常碰到的问题，其中包括阱内随机共振现象对多频模拟信号处理的应用、双稳态系统输出的波形畸变的消除及其他后处理、适用于多频信号的输出性能衡量指标、二进制数字信号输入情况下的系统输出的性能衡量，并将所得的结果应用到了一个自然界的噪声——海洋噪声背景下的信号检测中，这些研究对于随机共振理论的进一步发展及其在非线性信号处理中的应用具有重要的意义。 在对最近发现的一个很特别的现象——阱内随机共振现象进行研究中，我们发现阱内随机共振现象更有利于对多频信号的处理。同时，对于模拟信号输入的情况，大部分已有的结果都是集中在单频信号上的，这主要是由于双稳态系统的输出有严重的波形畸变。对于单频信号可以很好的利用频谱特性进行检测，或者通过带通滤波器进行处理，但是对于多频信号，没有很简单的方法。本文在仔细地分析了双稳态系统输出的线性特性的础上提出了一个简单的反演方法，并发展了相关的后处理操作。进一步地，我们还给出了阱内随机共振情形下，经过后处理操作，多频信号输入时系统输出性能的衡量指标。 对于二进制数字信号输入的情况，已有颇多研究结果，本文是在引入了系统响应速度的基础上，具体结合二进制信号的检测形式，对上述情况下的系统输出的统计性态进行了详细的研究，并最终得到了一个优于以前结果的系统输出误码率公式，给系统参数的选取提供了更好的依据。动态误码率公式，以及上面提到的多频信号输入时系统输出性能的衡量指标，已经被成功的应用在了我们对海洋噪声背景下的信号检测的研究中。 随机共振在信号处理中的应用的研究是一个跨学科的工作，本文还是主要着眼于随机共振现象的机理和在应用中的一些关键性制约因素，与信号处理领域的结合还不够紧密，随机共振如何更好地与信号处理相结合还需要大量进一步的工作。更多还原

【Abstract】 Stochastic resonance (SR) is a counterintuitive phenomenon of nonlinear dynamic systems wherein the noise (stochastic force) plays a constructive role. This phenomenon has then attracted much attention in the past two decades, and it has been observed that SR can occur in a wide variety of systems. With the development of SR, it has far been found to account for many natural phenomena and shown a large number of applications in different areas of technology, among which signal processing via stochastic resonance is a worth subject to be concerned.For a long time, SR was described as a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise. However, this description has served to limit the application of SR to signal processing. Parameter-tuning stochastic resonance (PSR) is a more realistic way to handle the phenomenon of SR in a broad sense. Based on the theory of PSR, some key problems of using SR in signal processing are studied, these issues include: the application of intrawell SR in multi-frequency analog signal processing, recovery of the waveform distortion caused by the bistable system and other post treatments, measure of system performance with multi-frequency analog digital input and measurement of system performance of binary digital input. The results are used in signal detecting under the background of the real sea noise. It is important for the development of SR theory and its application in nonlinear signal processing.With the work on a recently proposed phenomenon of SR ?the intrawell SR, we found that intrawell SR is a more effective way to process multi-frequency input. Most of the literatures considering analog input are focused on simple harmonic input, because the output waveform from a bistable system is greatly distorted. As for single harmonic input, the output information can be easily retrieved by some typical methods, such as frequency analysis and a bandpass filter. But when treating a multi-frequency analog signal, there is not a simple method. Based on the analysis of waveform distortion caused by bistable systems, a recovery formula is proposed, and some other post treatments are considered as a whole job. Then a measure on intrawell SR with multi-frequency input is obtained.There are many results on SR with binary digital input. As an extension of our previous works, a dynamic bit error rate (DBER) is obtained in this thesis. The DBER is a more accuracy measure to be used in SR with binary input, because the evaluation of system output is considered more detailedly with the concept of system response speed. The measure mentioned above, and the DBER have been used in the work of signal detection under the background of real sea noise.Using stochastic resonance in signal processing is a subject of more then two field of learning, only some of the key points of SR and the limitations in application are considered in this thesis. In order to join SR with signal processing more closely, further work needs to be done on the subject of using stochastic resonance in signal processing.更多还原