非平稳信号的小波分析与拟合问题研究

【作者】 刘毅；

【导师】 张彩明；

【作者基本信息】 山东大学 ， 计算机软件与理论， 2006， 博士

【摘要】 随着现代科学技术的发展，人类认识自身的能力也日益提高。自20世纪80年代起，综合了计算机信号处理、图像处理与分析、真实感计算机图形学、虚拟现实等技术的非平稳信号的分析与处理技术一直是国内外研究与应用的热点。借助计算机技术对医学数据进行处理与分析越来越多地受到人们的重视，成为一门新兴的、迅速发展的交叉学科领域。在医学数据的各个研究分支中，肺音分析无疑是非常重要的一个领域，其成果对于临床诊断、医学教学等方面都将起到重要的推动作用。同时，其实际应用的意义远远地超出医学范畴。 基于时间一频率的变换方法在音频信号处理领域扮演着重要的角色。它可以同时从时域和频域的角度对声音信号进行处理。这些以传统的傅立叶变换为主要工具的分析手段在研究声音的性质和组成成分时十分有用；但对非平稳信号来说，这种工具就显得力不从心。因为它是一种全频域、全时域的变换，它将信号从时域变换到了频域，在频域的定位性是完全准确的(即频域分辨率最高)，但其在时域却无任何分辨能力，不能提供任何局部时间段上的频率信息。相反，当一个函数用δ函数展开时，虽然其在时间域的定位性十分准确(即时域分辨率最高)，但其在频域却无任何定位性，它反应的是信号在该时间下的整体频域特征，不能提供任何频率所对应的时间信息，而这些对时变信号来讲都是非常重要的。对时变信号的分析，通常需要提取局部时间段(或瞬间)的频域特征信息，对此Fourier分析就无能为力了。因此本论文将仔细探讨如何应用近几年发展起来的小波和小波包变换对非平稳信号进行分析和处理。 之所以选择小波和小波包变换是因为小波变换本身就是多分辨率的，这使得它比那些固定分辨率的变换，比如STFT(短时傅立叶变换)更加适合人类的生理声学模型。对小波包变换而言，运用各种不同的基选择方法，能够很容易地获得任意分辨率下的时频信息。而且，通过某种手段对不同的时变信号可以自适应地选择不同的基，从而获得稳定高效的处理结果。 本论文的主要工作概括如下： (1)对约束五点所决定的二次曲线类型进行了研究。将五点决定一条二次曲线这个古老而经典的问题转化为可视化的图形表示，使五个点的几何位更多还原

【Abstract】 With the development of modern science and technology, the ability of human to understand itself is increasingly improved. From 1980’s, the techniques of non-stationary signal analysis and processing, which combine with computer signal processing, image analysis and processing, computer graphics and virtual reality, has been a hot topic research and application issue. The processing and analysis of medical data using computer technique has become a new cross subject and got more and more fast noticeable development speed. Among all the investigative branches of medical data, lung sounds analysis is an important research domain. Its research results would undoubtedly promote the application of clinic diagnosis, medical teaching, and so on. At the same time, the significance of the practical application of lung sounds analysis is far beyond medical category.The time-frequency transform plays an important role in sound analysis field. It makes us process sound signal from time domain and frequency domain synchronously. These traditional Fourier transform methods are very useful in studying the character and component of sounds. But as for the non-stationary signal, this tool is not useful because it is a fully time domain or fully frequency domain transform, it cannot provide the frequency information at any local time segment. Contrarily, when analyze a signal using a 8 function, its frequency resolving power is very poor although it has very high time discernment power. It is important to know what the time information corresponding to some frequencies information. For the time change signals, we need these information, but Fourier transform can not satisfy our requirement. So in this dissertation, we’ll discuss how to use wavelet and wavelet packet technique, which has been developed recently, to analyze the non-stationary signals in detail.We choose wavelet and wavelet packet because wavelet transform (WT) itself has the character of multiresolution. This character makes it more fit for mankind physiological acoustics model. At the mention of wavelet packet, it is better than those fixed resolution transform such as STFT(Short Time Fourier Transform), for example.更多还原