【作者】 倪豪；

【导师】 孙建刚；

【作者基本信息】 大庆石油学院 ， 防灾减灾工程及防护工程， 2004， 硕士

【摘要】 小波分析及小波变换是80年代中期发展起来的一门新兴的数学理论和方法，它被认为是傅里叶分析方法的突破性进展，它具有许多优良的特性。小波变换的基本思想类似于傅里叶变换就是用信号在一簇基函数张成的空间上的投影表征该信号。经典的傅里叶变换把信号按三角正、余弦基展开，将任意函数表示为具有不同频率的谐波函数的线性迭加，能较好的刻画信号的频率特性，但它在时空域上无任何分辨，不能做局部分析，这在理论和应用上都带来了许多不便。小波分析优于傅里叶之处在于，小波分析在时域和频域同时具有良好的局部化性质，因为小波函数是紧支集，而三角正、余弦的区间是无穷区间，所以小波变换可以对高频成分采用逐渐精细的时域或空间域取代步长，从而可以聚焦到对象的任意细节。因此，小波变换被誉为分析信号的显微镜，傅里叶分析发展史上的一个新的里程碑。小波分析是一个新的数学分支，它是泛函分析、傅里叶分析、数值分析的最完美结晶；在应用领域，特别是在信号处理、图象处理、语音分析、模式识别、量子物理、生物医学工程、计算机视觉、故障诊断及众多非线性科学领域都有广泛的应用。本文主要内容如下： 第一章简单介绍了小波发展的历史以及MATLAB软件的一些特点。 第二章介绍了小波分析理论以及小波分析中一些重要的概念。 第三章介绍了小波变换与时-频分析。 第四章介绍了小波变换模极大值和奇异性的定义。 第五章介绍了噪声以及小波消噪的目的、原理、方法并给出了小波消噪的例子。 第六章应用小波分析对地震波进行消噪，并比较消噪前后储罐的地震响应。应用小波分析对地震信号进行多层分解，提取我们想要得地震波数据进行储罐地震响应分析，得出这种方法是可行的。更多还原

【Abstract】 Wavelet analysis is a novel mathematical theory and method proposed In 1980s. It is regarded as a breakthrough of Fourier analysis because It has many wonderful characteristics. Fourier analysis consists of breaking up a signal Into slue waves of various frequencies. Similarly, wavelet analysis is the breaking-up a signal into shifted and scaled versions of the original wavelet. Lacking of space locality in time domain, Fourier analysis can only make certain of the Integral singularity of a function or signal. As a result; It Is difficult to detect the spatial position and distribution of broken signal by Fourier analysis. Wavelet analysis has the characteristic of spatial locality, and its wideness in both windows of the time and the frequency can be adjusted, so it can analyze the details of a signal. Therefore Wavelet analysis is called a microscope of signal analysis and a milestone of Fourier analysis. As a new embranchment of mathematics. Wavelet analysis is the most perfect combination of the functional analysis. Fourier analysis and numerical analysis Wavelet analysis has been widely used in signal processing, image manipulation, voice analysis, pattern recognition, quanta physics, biomedicine engineering, computer vision, fault diagnosis, some nonlinear fields and so on. The dissertation is outlined below.In chapter 1 we will briefly introduce the history of Wavelet analysis’s development, and also introduce some useful feature of the MATLAB software.In chapter 2 we introduce you the Wavelet analysis theory, and you can also find some important concept used in Wavelet analysis.In chapter 3 we introduce you the Wavelet analysis and time-frequency analysis.In chapter4 we will introduce the modulus maximum of Wavelet transform and the definition of singularity.In chapter 5 we will introduce the different noise, and you will know why and how we should transient signal denoise , you will also find some examples of transient signal denoise.Chapter 6 is devoted to use Wavelet analysis to transient the signal of ELCENTRO denoise, and to compare the Seismic response of tank to both signal. We also use the method of multiple-level decomposition to get what we want of the signal, and do some compare about the Seismic response of tank to this signal and the original signal. We find this method is practicable.更多还原