上海大学毕业设计
SHANGHAI UNIVERSITY
毕业设计（论文）
UNDERGRADUATE PROJECT (THESIS)
题目：时频分析在信号处理中应用
学院 通信与信息工程学院 专业 通信工程 学号 12120707 学生姓名 王文森 指导教师 张海燕 起讫日期 2016年3月- 6月
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上海大学毕业设计
目录
目录································2 中文摘要······························4 ABSTRACT·····························5 第一章 绪论
1.1 研究背景及其意义························ 7 1.2 国内外发展现状··························8 1.3 本文内容及其安排························10 第二章 短时傅里叶变换
2.1 引言······························11 2.2 短时傅里叶变换原理·······················11 2.3 短时傅里叶变换特点·······················12 2.4 短时傅里叶变换的优缺点·····················16 2.5 短时傅里叶变化在信号处理中应用·················17 第三章 小波变换
3.1 引言······························20 3.2 小波变换的定理·························20 3.3 小波变换的特点及性质······················22 3.4 小波变换的时频分析·······················23 3.5 小波变换和其他变换的对比····················26 3.6小波变换的在信号处理中的除噪性能················31 第四章 S变换
4.1 引言······························34 4.2 S变换的基本原理························34 4.3 S变换与STFT和CWT的区别和联系···············36 4.4 S变换的时频特性························37 4.5 S变换在信号处理中的作用····················39
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上海大学毕业设计 第五章 Wigner-Ville分布
5.1 引言·······························41 5.2 Wigner-Ville分布的原理·····················41 5.3 Wigner-Ville分布的性质和特点··················43 5.4 Wigner-Ville分布的交叉干扰问题················44 5.5 Wigner-Ville分布的相关应用·················· 44 第六章 外文文献翻译 第七章 参考文献
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上海大学毕业设计
中文摘要
时频分析是目前兴起的一个信号处理方式，提供着信号从时间域到时间频率域的变化，可以有效的反映信号在特定的时刻在某个频率的能量的聚集情况。目前许多传统的信号处理方式都是在非常严格的数学限定条件下演变分析的，而且处理的信号绝大多数都是平稳的线性的信号。然而在我们现实的生活中，大部分的信号是非线性或者非平稳的，这样就容易发现传统的信号分析方法的不足之处，例如近些年发展的地震资料的解释，和储层油气的分析。这些都需要我们利用合理的时频分析方法去准确提取时频属性，进而更好的得出相关的结论。
因此本文以时频分析方法为切入点，将会在重点介绍短时傅里叶变换，小波变换，S变换，和Wigner-Ville分布四种时频分析的方法，并且会使用matlab软件对其进行相关的图像仿真，并且分析比较四种时频分析方法的性能。
短时傅里叶变换（STFT）是所以时频分析方法中最为简单的一种，其理论基础仍然是傅里叶分析，其为了克服傅里叶变换只能整体分析的特点，采用了一个时间有限的窗函数来截取信号，并且假设时间窗内的信号是平稳的，这样就得出了局部信号的时频关系。
小波变换继承了STFT关于局部化分析信号的思想，但与STFT不同的是，其窗口面积固定但是形状可变的，这使得小波变换具有多尺度特性。
S变换是基本小波Morlet小波的连续小波变换扩展，S变换中的基本小波成分和连续小波变换的相同，都是由简谐波和高斯函数的乘积构成，但是其中的简谐波只是在时间域上进行伸缩变换，而高斯函数则可以进行伸缩和平移。
Wigner-Ville分布是双线性时频分布，其利用时间和频率的的联合函数来更好的表征了时频聚集性，具有很高的时频分辨率，
关键词：时频分析，短时傅里叶变换 ，小波变换，S变换，Wigner-Ville分布
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上海大学毕业设计
Abstract
Time-frequency analysis is a new signal processing method, itprovides the signal
from time domain to the change of time and frequency domain.Itcan effectively reflect the energy of the signal at a particular moment in a certain frequency of aggregation. Now a lot of traditional signal processingwayare based on very strict mathematical qualification evolution analysis, and the signal that they process is smooth liner. But in our life, Most of the signals are nonlinear and non-stationary. We can easily find the deficiency of traditional signal analysis methods.For example, the interpretation of the seismic data and the analysis of the oil and gas reservoir. We need to use all these reasonable time-frequency analysis methods to accurately extract time-frequency attributes. We need touse all thesereasonable time-frequency analysis methods to accurately extract time-frequency attributesto reach appropriate conclusions.
This article will focus on short time Fourier transform, wavelet transform and S transform, and Wigner-Ville distribution of four kinds of time-frequency analysis method. Beside it also use MATLAB software to related image simulation.
STFT is the simplest way of all frequency analysis methods.Its theoretical basis is the Fourier analysis. It takes a time-window to intercept the signal in order to overcome the limit of Fourier analysis, assuming that the signal in the window is smooth. We can get the local signal relationship between time and frequency.
Wavelet transform inherits the STFT ideas about the localization analysis of signal, but unlike STFT, the window areais stable but the shape is variable, which makes wavelet transform multi-scale characteristics.
S transform is the basic wavelet Morlet wavelet to conduct continuous wavelet transform of the extension, the basic wavelet composition of S transform is the same as continuous wavelet transform. They are made up of the product between simple harmonic and Gaussian function, but the simple harmonic just scale transform in time domain, while the Gaussian function can be scaling and translation.
Wigner Ville distribution is bilinear time-frequency distribution, it use time and
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