摘要：信号去噪的研究是信号处理领域中一个永恒的话题。经典的信号去噪方法，例如时域，频域，加窗傅里叶变换和维纳分布等，都有其局限性，限制了它们的应用范围。小波分析是20世纪90年代前后开发的一种新的时频分析方法。它来自于拉伸和平移的方法。小波理论之所以能够兴起主要是因为它不仅在信号的时域而且在频域上都有非常良好的定位以及多分辨率分析的能力，这也让它有了很好的发展。小波去噪论，近年来，得到了迅速的应用和发展。

目前，基于MATLAB的小波分析方法已被广泛应用于许多工程领域，已成为广大科技工作者经常使用的工具之一。作为一款在数值计算和可视化方面非常优秀和可靠的软件，经过各个领域专家的共同努力和不断研究，MATLAB已被应用于图像处理，信号处理，通信与小波分析，优化与控制系统仿真等各个领域。

关键词： 小波分析；语音信号去噪；Matlab；信噪比；傅里叶变换

Wavelet denoising analysis of speech signals based on MATLAB

Abstract:The research of signal denoising is an eternal topic in the field of signal processing. Classical signal denoising methods, such as time domain, frequency domain, windowed Fu Liye transform and Wiener distribution, have their limitations, which limits their application. Wavelet analysis is a new time-frequency analysis method developed before and after the 90s. It comes from the method of stretching and translation. The rise of wavelet theory has benefited from its good localization and multi-resolution analysis in the time and frequency domain of the signal, which has made it an unprecedented development in the field of signal processing. Wavelet denoising theory, as a very important branch of wavelet analysis theory, has been applied and developed rapidly in recent years.

 At present, the wavelet analysis method based on MATLAB has been widely used in many fields of engineering, and has become one of the tools often used by the vast number of scientists and technicians. As a good and reliable software for numerical calculation and visualization, MATLAB has been applied to various fields such as image processing, signal processing, communication and wavelet analysis, and optimization and control system simulation after the joint efforts and continuous research of experts in various fields.

Keywords: Wavelet analysis; speech signal denoising; Matlab; signal to noise ratio; Fourier transform

目录

摘要 i

Abstract i

目录 ii

1 绪论 1

1.1 小波去噪研究意义 1

1.2 小波理论发展现状 2

1.3 小波理论发展趋势 3

1.4 本文主要工作 6

2 傅里叶变换与小波分析 7

2.1 傅里叶变换 7

2.2 短时傅里叶变换 13

2.3 傅里叶变换的性质 14

2.3.1 线性性质 14

2.3.2 时移性质 15

2.3.3 频移性质 15

2.4 小波的定义 15

2.5 连续小波变换 16

2.6 离散小波变换（DBT） 17

2.6.1 尺度离散化 17

2.6.2 位移离散化 18

2.7 多分辨分析 18

2.8 小波分析与傅里叶变换的比较 19

2.9 小波变换在语音压缩编码中的应用 20

2.10 信号和噪声在小波域各个尺度上的传播特性 22

2.11小波变换在语音增强中的应用 23

2.12基于小波变换的语音信号特征提取 23

3 小波的三种去噪方法 25

3.1 模极大值相关去噪 25

3.1 空域相关去噪 26

3.2 小波阈值去噪 27

3.2.1 阈值选取方法 29

3.2.2 小波阈值处理方法 32

4 语音信号小波去噪 36

4.1 语音信号小波变换阈值去噪法 36

4.2 小波阈值处理方式的优化 37

4.3 基于MATLAB的小波变换的相关特点 38

4.3.1 基于MATLAB的小波滤波器的镜像 38

4.3.2 利用A*A 的比例尺的矩阵来分析小波 39

4.3 语音信号的小波去噪实现 39