小波变换去噪论文

摘要

小波变换归属于数学领域的调和函数的范畴，是调和分析几十年来的一个突破性进展，并且在很多科技领域内得到了广泛应用。本文旨在探讨小波变换理论，并结合专业中的地震信号去噪展开研究。

论文以小波变换为核心，首先介绍了论文研究的目的、意义及主要研究内容，由此引出了小波变换理论，并对其原理做了详细阐述。这不仅包括连续小波，离散小波，多分辨率分析方法还包括与传统傅氏变换等的对比，从而在理论上明确其性能特点的优越性。本文选定了小波阈值去噪方法。由此结合给定的信号应用matlab 进行处理，并通过对比处理结果为本文后面的处理工作选定合适的参数。从所做例子来看，小波阈值处理达到了很好的去噪效果。论文应用matlab 模拟微地震信号，结合小波阈值去噪方法对微地震信号进行了处理。在文中给出了信号的原始模拟信号，加噪信号及处理后的效果图，从图中可以看出，小波阈值去噪完成了模拟微地震信号的去噪处理。另外，对实际的微地震资料进行了试处理，达到了去噪的目的。

关键词：小波变换；去噪；微地震；分解；重构

ABSTRACT

The wavelet transform attributables to the mathematical field of harmonic function areas, it’s a breakthrough progress, and in many areas of science and technology has been widely used. This study aims to explore wavelet transform theory, and the combination of professional study of seismic signal de-noising.

Papers to wavelet transform at the core, first of all, on paper the purpose of thestudy, the significance and major research content, which leads to the wavelettransform theory, and its principles expounded in detail.This includes not only thecontinuous wavelet, wavelet, multire solution analysis methods include traditional Fourier transform contrast, in theory, clear the superiority of its performance characteristics. The paper selected through comparative study of wavelet de-noising threshold method.This combination of a given signal processing applications matlab,and by comparing the results of this paper to the back of the appropriate handling of the selected parameters. From doing example, wavelet thresholding to deal with a very good de-noising effect. Papers matlab simulated micro-seismic signal applications, wavelet de-noising threshold with this method micro-seismic signal processing. In this paper the original analog signal, the signal plus noise and the effects of treatment plans, as can be seen from Fig, wavelet de-noising threshold completed micro-seismic signal de-noising analog processing.

Key words: wavelet；de-noising；micro-seismic；decompose；compose

目录

第 1 章前言 (1)

1.1 小波分析的发展状况 (1)

1.2 小波分析的应用研究 (2)

1.3 本文主要研究内容及成果 (3)

第 2 章微地震监测原理及信号特征 (4)

2.1 微地震监测原理 (4)

2.1.1 裂缝尖端效应和漏泄效应 (5)

2.1.2 混合破裂机制 (5)

2.2 微地震信号的特征 (6)

2.2.1 微地震的波场 (6)

2.2.2 微地震信号的频谱 (7)

2.2.3 微震的强度 (7)

第 3 章小波变换基本理论 (8)

3.1 傅里叶变换 (8)

3.2 小波变换原理 (10)

3.2.1 连续小波变换的定义 (10)

3.2.2 小波变换的条件 (11)

3.2.3 时频的分析窗口 (12)

3.2.4 连续小波变换的逆变换公式 (13)

3.3 离散小波变换 (14)

第 4 章基于小波的阈值去噪方法 (16)

4.1 小波阈值去噪的主要理论依据 (16)

4.2 小波阈值处理方法 (17)

4.3 小波阈值去噪方法的具体步骤 (17)

4.4 matlab小波变换的相关函数 (19)

第 5 章模拟微地震信号以及实际信号小波去噪 (22)

5.1 模拟微地震信号去噪 (22)