【作者】 安蕴；

【导师】 孟立凡；

【作者基本信息】 中北大学 ， 测试计量技术及仪器， 2012， 硕士

【摘要】 信号与信号处理是近二十年来发展最为迅速的学科，而信号去噪是信号处理中最常见的处理过程，经典的信号去噪方法如纯时域法，纯频域法，Fourier变换，等各自都有其应用的局限性。傅里叶变换是一种全局变换，即对信号的表征要么在时域，要么在频域。作为频域表示的频谱或功率谱并不能告诉我们其中的某种频率分量出现在什么时候以及它的变化情况，所以这对于非平稳信号的处理来说是远远不够的。小波变换作为一种出色的数学分析工具，在很多工程应用领域已经取代传统傅里叶变换的作用。因为小波变换的时间－尺度分析方法具有多分辨率的特点，所以它在时间和频率域都具有良好的局部化性质，它可以对任何频率成分进行精细的描述，有“数学显微镜”之称。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。本文以小波变换为核心，并对其原理做出了深入的分析。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的对比，从而在理论上明确其性能特点的优越性。在对信号噪声特点研究的基础上，特别是地震信号的噪声特点，分析研究了小波去噪的过程框图。对于信号去噪过程中的分解重构进行了理论讲述，并采用二次函数和反正切函数的组合方法，构造出新的阈值函数，用matlab模拟实验仿真，结果表明，新的阈值函数达到的去噪效果比常用的几种阈值函数的去噪效果好，可以用于地震信号去噪的处理与分析。更多还原

【Abstract】 Signal and signal processing is the fastest growing disciplines in the last twodecades, signal de-noising is the most common signal processing process, the classicsignal de-noising methods, such as pure time-domain method, pure frequency domainmethod, Fourier transform, etc. , each has its application limitations. The Fouriertransform is a global transformation, that is, the characterization of the signal either inthe time domain or frequency domain. Expressed as a frequency domain spectrum orpower spectrum, frequency domain does not tell us of a certain frequency componentsappear at what time and how it changes, so this is not enough for the non-stationarysignal processingAs an excellent mathematical analysis tool，Wavelet transform is being more andmore important in engineering practice and has replaced the role of the conventionalFourier transform in many research fields. The wavelet transform-scale analysis methodhas the characteristics of multi-resolution, which in the time and frequency domainhave a good localized nature it can be carried out on any frequency components finedescription of a "mathematical microscope," This study aims to explore wavelettransform theory, and the combination of professional study of seismic signalde-noising.This text regards the wavelet transform as the core explains its principles in detail,which leads to the wavelet transform theory. This includes not only the continuouswavelet, multire solution analysis methods also include the comparison of traditionalFourier transform clear the superiority of its performance characteristics in theory.Noise in the signal, on the basis of characteristics, so we can particularly the noisecharacteristics of the seismic signal is given wavelet de-noising diagram of the process.The signal de-noising decomposition in the process of remodeling on the theoreticalmethod, and the combination with a quadratic function and the inverse tangent function,construct a new threshold function using matlab simulation simulation results show that the new thresholddenoising function to achieve better than the commonly usedfunctions of several threshold denoising can be used for the processing and analysis ofthe seismic signal denoising.更多还原