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河南农业大学本科生毕业论文题目基于小波变换的信号去噪研究学院理学院专业班级信安3班学生姓名秦学珍指导教师吴莉莉撰写日期：年月日基于小波变换的信号去噪研究秦学珍摘要小波变换是一种新型的数学分析工具，是80年代后期迅速发展起来的新兴学科。小波变换具有多分辨率的特点，在时域和频域都具有表征信号局部特征能力，适合分析非平稳信号，可以由粗及精地逐步观察信号。小波分析的理论和方法在信号处理、图像处理、语音处理、模式识别、量子物理等领域得到越来越广泛的应用，它被认为是近年来在工具及方法上的重大突破。信号的采集与传输过程中，不可避免会受到大量噪声信号的干扰，对信号进行去噪，提取出原始信号是一个重要的课题。那么究竟应该如何从含噪声的信号中提取出原始的信号，这就成了最重要的问题。经过长期的探索与努力、实验仿真，对比于加窗傅里叶对信号去噪，提取原始信号的方法，终于找到了一种全新的信号处理方法——小波分析。它将信号中各种不同的频率成分分解到互不重叠的频带上，为信号滤波、信噪分离和特征提取提供了有效途径，特别在信号去噪方面显出了独特的优势。本文从小波变换的定义和信号与噪声的不同特性出发，在对比分析了各种去噪方法的优缺点基础上，运用了对小波分解系数进行阈值化的方法来对一维信号去噪，该方法对去除一维平稳信号含有的白噪声有非常满意的效果，具有有效性和通用性，能提高信号的信噪比。与此同时，本文还补充介绍了强制消噪处理、默认阈值处理、给定软阈值处理等对信号消噪的方法。在对含噪信号运用阈值进行消噪的过程中，对比了用不同分解层数进行处理的去噪效果。本文采用的是用传感器采集的微弱生物信号。生物信号通常是噪声背景小的低频信号，而噪声信号通常集中在信号的高频部分。因此，应用小波分解，把信号分解成不同频率的波形信号，并对高频波进行相关的处理，处理后的高频信号在和分离出的低频信号进行重构，竟而，就得到了含少量噪声的原始信号。而且，随着分解层数的不同，小波去噪的效果也是不同的。并对此进行了深入的分析。关键词：小波变换；声信号；默认阈值处理；降噪小波重构河南农业大学理学院本科毕业论文ThesignaldenoisingbasedonwavelettransformQINGXue-zhenAbstractWavelettransformisanew-stylemathematicanalysistool.Itisanewsubjectwhichwasrapidlydevelopedinlate1980s.Thewavelettransformhasthecharacteristicofmulti-analysisandtheabilitytoanalysepartialcharacteristicbothinthetimedomainandthefrequencyrange,soitissuitabletoanalyzenon-steadystatesignalandobservesignalgraduallyfromcoarsetofine.Themethodhasbeenusedinmanydomainssuchassignalprocessing,imageprocessing,pronunciationdistinction,patternrecognition,quantumphysicsandsoon.Itisconsideredasagreatbreakthroughoftoolsandmethodsrecently.Itisinevitabletobeinterferedbyalargeamountofnoisesignalintheprocessofsignalgatheringandtransmission.It’samaintopictodenioseandextractoriginalsignal.Howshouldcontainthenoisesignalfromtheoriginalsignal,whichbecameamostimportantproblem.Afteralongperiodofexplorationandefforts,experimentalsimulation,comparedtoaddwindowFouriertosignaldenoising,extractionmethodoforiginalsignal,finallyfoundanewsignalprocessingmethod,waveletanalysis.Itwillsignalindifferentfrequencycomponentsofthedecompositionintonon-overlappingband,signal-to-noiseratio(SNR)forsignalfiltering,featureextractionseparationandprovideseffectiveways,especiallyintheaspectofsignaldenoisingshowauniqueadvantage.Thisarticlefromthedefinitionofwavelettransformandthedifferentcharacteristicsofsignalandnoise,thecomparisonandanalysistheadvantagesanddisadvantagesofvariousdenoisingmethod,basedontheuseofthewaveletdecompositioncoefficientmethodforone-dimensionalsignalthresholddenoising,themethodfordenoisingthewhitenoiseofonedimensionalsteadysignalcontainsaverysatisfactoryresults,withtheeffectivenessandgenerality,canimprovetheSNRofsignal.Atthesametime,thispaperaddsthecompulsorytreatment,thedefaultthresholddenoising,giventhesoftthresholdprocessingmethodforsignalde-noising.Onnoisesignalusingthethresholdde-noising,comparedwithdifferentdecompositionlayersforprocessingthedenoisingeffect.河南农业大学理学院本科毕业论文ThisarticleUSESthesensorwithaweakbiologicalsignalacquisition.Biologicalsignalisusuallylowfrequencysignalofbackgroundnoise,thenoisesignalisusuallyfocusedonthehighfrequencypartofsignal.Waveletdecomposition,therefore,thesignalisdecomposedintodifferentfrequencywaveformsignal,andthehighfrequencywavearerelatedtoprocessing,processingofhighfrequencysignalinlowfrequencysignalandisolatedrefactoring,unexpectedlyand,gettheoriginalsignalcontainingasmallamountofnoise.Andasthenumberofdecompositionlayers,waveletdenoisingeffectsarealsodifferent.Andcarriedonthethoroughanalysis.Keywords:wavelettransform;pronunciationsignal;Thedefaultthresholdprocessing；waveletreconstructionI目录1绪论............................................................................11.1研究背景..........................................................................................................................................11.2小波分析的研究现状.......................................................................................................................31.3本文研究的内容...............................................................................................................................32小波分析概述....................................................................52.1小波分析的定义...............................................................................................................................52.2小波变化的时、频局部性...............................................................................................................62.3小波去噪常用的算法.......................................................................................................................73实验仿真........................................................................83.1一维小波去噪原理...........................................................................................................................83.1.1小波降噪的两个准则............................................................................................................83.1.2小波分析用于降噪的步骤....................................................................................................83.1.3小波去噪的基本模型................................................................................