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武汉理工大学《Matlab课程设计》报告目录摘要.................................................................................................................................................IAbstract..........................................................................................................................................II1原理说明....................................................................................................................................11.1数字滤波技术...................................................................................................................11.2FIR滤波器........................................................................................................................11.3窗函数...............................................................................................................................21.4MATLAB简介......................................................................................................................41.5MATLAB结合窗函数设计法原理......................................................................................42滤波器设计...............................................................................................................................22.1滤波器设计要求...............................................................................................................22.2设计函数的选取...............................................................................................................22.3窗函数构造.......................................................................................................................32.4设计步骤...........................................................................................................................42.5利用MATLAB自带函数设计.............................................................................................43滤波器测试...............................................................................................................................93.1滤波器滤波性能测试.......................................................................................................93.2滤波器时延测量................................................................................错误!未定义书签。3.3滤波器稳定性测量............................................................................错误!未定义书签。5参考文献..................................................................................................................................12附件一：........................................................................................................错误!未定义书签。武汉理工大学《Matlab课程设计》报告I摘要现代图像、语声、数据通信对线性相位的要求是普遍的。数字滤波器是一种用来过滤时间离散信号的数字系统，通过对抽样数据进行数学处理来达到频域滤波的目的。根据其单位冲激响应函数的时域特性可分为两类：无限冲激响应（IIR）滤波器和有限冲激响应（FIR）滤波器。与IIR滤波器相比，FIR的实现是非递归的，总是稳定的；更重要的是，FIR滤波器在满足幅频响应要求的同时，可以获得严格的线性相位特性。因此，具有线性相位的FIR数字滤波器在高保真的信号处理，如数字音频、图像处理、数据传输、生物医学等领域得到广泛应用。在实际进行数字信号处理时，往往需要把信号的观察时间限制在一定的时间间隔内，只需要选择一段时间信号对其进行分析。这样，取用有限个数据，即将信号数据截断的过程，就等于将信号进行加窗函数操作。而这样操作以后，常常会发生频谱分量从其正常频谱扩展开来的现象，即所谓的“频谱泄漏”。当进行离散傅立叶变换时，时域中的截断是必需的，因此泄漏效应也是离散傅立叶变换所固有的，可以通过窗函数加权抑制DFT的等效滤波器的振幅特性的副瓣，或用窗函数加权使有限长度的输入信号周期延拓后在边界上尽量减少不连续程度的方法实现抑制。FIR滤波器的设计中，为获得有限长单位取样响应，需要用窗函数截断无限长单位取样响应序列。另外，在功率谱估计中也要遇到窗函数加权问题。由此可见，窗函数加权技术在数字信号处理中的重要地位。此次课设基于MATLAB环境下，用窗函数法设计FIR滤波器的过程和设计实例。通过利用不同的窗函数方法设计FIR滤波器，对所设计的滤波器进行分析比较，得出各种方法设计的滤波器的优缺点及其不同的使用场合，从而可以在设计滤波器时能够正确的选择FIR数字滤波器的窗函数的选取及设计方法。关键词：数字滤波器，MATLAB，有限冲激响应，窗函数，线性相位武汉理工大学《Matlab课程设计》报告IIAbstractAmodernimage,Voiceanddatacommunicationstothelinearphaserequirementisuniversal.Digitalfilterisatimediscretesignalwhichisusedtofilterdigitalsystem,throughthemathematicaltreatmentofthesampledatatoachievethefrequency-domainfilteringpurposes.Inaccordancewithitsunitimpulseresponsefunctionofthetime-domaincharacteristicscanbedividedintotwocategories:InfiniteImpulseResponse(IIR)filterandfiniteimpulseresponse(FIR)filters.ComparedwiththeIIRfilters,FIRrealizationofanon-recursive,isalwaysstable;moreimportantly,FIRfilterstomeettherequirementsoftheamplitude-frequencyresponseatthesametime,getastrictlylinearphasecharacteristics.Therefore,itishigh-fidelitysignalprocessing,suchasdigitalaudio,imageprocessing,datatransmission,biomedicalareassuchaswidelyused.Inpractice,digitalsignalprocessing,theyoftenneedtoobservethetimelimitforthesignalinacertaintimeinterval,onlyneedtoselectaperiodoftimetoanalyzethesignals.Inthisway,accesstoafinitenumberofdataabouttheprocessofsignaldatatruncationisequivalenttothesignal,theadditionalwindowfunctionoperation.Andthisaftertheoperation,oftenoccurfromthenormalcomponentofthespectrumspreadspectrumopentothephenomenonofso-calledspectralleakage.WhenitcomestodiscreteFouriertransform,thetimedomaintruncationisnecessary,therefore,leakageeffectsarealsoinherentindiscreteFouriertransform,andmustbeinhibited.UndertheMATLABenvironment,withthewindowfunctionmethodforFIRfilterdesignprocessanddesignexamples.ThroughtheuseofdifferentwindowfunctionsdesignedFIRfilter,thefilterdesignedtoanalyzeandcompareavarietyofmethodsdesignedtofilterobtainedtheadvantagesanddisadvantagesoftheuseoftheirdifferentoccasions,soyoucandesignafiltertocorrectthechoiceo