零极点累试法设计滤波器

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1、DoubleDoubleNotchNotchFilterFilterDesignDesignXunWang10112746101.IntroductionAlotofsignalsinrealsituationareoftenassociatedwithnoiseinsignalprocessing.Inordertoreduceoreliminatetheinfluenceofnoiseandextractusefulsignals,weuseafiltertodecreasethescaleofnoisesignal.Filtercanbedefinedasasystemwhic

2、hcanproducetheresponsewhichweneedbyinputingtheoriginalsignaltothesystem.Therequirementofresponsecanbeexistintimedomainorfrequencydomain.Thefunctionoffilterismainlydecidedbythesystemfunction.Thepolelocationhaveasignificanteffectonthepropertiesofamplitude,thepositionofthepeakofwaveandextentofacui

3、ty.Thezerolocationmainlyaffectthepositionoftroughofwaveandtheextentofhollow.Wecanqualitativelydrawtheshapeofamplitudeaccordingtotheanalysisofpoleandzeropoints.Thistheoryprovideusamethodtodirectlydesignthefilter:Atfirstwecansetthepositionofpolesaccordingtothepropertiesofamplitude,andmakesurewhat

4、thesystemfunctionis.Comparingitwiththeoneweneed,ifthesystemfunctioncannotsatisfyourrequirement,wecanreviseitbyaddingordeletingthenumberofzeropoints,orbymovethepositionsofzeropoints.Thismethodiscalledpole-zeroplacementfilterdesignmethod.ItcanbeusednotonlyindesigningIIRdigitalfiltersbutalsoindesi

5、gningFIRdigitalfilters.2.FilterdesignInordertoobtainthesystemfunction,wemusttrymanytimestosetthethepolesandzerosofthesystemandobserveifthepropertiescansatisfytherequirement.Ifitdoesnot,wemusttrythesestepsagainandagaintomakethefiltersatisfyourrequirement.Infactitisaprocessofapproaching.Weshouldo

6、beysomeruleswhenusingthismethod.(1)weshouldconsiderwhichkindoffilteritbelongsto.IfweneedtodesignaFIRfilter,weshouldnotsetpoles,andjustneedtosetzeros.Bydoingthiswecandesignanon-recursivefilter.Itispossiblethatitbecomestorecursiveifwesetsomepolesinthedesigningprocess.(2)Ifwewanttofilterapointoffr

7、equency,wecansetazeroatthispointofdigitalfrequency.(3)Thepolesmustbeintheunitcircleaccordingtotherequirementofastablesystem.(4)Aimingataccomplishthestructureoffilter,thepolesarezerosarebothshouldbesetsymmetrically(otherthantheyare