matlab-滤波器-外文翻译-外文文献-英文文献-IIR数字滤波器的设计

IIRDigitalFilterDesignAnimportantstepinthedevelopmentofadigitalfilteristhedeterminationofarealizabletransferfunctionG(z)approximatingthegivenfrequencyresponsespecifications.IfanIIRfilterisdesired,itisalsonecessarytoensurethatG(z)isstable.TheprocessofderivingthetransferfunctionG(z)iscalleddigitalfilterdesign.AfterG(z)hasbeenobtained,thenextstepistorealizeitintheformofasuitablefilterstructure.Inchapter8,weoutlinedavarietyofbasicstructuresfortherealizationofFIRandIIRtransferfunctions.Inthischapter,weconsidertheIIRdigitalfilterdesignproblem.ThedesignofFIRdigitalfiltersistreatedinchapter10.Firstwereviewsomeoftheissuesassociatedwiththefilterdesignproblem.AwidelyusedapproachtoIIRfilterdesignbasedontheconversionofaprototypeanalogtransferfunctiontoadigitaltransferfunctionisdiscussednext.Typicaldesignexamplesareincludedtoillustratethisapproach.WethenconsiderthetransformationofonetypeofIIRfiltertransferfunctionintoanothertype,whichisachievedbyreplacingthecomplexvariablezbyafunctionofz.Fourcommonlyusedtransformationsaresummarized.Finallyweconsiderthecomputer-aideddesignofIIRdigitalfilter.Tothisend,werestrictourdiscussiontotheuseofmatlabindeterminingthetransferfunctions.9.1preliminaryconsiderationsTherearetwomajorissuesthatneedtobeansweredbeforeonecandevelopthedigitaltransferfunctionG(z).Thefirstandforemostissueisthedevelopmentofareasonablefilterfrequencyresponsespecificationfromtherequirementsoftheoverallsysteminwhichthedigitalfilteristobeemployed.ThesecondissueistodeterminewhetheranFIRorIIRdigitalfilteristobedesigned.Inthesection,weexaminethesetwoissuesfirst.NextwereviewthebasicanalyticalapproachtothedesignofIIRdigitalfiltersandthenconsiderthedeterminationofthefilterorderthatmeetstheprescribedspecifications.Wealsodiscussappropriatescalingofthetransferfunction.9.1.1DigitalFilterSpecificationsAsinthecaseoftheanalogfilter,eitherthemagnitudeand/orthephase(delay)responseisspecifiedforthedesignofadigitalfilterformostapplications.Insomesituations,theunitsampleresponseorstepresponsemaybespecified.Inmostpracticalapplications,theproblemofinterestisthedevelopmentofarealizableapproximationtoagivenmagnituderesponsespecification.Asindicatedinsection4.6.3,thephaseresponseofthedesignedfiltercanbecorrectedbycascadingitwithanallpasssection.Thedesignofallpassphaseequalizershasreceivedafairamountofattentioninthelastfewyears.Werestrictourattentioninthischaptertothemagnitudeapproximationproblemonly.Wepointedoutinsection4.4.1thattherearefourbasictypesoffilters,whosemagnituderesponsesareshowninFigure4.10.Sincetheimpulseresponsecorrespondingtoeachoftheseisnoncausalandofinfinitelength,theseidealfiltersarenotrealizable.OnewayofdevelopingarealizableapproximationtothesefilterwouldbetotruncatetheimpulseresponseasindicatedinEq.(4.72)foralowpassfilter.ThemagnituderesponseoftheFIRlowpassfilterobtainedbytruncatingtheimpulseresponseoftheideallowpassfilterdoesnothaveasharptransitionfrompassbandtostopbandbut,rather,exhibitsagradualroll-off.Thus,asinthecaseoftheanalogfilterdesignproblemoutlinedinsection5.4.1,themagnituderesponsespecificationsofadigitalfilterinthepassbandandinthestopbandaregivenwithsomeacceptabletolerances.Inaddition,atransitionbandisspecifiedbetweenthepassbandandthestopbandtopermitthemagnitudetodropoffsmoothly.Forexample,themagnitude)(jeGofalowpassfiltermaybegivenasshowninFigure7.1.Asindicatedinthefigure,inthepassbanddefinedby0p,werequirethatthemagnitudeapproximatesunitywithanerrorofp,i.e.,ppjpforeG,1)(1.Inthestopband,definedbys,werequirethatthemagnitudeapproximateszerowithanerrorofis,.e.,,)(sjeGfors.Thefrequenciespandsare,respectively,calledthepassbandedgefrequencyandthestopbandedgefrequency.Thelimitsofthetolerancesinthepassbandandstopband,pands,areusuallycalledthepeakripplevalues.Notethatthefrequencyresponse)(jeGofadigitalfilterisaperiodicfunctionof,andthemagnituderesponseofareal-coefficientdigitalfilterisanevenfunctionof.Asaresult,thedigitalfilterspecificationsaregivenonlyfortherange0.Digitalfilterspecificationsareoftengivenintermsofthelossfunction,)(log20)(10jeG,indB.HerethepeakpassbandripplepandtheminimumstopbandattenuationsaregivenindB,i.e.,thelossspecificationsofadigitalfilteraregivenbydBpp)1(log2010,dBss)(log2010.9.1PreliminaryConsiderationsAsinthecaseofananaloglowpassfilter,thespecificationsforadigitallowpassfiltermayalternativelybegivenintermsofitsmagnituderesponse,asinFigure7.2.Herethemaximumvalueofthemagnitudeinthepassbandisassumedtobeunity,andthemaximumpassbanddeviation,denotedas1/21,isgivenbytheminimumvalueofthemagnitudeinthepassband.Themaximumstopbandmagnitudeisdenotedby1/A.Forthenormalizedspecification,themaximumvalueofthegainfunctionortheminimumvalueofthelossfunctionistherefore0dB.ThequantitymaxgivenbyIscalledthemaximumpassbandattenuation.Forp1,asistypicallythecase,itcanbeshownthatThepassbandandstopbandedgefrequencies,inmostapplications,arespecifiedinHz,alongwiththesamplingrateofthedigitalfilter.Sinceallfilterdesigntechniquesaredevelopedintermsofnormalizedang