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1、IIRDigitalFilterDesignAnimptantstepinthedevelopmentofadigitalfilteristhedeterminationofarealizabletransferfunctionG(z)approximatingthegivenfrequencyresponsespecifications.IfanIIRfilterisdesireditisalsonecessarytoensureth

2、atG(z)isstable.TheprocessofderivingthetransferfunctionG(z)iscalleddigitalfilterdesign.AfterG(z)hasbeenobtainedthenextstepistorealizeitinthefmofasuitablefilterstructure.Inchapter8weoutlinedavarietyofbasicstructuresftherea

3、lizationofFIRIIRtransferfunctions.InthischapterweconsidertheIIRdigitalfilterdesignproblem.ThedesignofFIRdigitalfiltersistreatedinchapter10.Firstwereviewsomeoftheissuesassociatedwiththefilterdesignproblem.Awidelyusedappro

4、achtoIIRfilterdesignbasedontheconversionofaprototypeanalogtransferfunctiontoadigitaltransferfunctionisdiscussednext.Typicaldesignexamplesareincludedtoillustratethisapproach.WethenconsiderthetransfmationofonetypeofIIRfilt

5、ertransferfunctionintoanothertypewhichisachievedbyreplacingthecomplexvariablezbyafunctionofz.Fourcommonlyusedtransfmationsaresummarized.FinallyweconsiderthecomputeraideddesignofIIRdigitalfilter.Tothisendwerestrictourdisc

6、ussiontotheuseofmatlabindeterminingthetransferfunctions.9.1preliminaryconsiderationsTherearetwomajissuesthatneedtobeansweredbefeonecandevelopthedigitaltransferfunctionG(z).Thefirstfemostissueisthedevelopmentofareasonable

7、filterfrequencyresponsespecificationfromtherequirementsoftheoverallsysteminwhichthedigitalfilteristobeemployed.ThesecondissueistodeterminewhetheranFIRIIRdigitalfilteristobedesigned.Inthesectionweexaminethesetwoissuesfirs

8、t.NextwereviewthebasicanalyticalapproachtothedesignofIIRdigitalfiltersthenconsiderthedeterminationofthefilterderthatmeetstheprescribedspecifications.Wealsodiscussappropriatescalingofthetransferfunction.9.1.1DigitalFilter

9、Specificationserrof.e.is?f.)(sjeG????????sThefrequenciesarerespectivelycalledthepassbedgefrequencythep?s?stopbedgefrequency.Thelimitsofthetolerancesinthepassbstopbp?s?areusuallycalledthepeakripplevalues.Notethatthefreque

10、ncyresponseofadigital)(?jeGfilterisaperiodicfunctionofthemagnituderesponseofarealcoefficientdigitalfilterisan?evenfunctionof.Asaresultthedigitalfilterspecificationsaregivenonlyftherange?.????0Digitalfilterspecificationsa

11、reoftengivenintermsofthelossfunctionindB.Herethepeakpassbrippletheminimumstopb)(log20)(10???jeG??p?attenuationaregivenindBi.e.thelossspecificationsofadigitalfilteraregivenbys?dBpp)1(log2010?????.dBss)(log2010????9.1Preli

12、minaryConsiderationsAsinthecaseofananaloglowpassfilterthespecificationsfadigitallowpassfiltermayalternativelybegivenintermsofitsmagnituderesponseasinFigure7.2.Herethemaximumvalueofthemagnitudeinthepassbisassumedtobeunity

13、themaximumpassbdeviationdenotedas1isgivenbytheminimumvalueofthemagnitudeinthepassb.21??Themaximumstopbmagnitudeisdenotedby1A.Fthenmalizedspecificationthemaximumvalueofthegainfunctiontheminimumvalueofthelossfunctionisther

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