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IIRDigitalFilterDesign AnimportantstepinthedevelopmentofadigitalfilteristhedeterminationofarealizabletransferfunctionG(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. 9.1preliminaryconsiderations TherearetwomajorissuesthatneedtobeansweredbeforeonecandevelopthedigitaltransferfunctionG(z).Thefirstandforemostissueisthedevelopmentofareasonablefilterfrequencyresponsespecificationfromtherequirementsoftheoverallsysteminwhichthedigitalfilteristobeemployed.ThesecondissueistodeterminewhetheranFIRorIIRdigitalfilteristobedesigned.Inthesection,weexaminethesetwoissuesfirst.NextwereviewthebasicanalyticalapproachtothedesignofIIRdigitalfiltersandthenconsiderthedeterminationofthefilterorderthatmeetstheprescribedspecifications.Wealsodiscussappropriatescalingofthetransferfunction. DigitalFilterSpecifications Asinthecaseoftheanalogfilter,eitherthemagnitudeand/orthephase(delay)responseisspecifiedforthedesignofadigitalfilterformostapplications.Insomesituations,theunitsampleresponseorstepresponse