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1、附录AMultirateFilterDesignsUsingCombFiltersSHUN1CHU,MEMBER,IEEE,ANDC.SIDNEYBURRUS,FELLOW,IEEEAbstract-Resultsonmultistagemultiratedigitalfilterdesignindicatemostofthestagescanbedesignedtocontrolaliasingwithonlyslightregardforthepassbandwhichiscontrolledbyasinglestagecompensator.Becauseofthis,thealias
2、ingcontrollingstagescanbemadeverysimple.Thispaperconsiderscombfilterstructuresfordecimatorsandinterpolatorsinmultistagestructures.Designproceduresaredevelopedandexamplesshownthathaveaverylowmultiplicationrate,veryfewfiltercoefficients,lowstoragerequirements,andasimplestructure.IntroductionMultirate
3、filtersaremembersofaclasswhichhasdifferentsamplingratesinvariousstagesofthefilteringoperation.Thisclassoffiltersincludesdecimators,interpolators,andnarrow-bandlow-passfiltersimplementedwithdecimation,low-passfiltering,andinterpolation.Amultistageimplementationofthesefiltershasthesampleratechangedin
4、severalstepswhereeachstepisacombinedfilteringandsampleratechangeoperation.CrochiereandRabiner[1]-[4]gavethestandardmultistagedesignmethodforthesefilterswhichhaseachstageasalow-passfilterwhereoneoptimallychoosesthedecimation(orinterpolation)ratioateachstage.Adesignmethodwaspresentedin[5]whichusesadi
5、fferentdesigncriterionforeachstage.Itonlyrequiresthateachstagehaveenoughaliasingattenuationbuthasnopassbandspecifications.Usingthedesigndescribedin[5]withnopassbandspecificationsforeachstageallowssimplefilterstobeemployedandgivesasatisfactoryfrequencyresponse.LetH(z)andDbethetransferfunctionanddeci
6、mationratioofonestageofamultistagedecimator.WeproposetodesignH(z)suchthatH(z)=f(z)g(zD).Intheimplementation,bythecommutativerule[5],thetransferfunctiong(zD)canbeimplementedatthelowerrate(afterdecimation)asg(z).Thisimplementationreducesthefilterorder,storagerequirement,andthearithmetic.Inthispaper,t
7、osimplifyarithmetic,furtherrequirementsareputonH(z)toallowonlysimpleintegercoefficients.Thisisfeasiblebecausetherearenopassbandspecificationsonthefrequencyresponse.Acascadeofcombfiltersisaparticularcaseofth