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1、附录AMultirateFilterDesignsUsingCombFiltersSHUN1CHU,MEMBER,IEEE,ANDC.SIDNEYBURRUS,FELLOW,IEEEAbstract-Resultsonmultistagemultiratedigitalfilterdesignindicatemostofthestagescanbedesignedtocontrolaliasingwithonlyslightregardforthepassbandwhichiscontrolledbyasinglestagecompensator.Becauseofth
2、is,thealiasingcontrollingstagescanbemadeverysimple.Thispaperconsiderscombfilterstructuresfordecimatorsandinterpolatorsinmultistagestructures.Designproceduresaredevelopedandexamplesshownthathaveaverylowmultiplicationrate,veryfewfiltercoefficients,lowstoragerequirements,andasimplestructure
3、.IntroductionMultiratefiltersaremembersofaclasswhichhasdifferentsamplingratesinvariousstagesofthefilteringoperation.Thisclassoffiltersincludesdecimators,interpolators,andnarrow-bandlow-passfiltersimplementedwithdecimation,low-passfiltering,andinterpolation.Amultistageimplementationofthes
4、efiltershasthesampleratechangedinseveralstepswhereeachstepisacombinedfilteringandsampleratechangeoperation.CrochiereandRabiner[1]-[4]gavethestandardmultistagedesignmethodforthesefilterswhichhaseachstageasalow-passfilterwhereoneoptimallychoosesthedecimation(orinterpolation)ratioateachstag
5、e.Adesignmethodwaspresentedin[5]whichusesadifferentdesigncriterionforeachstage.Itonlyrequiresthateachstagehaveenoughaliasingattenuationbuthasnopassbandspecifications.Usingthedesigndescribedin[5]withnopassbandspecificationsforeachstageallowssimplefilterstobeemployedandgivesasatisfactoryfr
6、equencyresponse.LetH(z)andDbethetransferfunctionanddecimationratioofonestageofamultistagedecimator.WeproposetodesignH(z)suchthatH(z)=f(z)g(zD).Intheimplementation,bythecommutativerule[5],thetransferfunctiong(zD)canbeimplementedatthelowerrate(afterdecimation)asg(z).Thisimplementationreduc
7、esthefilterorder,storagerequirement,andthearithmetic.Inthispaper,tosimplifyarithmetic,furtherrequirementsareputonH(z)toallowonlysimpleintegercoefficients.Thisisfeasiblebecausetherearenopassbandspecificationsonthefrequencyresponse.Acascadeofcombfiltersisaparticularcaseofth
