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1、附录AMultirateFilterDesignsUsingCombFiltersSHUN1CHU,MEMBER,IEEE,ANDC.SIDNEYBURRUS,FELLOW,IEEEAbstract-Resultsonmultistagemultiratedigitalfilterdesignindicatemostofthestagescanbedesignedtocontrolaliasingwithonlyslightregardforthepassbandwhichiscontrolledbyasinglestagecompensator.Becauseofthis
2、,thealiasingcontrollingstagescanbemadeverysimple.Thispaperconsiderscombfilterstructuresfordecimatorsandinterpolatorsinmultistagestructures.Designproceduresaredevelopedandexamplesshownthathaveaverylowmultiplicationrate,veryfewfiltercoefficients,lowstoragerequirements,andasimplestructure.Int
3、roductionMultiratefiltersaremembersofaclasswhichhasdifferentsamplingratesinvariousstagesofthefilteringoperation.Thisclassoffiltersincludesdecimators,interpolators,andnarrow-bandlow-passfiltersimplementedwithdecimation,low-passfiltering,andinterpolation.Amultistageimplementationofthesefilte
4、rshasthesampleratechangedinseveralstepswhereeachstepisacombinedfilteringandsampleratechangeoperation.CrochiereandRabiner[1]-[4]gavethestandardmultistagedesignmethodforthesefilterswhichhaseachstageasalow-passfilterwhereoneoptimallychoosesthedecimation(orinterpolation)ratioateachstage.Adesig
5、nmethodwaspresentedin[5]whichusesadifferentdesigncriterionforeachstage.Itonlyrequiresthateachstagehaveenoughaliasingattenuationbuthasnopassbandspecifications.Usingthedesigndescribedin[5]withnopassbandspecificationsforeachstageallowssimplefilterstobeemployedandgivesasatisfactoryfrequencyres
6、ponse.LetH(z)andDbethetransferfunctionanddecimationratioofonestageofamultistagedecimator.WeproposetodesignH(z)suchthatH(z)=f(z)g(zD).Intheimplementation,bythecommutativerule[5],thetransferfunctiong(zD)canbeimplementedatthelowerrate(afterdecimation)asg(z).Thisimplementationreducesthefiltero
7、rder,storagerequirement,andthearithmetic.Inthispaper,tosimplifyarithmetic,furtherrequirementsareputonH(z)toallowonlysimpleintegercoefficients.Thisisfeasiblebecausetherearenopassbandspecificationsonthefrequencyresponse.Acascadeofcombfiltersisaparticularcaseofth
