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1、CICFilterIntroductionMatthewP.Donadiom.p.donadio@ieee.org18July2000ForFreePublicationbyIowegian1IntroductionAsdataconvertersbecomefasterandfaster,theapplicationofnarrow-bandextractionfromwidebandsources,andnarrow-bandconstructionofwidebandsignalsisbecomingmoreimportant.Thesefu
2、nctionsrequiretwobasicsignalprocessingprocedures:decimationandinterpolation.Andwhiledigitalhardwareisbecomingfaster,thereisstilltheneedforecientsolutions.Techniquesfoundin[CR83]workverywellinpractice,butlargeratechangesrequireverynarrowbandlters.Largeratechangesrequirefastmu
3、ltipliersandverylonglters.ThiscanendupbeingthelargestbottleneckinaDSPsystem.In[Hog81],anecientwayofperfomingdecimationandinterpolationwasintroduced.Hogenauerdeviseda
exible,multiplier-freeltersuitableforhardwareimplementation,thatcanalsohandlearbitraryandlargeratechanges.Th
4、eseareknownascascadedintegrator-comblters,orCICltersforshort.Thispapersumarizesthendingspublishedin[Hog81].Anoverviewcanalsobefoundin[Fre94].AnextensionofCICltershasbeenpublishedin[KJW97],andisbrie
ymentionedhere.Whenindoubt,thereadershouldrefertothesesources.2BuildingBloc
5、ksThetwobasicbuildingblocksofaCIClterareanintegratorandacomb.Anintegratorissimplyasingle-poleIIRlterwithaunityfeedbackcoecient:y[n]=y[n 1]+x[n](1)Thissystemisalsoknownasanaccumulator.Thetransferfunctionforanintegratoronthez-planeis1HI(z)=(2)1 z 11Usingtheequationsfrom[OS89]
6、forasinglepolesystem,wecandeterminethatjH(ej!)j2=1I2(1 cos!)ARG[H(ej!)]= tan 1sin!I1 cos!(3)j!undened!=0grd[HI(e)]=1 !6=02Thepowerresponseisbasicallyalow-passlterwitha 20dBperdecade( 6dBperoctave)rollo,butwithinnitegainatDC.Thisisduetothesinglepoleatz=1;theoutputcangrow
7、withoutboundforaboundedinput.Inotherwords,asingleintegratorbyitselfisunstable.z 1#?--"!Figure1:BasicIntegratorAcomblterrunningatthehighsamplingrate,fs,foraratechangeofRisanodd-symetricFIRlterdescribedbyy[n]=x[n] x[n RM](4)Inthisequation,Misadesignparameterandiscalledthedie
8、rentialdelay.Mcanbeanypositiveinteger,butitisusallylimitedto1