CIC Filter Introduction

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1、CICFilterIntroductionMatthewP.Donadiom.p.donadio@ieee.org18July2000ForFreePublicationbyIowegian1IntroductionAsdataconvertersbecomefasterandfaster,theapplicationofnarrow-bandextractionfromwidebandsources,andnarrow-bandconstructionofwidebandsignalsisbecomingmoreimportant.Thesefu

2、nctionsrequiretwobasicsignalprocessingprocedures:decimationandinterpolation.Andwhiledigitalhardwareisbecomingfaster,thereisstilltheneedforecientsolutions.Techniquesfoundin[CR83]workverywellinpractice,butlargeratechangesrequireverynarrowbandlters.Largeratechangesrequirefastmu

3、ltipliersandverylonglters.ThiscanendupbeingthelargestbottleneckinaDSPsystem.In[Hog81],anecientwayofperfomingdecimationandinterpolationwasintroduced.Hogenauerdeviseda exible,multiplier-freeltersuitableforhardwareimplementation,thatcanalsohandlearbitraryandlargeratechanges.Th

4、eseareknownascascadedintegrator-comblters,orCICltersforshort.Thispapersumarizesthendingspublishedin[Hog81].Anoverviewcanalsobefoundin[Fre94].AnextensionofCICltershasbeenpublishedin[KJW97],andisbrie ymentionedhere.Whenindoubt,thereadershouldrefertothesesources.2BuildingBloc

5、ksThetwobasicbuildingblocksofaCIClterareanintegratorandacomb.Anintegratorissimplyasingle-poleIIRlterwithaunityfeedbackcoecient:y[n]=y[n1]+x[n](1)Thissystemisalsoknownasanaccumulator.Thetransferfunctionforanintegratoronthez-planeis1HI(z)=(2)1z11Usingtheequationsfrom[OS89]

6、forasinglepolesystem,wecandeterminethatjH(ej!)j2=1I2(1cos!)ARG[H(ej!)]=tan1sin!I1cos!(3)j!undened!=0grd[HI(e)]=1!6=02Thepowerresponseisbasicallyalow-passlterwitha20dBperdecade(6dBperoctave)rollo,butwithinnitegainatDC.Thisisduetothesinglepoleatz=1;theoutputcangrow

7、withoutboundforaboundedinput.Inotherwords,asingleintegratorbyitselfisunstable.z1#?--"!Figure1:BasicIntegratorAcomblterrunningatthehighsamplingrate,fs,foraratechangeofRisanodd-symetricFIRlterdescribedbyy[n]=x[n]x[nRM](4)Inthisequation,Misadesignparameterandiscalledthedie

8、rentialdelay.Mcanbeanypositiveinteger,butitisusallylimitedto1