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1、IEEETRANSACTIONSONACOUSTICS.SPEECH,ANDSIGNALPROCESSING,VOL.36.NOI.JANUARY198881LatticeStructuresforOptimalDesignandRobustImplementationofTwo-ChannelPerfect-ReconstructionQMFBanksAbstruct-AlatticestructureandanalgorithmarepresentedfortheZpT-designoftwo-channelQMFbanks,satisfyingasuff
2、icientconditionforperfectreconstruction.Thestructureinherentlyhastheperfect-recon-x(n)...;(n)structionproperty,Hhilethealgorithmensuresagoodstophandatten-HI(2)F,(2)uationforeachoftheanalysisfilters.Implementationsofsuchlatticex,(n)Y,(n)structuresarerobustinthesensethattheperfect-rec
3、onstructionprop-Fig.1.Atwo-channelQMFbank.ertyispreservedinspiteofcoefficientquantization.Thelatticestruc-turehasahierarchicalproperty,inthesensethatahigherorderper-fect-reconstructionQMI;hankcanheobtainedfromalowerorderItiswellknown[I]-[3]thatthechoiceofsynthesisfiltersperfect-reco
4、nstructionQMFbank,siniplybyaddingmorelatticesec-Fk(z)accordingtotions.Severalnumericalexamplesareprovidedintheformofdesigntables.Fo(z)=-H1(-z),F,(z)=4d-Z)(2)I.INTRODUCTIONcancelsthealiasingterm[secondtermin(l)],leadingtotheresultTHEproblemofquadraturemirrorfiltering(QMF)hasreceiveds
5、ubstantialattentionrecently[I]-[141.Thesefiltersfindapplicationwhenasignalistobesplitintotwoormorefrequencybands,witheachbandsubsequentlyprocessedinanindependentmanner.Fig.1showsatwo-+Hdz)Hid-41.(3)bandQMFbankwhereH,(z)andH,(z)arethe“analysisOncealiasingisthuscancelled,theQMFbankisa
6、time-filters”(low-passandhigh-pass,respectively).Thesub-invariantsystemcharacterizedbythetransferfunctionbandsignalsxo(n)andx,(n)areundersampled(or“de-T(z).Thus,ingeneral,thereconstructedsignalR(z)suf-cimated”)byafactoroftwo,thentransmittedafterpos-fersfromamplitudedistortion(dueton
7、onconstantsibleencoding[2].Atthereceiverend.thesignalsareIT(eJ”)I)andphasedistortion(duetononlinearargupsampled,filtered,andrecombinedtoproducethere-[T(e’”)]).IthasbeenknownforsometimehowphaseconstructedsignalR(n).Inordertoavoidaspectralgap,oramplitudedistortioncanbecompletelyelimin
8、ated[2],theresponse
