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1、IEEETRANSACTIONSONACOUSTICS,SPEECH,ANDSIGNALPROCESSING,VOL.36,NO.IO,OCTOBER19881561GeneralSynthesisProceduresforFIRLosslessTransferMatrices,forPerfect-ReconstructionMultirateFilterBankApplicationsZINNURDOGANATA,STUDENTMEMBER,IEEE,P.P.VAIDYANATHAN,SENIORMEMBER,IEEE,ANDTRUONGQ.NG
2、UYEN,STUDENTMEMBER,IEEEAbstract-ArecentlyreportedprocedureforthedesignofM-chan-andisgeneralinthesensethateveryQMFbankwithFIRne1perfect-reconstructionquadraturemirrorfilterbanksusesthecon-analysisandsynthesisfilters,whichhasalosslessACma-ceptof“losslessalias-componentmatrices.”T
3、hesynthesisofsuchtrix,iscovered.AnalgorithmfortheoptimizationoftheQMFbankscentersaroundthegenerationofalosslessMXMFIRtransfermatrixE(z).Recentresultsforsuchgenerationhavebeenanalysisfiltersisdeveloped,whichguaranteesthatthesomewhatadhoc,Le.,notsufficientlygeneral.Inthispaper,ag
4、eneralsearchisautomaticallyconductedoverthesetofallfiltersprocedureisoutlinedforthegenerationofsuchtransfermatricesE(z).withlosslessACmatrices.SomeportionsoftheseresultsTheprocedureisbasedonacascaded-latticestructure,derivedfromhaveappearedinarecentconferenceproceedings[181.ast
5、ate-spaceviewpoint.ThestructureissuchthatitgeneratesonlyMThefollowingnotationsareusedinthepaper.Super-XMlosslessFIRtransfermatrices(regardlessofparametervalues),andconversely,anyMXMlosslessFIRtransfermatrixcanheob-scriptTstandsformatrix(orvector)transposition,tainedbyasuitablec
6、hoiceofparameters.Theseparametersturnoutwhereassuperscriptdagger(t)standsfortranspositiontobeanglesOk,andthestructureissuchthatthenumberofanglesisfollowedbycomplexconjugation.Boldfaceitaliclettersminimal.Adesignexampleispresentedtodemonstratethemainre-indicatematricesandvectors
7、.Therowandcolumnin-sults.dexesofmatricesandvectorsbeginwith“zero.”The(i,j)thentriesofmatricesUanduk,1aredenotedbyI.INTRODUCTIONUi,jandU!;;,respectively.Superscriptasterisk(*)standsUADRATUREmirrorfilter(QMF)banksandtheirforcomplexconjugation,whilesubscriptasteriskdenotesQapplica
8、tionshavereceivedconsiderableattentioninconjugationofc
