1988-Maximally decimated perfect-reconstruction FIR filter banks with pairwise mirror-image analysis (and synthesis) frequency responses文稿

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1、IEEETRANSACTIONSONACOUSTICS,SPEECH,ANDSIGNALPROCESSING,VOL.36,NO.5,MAY1988693MaximallyDecimatedPerfect-ReconstructionFIRFilterBankswithPairwiseMirror-ImageAnalysis(andSynthesis)FrequencyResponsesAbstract-Newstructuresarepresentedfortheperfect-reconstruc-x(n)xTt+&gqJt

2、ionQMFbank,basedonlosslessbuildingblocks.Thesestructuresensurethatthefrequencyresponsesoftheanalysis(andsynthesis)fil-H,(Z)tershavepairwisesymmetrywithrespectto~/2,andrequirefewer..parametersthanrecentlyreportedstructures(alsobasedonlosslessbuildingblocks).Thedesign-

3、timebasedonthenewstructuresiscor-4p&ii+.:.-++(&+;(”)respondinglymuchlessthantheearliermethodswhichdidnotincor-poratesuchsymmetry.Fig.1.TheM-channelmaximallydecimatedparallelQMFbank.I.INTRODUCTIONbuildingblocks.Withthelatticestructuresgivenin[7],UADRATUREmirrorfilters

4、(inshort,QMF)aretherelationsamongtheanalysisfiltersarenotexplicitlyQusedinanumberofcommunicationapplicationssuchdescribable,Le.,theyarenotrelatedinanobviousway.assubbandcodersforspeechsignals[1]-[3],andfre-Theobjectofthispaperistodescribeperfectreconstruc-quencydomai

5、nspeechscramblers[4].Fig.1showsatyp-tionstructuresforarbitraryMinwhichtheanalysisfiltersicalM-channelmaximallydecimatedparallelQMFbankHk(z)havepairwisesymmetryoffrequencyresponseswhereHk(z)andFk(z),0IkIM-1,areanalysisaboutn/2.Tobeprecise,weconsideranalysisbanksofands

6、ynthesisfilters,respectively(weconsideronlyfinitetheformimpulseresponse(FIR)filtersinthispaper).ThebasicpurposeandoperationofthefiltersHk(z),Fk(z)canbefoundinanumberofreferences[1]-[3],[7]-[8],[11]-[141.Usually,thereconstructedsignal2(n)suffersfromaliasing,amplitude,

7、andphasedistortions[5].Itissome-for0IkIM-1andwhererisapositiveintegerlargetimesdesirabletoeliminateallthesedistortions,sothatenoughtoensurethecausalityofHM-l-k(z).Ananaly-a(n)=cx(n-no);suchasystemiscalledaperfectsisbanksatisfying(1)willbecalleda“pairwisesym-reconstru

8、ctionsystem(PRS).metricanalysisbank”inthispaper.InSectionI1were-ThetheoryofperfectreconstructionwhenMisapowercapitulateresultsonper