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1,SpeechSignalProcessingLecture7,SpeechCodingMethodsBasedonSpeechWaveformRepresentationsandSpeechModelsAdaptiveandDifferentialCoding,2,QuantizationDilemma,Wanttochoosequantizationstepsizelargeenoughtoaccommodatemaximumpeak-to-peakrangeofx(n);atthesametimeneedtomakethequantizationstepsizesmallsoastominimizethequantizationerrorthenon-stationarynatureofspeech(variabilityacrosssounds,speakers,backgrounds)compoundsthisproblemgreatly,3,SolutionstoQuantizationDilemma,Solution1-letvarytomatchthevarianceoftheinputsignal=(n)Solution2-useavariablegain,G(n),followedbyafixedquantizerstepsize,=keepsignalvarianceofy(n)=G(n)x(n)constant,Case1:(n)proportionaltox2=quantizationlevelsandrangeswouldbelinearlyscaledtomatchx2=needtoreliablyestimatex2Case2:G(n)proportionalto1/x2togivey2constantneedreliableestimateofx2forbothtypesofadaptivequantization,AdaptiveQuantization:,4,TypesofAdaptiveQuantization,Classification1:instantaneous-amplitudechangesreflectsample-to-samplevariationsinx(n)=rapidadaptationsyllabic-amplitudechangesreflectsyllable-to-syllablevariationsinx(n)=slowadaptationClassification2:feed-forward-adaptivequantizersthatestimatex2fromx(n)itselffeedback-adaptivequantizersthatadaptthestepsize,onthebasisofthequantizedsignal,(orequivalentlythecodewords,c(n),5,FeedForwardAdaptation,Variablestepsizeassumeuniformquantizerwithstepsize(n)x(n)isquantizedusing(n)=c(n)and(n)needtobetransmittedtothedecoderifc(n)=c(n)and(n)=(n)=noerrorsinchannel,and,Donthavex(n)atthedecodertoestimate(n)=needtotransmit(n);thisisamajordrawbackoffeedforwardadaptation,6,Feed-ForwardQuantizer,timevaryinggain,G(n)=c(n)andG(n)needtobetransmittedtothedecoder,CantestimateG(n)atthedecoder=ithastobetransmitted,7,FeedForwardQuantizers,feedforwardsystemsmakeestimatesofx2,thenmakeorthequantizationlevelsproportionaltox,orthegainisinverselyproportionaltox,8,FeedForwardQuantizer,theparametercontrolstheeffectiveintervalofx(n)thatcontributestotheestimateof,=0.99=bringsuplevelinlowamplituderegions=syllabicrate,=0.9=systemreactstoamplitudevariationsmorerapidly=instantaneousrate,9,FeedForwardQuantizers,(n)andG(n)varyslowlycomparedtox(n)theymustbesampledandtransmittedaspartofthewaveformcoderparametersrateofsamplingdependsonthebandwidthofthelowpassfilter,h(n)for=0.99,therateisabout13Hz;for=0.9,therateisabout135Hz,10,FeedForwardAdaptationGain,lessgainforM=1024thanM=128by3dB=M=1024istoolonganinterval,11,FeedbackAdaptation,2(n)estimatedfromquantizeroutput(orthecodewords)advantageoffeedbackadaptationisthatneither(n)norG(n)needstobetransmittedtothedecodersincetheycanbederivedfromthecodewordsdisadvantageoffeedbackadaptationisincreasedsensitivitytoerrorsincodewords,sincesucherrorsaffect(n)andG(n),12,FeedbackAdaptation,13,PerformanceComparisonofAdaptiveQuantizationandPCM,improvementsinSNR,4-7dBimprovementover-law,14,DifferentialQuantization,wehavecarriedinstantaneousquantizationofx(n)asfaraspossibletimetoconsidercorrelationsbetweenspeechsamplesseparatedintime=differentialquantizationhighcorrelationvalues=signaldoesnotchangerapidlyintime=differencebetweenadjacentsamplesshouldhavelowervariancethanthesignalitself,differentialquantizationcanincreaseSNRatagivenbitrate,orlowerbitrateforagivenSNR,15,DifferentialQuantization,16,DifferentialQuantization,differencesignal,d(n),isquantized-notx(n)quantizercanbefixed,oradaptive,uniformornon-uniformquantizerparametersareadjustedtomatchthevarianceofd(n),17,DifferentialQuantization,quantizeddifferencesignalisencodedintoc(n)fortransmission,firstreconstructthequantizeddifferencesignalfromthedecodercodeword,c(n)andthestepsizenextreconstructthequantizedinputsignalusingthesamepredictor,P,asusedintheencoder,18,SNRforDifferentialQuantization,19,SNRforDifferentialQuantization,20,PredictorforDifferentialQuantization,21,PredictorforDifferentialQuantization,22,SolutionforOptimumPredictor,23,SolutionforOptimumPredictor,24,SolutionforOptimumPredictor,25,SolutionforOptimumPredictor,26,FirstOrderPredictorSolution,27,ActualPredictionGainsforSpeech,variationingainacross4speakerscangetabout6dBimprovementinSNR=1extrabitequivalentinquantizationbutatapriceofincreasedcomplexityinquantization,differentialquantizationworks!gaininSNRdependsonsignalcorrelationsfixedpredictorcannotbeoptimumforallspeakersandforallspeechmaterial,28,DeltaModulation,simplestformofdifferentialquantizationisindeltamodulation(DM)samplingratechosentobemanytimestheNyquistratefortheinputsignal=adjacentsamplesarehighlycorrelatedinthelimitasT0,weexpectthisleadstoahighabilitytopredictx(n)frompastsamples,withthevarianceofthepredictionerrorbeingverylow,leadingtoahighpredictiongain=canusesimple1-bit(2-level)quantizer=thebitrateforDMsystemsisjustthe(high)samplingrateofthesignal,29,LinearDeltaModulation,30,LinearDeltaModulation,31,DMSlopeOverloadDistortion,slopeoverload,32,DMGranularNoise,needlargestepsizetohandlewidedynamicrangeneedsmallstepsizetoaccuratelyrepresentlowlevelsignals,choosetomaximizemean-squaredquantizationerror(acompromisebetweenslopeoverloadandgranularnoise),granularnoise,33,PerformanceofDMSystems,forgivenvalueofF0,thereisanoptimumvalueofoptimumSNRincreasesby9dBforeachdoublingofF0curvesareverysharparoundoptimumvalueof=SNRisverysensitivetoinputlevelforSNR=35dB,forFN=3kHz=200Kbpsratefortollqualityneedmuchhigherrates,34,AdaptiveDeltaMod,35,AdaptiveDMPerformance,slopeoverloadinLDMcausesrunsof0sor1sgranularitycausesrunsofalternating0sand1showadaptiveDMperforms:duringslopeoverload,stepsizeincreasesexponentiallytofollowincreaseinwaveformslopeduringgranularity,stepsizedecreasesexponentiallytominandstaysthereaslongassloperemainssmall,36,ADMParameterBehavior,ADMparametersareP,Q,minan
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