3WindowingSpeechisnon-stationarysignalwherepropertieschangequiterapidl - PDF document

3WindowingSpeechisnon-stationarysignalwherepropertieschangequiterapidlyovertime.ThisisfullynaturalandnicethingbutmakestheuseofDFTorautocorrelationasasuchimpossible.Formostphonemesthepropertiesofthespeechremaininvariantforashortperiodoftime(5-100ms).Thusforashortwindowoftime,traditionalsignalprocessingmethodscanbeappliedrelativelysuccessfully.Mostofspeechprocessinginfactisdoneinthisway:bytakingshortwindows(overlappingpossibly)andprocessingthem.Theshortwindowofsignallikethisiscalledframe.InimplementationalviewthewindowingcorrespondstowhatisunderstoodsinÞlterdesignaswindow-method:alongsignal(ofspeechforinstanceoridealimpulseresponse)ismultipliedwithawindowfunctionofÞnitelength,givingÞnitelengthweighted(usually)versionoftheoriginalsignal.IllustrationisinÞgure1. 3900 4000 4100 4200 4300 4400 4500 4600 4700 480 0 1 0.5 0 0.5 1 Alkuperäinen signaali ja Hanningikkuna... 100 200 300 400 500 600 700 800 900 100 0 0.03 0.02 0.01 0 0.01 0.02 0.03 ...tadaa! Ikkunoitu kehys signaalista Figure1:Theoriginalsignalanditswindowedversionbelow.InspeechprocessingtheshapeofthewindowfunctionisnotthatcrucialbutusuallysomesoftwindowlikeHanning,Hamming,triangle,halfparallerogram,notwithrightangles.ThereasonissameasinÞlterdesign,sidebandlobesassubstantiallysmallerthaninarectangularwindow.(Þgure2).MoreoverinLPC-analysis(tobestudiedlateron)thesignalispresumedtobe0outsidethewindow,hencetherectangularwindowproducesabruptchangeinthesignal,whichusuallydistortstheanalysis.Wemustkeepinmindthatinspeechprocessing(unlikeinÞlterdesignforinstance)themethodsareseldomwellgroundedmathematically.Usuallythegoalistoimplementasystemworkingaswellaspossibleinsomeapplication.Thecriteriaoftheapplicationmaybeburiedundercomplexhuman-relatedcriteria/preferenceshinderingprecisemathematicalmodeling.Forinstancethequalityofcodedspeech,intelligibilityofsynthesizedspeechorpleasantnessofenchancedspeech. 0 50 100 150 200 250 300 350 400 450 500 0 0.2 0.4 0.6 0.8 1 Muutama ikkunatyyppi... 0.005 0.01 0.015 0.02 0.025 0.03 0.035 60 50 40 30 20 10 0 10 ...ja niiden vasteet (normalisoituna)Normalisoitu taajuus (1=Nyquist)Vaste, dB Figure2:Abunchofwindowsandtheiramplituderesponses.Basedonthis,thewindowingshouldbeconfrontedwithcertaindegreeoffreedombeingpreparedtochangethewindowfunctionwhennecessary.Example:inspeechcodingthesampleswillbepursuedtoberepresentedexactlyastheyarewhentherectangularwindowisused.OntheotherhandwhentheLPC-parametersareanalyzed,asoftnon-symmetricwindowisusedinordertominimizethedelay.Inspeechrecognitionthewindowsareusuallyoverlapping10mswindows,whichareanalyzedinordertomakehypothesisofthecur-rentphoneme.ThehypothesesarecombinedoverseveralframesandÞnallythedecisionismadetomaximizethejointprobability.Ifonedesirestoshapethespeech(notonlyanalyze),itisagoodideatouseoverlappingwindowssummingapproximatelyto1.Forinstance:thecoarsestcodingsystemintheworld,whereineachframethe10highestsamplesofDFTarequantizedandothersaresetto0.Theinversetransformthenrestorestheoriginalsignal.LetÕsimplementthis,becauseitbringsupnicelydifferentaspectsrelatedtowindowing,analyza-tionandsynthesis.TheMatlab-sourcescriptcanbefoundinandbelow.functionsyn=FFT_coding_en(ind,N);%syn=FFT_coding_en(ind,N); %ThisistheEnglishversionofFFT_koodaus_fi.m.Theoperationof%FFT_coding_en.misidenticaltothatofFFT_koodaus_fi.m.%Windowingdemo:thespeechisprocessedin%windowsoflength60msandroundedges(ifind==0),orin%windowsoflength30msandarectangularshape(ifind==1).%FFTiscalculatedandallbutN+1biggest-amplitudefrequencybinsare%settozero.Then,theoutputspeech(’syn’)issynthesizedusingIFFT.%Thespeechdatausedbythisfunctionisyhdeksän16.mat.loadyhdeksän16.matx=x(:);%forceascolumnvectorfs=16000;%samplingfrequencyif(ind==0),awinlen=round(fs*0.06);%lengthoftheanalysiswindow,60ms%thewindowfunctionisalmostabritrarilychosen:%wemakeawindowthatisflatinthemiddleandhassoftedgestemp=hanning(fs*0.01);%thesoftedgesarehereawinfun=[temp(1:length(temp)/2);ones(awinlen-length(temp),1);...swinlen=round(awinlen/2);%lengthofthesynthesiswindowis%halfoftheanalysiswindowswinfun=hanning(swinlen);%windowfunctionforsynthesisnforward=swinlen/2;%howmanyfrequencybinstherearebetween%successiveframesif(ind==1),awinlen=round(fs*0.03);%lengthoftheanalysiswindow,30msawinfun=boxcar(awinlen);%nowarectangularwindowshapeischosenswinlen=round(awinlen);%nowthelengthofthesynthesiswindow=%lengthoftheanalysiswindowswinfun=boxcar(swinlen);%windowfunctionforsynthesisnforward=swinlen;%howmanyfrequencybinstherearebetween%successiveframesholdon-1),swinfun,’r-.’);title(’analysiswindow(blue)andsynthesiswindow(red)’)axis([0100001.4])print-depsca_and_s_window.eps fftind=1:floor(awinlen/2)+1;%indicesofhalfofFFTvectorn=1+ceil(awinlen/2);%themiddlesampleoftheframesyn=zeros(size(x));flag=0;%flagfordoingsomedecisionsrelatedtodrawingwhile(n+ceil(awinlen/2)length(x))awinind=n-ceil(awinlen/2)+(0:awinlen-1);%indicesoftheanalysis%windowincurrentframeframe=x(awinind).*awinfun;%frameFrame=fft(frame);%FFToftheframe%wesearch(N+1)thlargestabsolutevalue[val,sind]=sort(abs(Frame(fftind)));valN=val(end-N);Frame(abs(Frame)valN)=0;%settozeroallbutN+1highest-amplitude%frequencybinsiframe=real(ifft(Frame));%inverseFFT,therealpartistaken%toavoidprecisionproblems=n-swinlen/2+(0:swinlen-1);%synthesiswindowingswin=iframe(1+awinlen/2-swinlen/2+(0:swinlen-1)).*swinfun;syn(swinind)=syn(swinind)+swin;%overlap-addif((n&#x-597;&#x.300;3000)&~flag)%drawapitcureoftheframeplot(x(awinind),’k’);%thisonecanhardlybeseeninthepicture%iftherectangularwindowisusedholdonplot(frame,’b-.’);plot(awinlen/2-swinlen/2+(0:swinlen-1),swin,’r-.’);title(’originalspeech(black),analysiswindow(blue)andsynthesiswi print-depscframe.epsflag=1;n=n+nforward;holdontitle(’originalspeech(black)andmodifiedspeech(red)’);print-depscresult.eps Theideaisthefollowing:thespeechisÞrstwindowedforFFTanalysiswithrelativelylong(60ms)andquiterectangularwindow.Thepurposeistogetsomeideaofthefrequencycontentinthewindow,butsothatthewindowingwillnotexcessivelyaffecttheshapeoftheframe.Asa(cautionary)example,thefunctionhasalsobeenwrittentocontainapossibilityofusingarectangularwindowoflength30ms,butinpracticeitisnotadvisabletousethisoptionsinceitconsiderablydegradesthespeechquality.NexttheFFToftheanalysisframeiscalculatedandallsmall-energyfrequenciesaresettozero.TheinverseFFTisthenappliedtothispartiallyzerospectrumtogetthetimedomainsignal.Thenextthingtodoisanewwindowingsystem(incasethe60mswindowwaschosen):wewindowonlythecentralpartoftheframeandedgeswillbefaded.WeuseHanning-windowthathasthenicepropertyofsummingto1whenthetimedifferencebetweensuccessivewindowsishalfofthelengthofthewindow(exactly1whenthelengthisoddinteger).Themethodofusingoverlappingshort-timesignalsandformingthereconstructionbysummingpartiallyoverlappingframesiscalledoverlap-addIf,asanexperiment,the30msrectangularwindowischosen,thesuccessiveframesdonotoverlapatall,butinstead,thesynthesisconsistsofcatenatingthetimedomainframesproducedbytheinverseFFTassuch.Inthiscase,discontinuitieswilloccurattheframeboundaries,whichmakestheoutputspeechsoundveryunnatural. 200 400 600 800 1000 120 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Puoliksi päällekkäisten Hanningikkunoiden summa Figure3:ThesumofHanning-windowswithtimedifferencehalfofthelengthisalmost1,whichmakesthemattractiveinsynthesiswindowing.Whenthe60mswindowisused(i.e.,ind=0),andthevalueof9ischosenforN(i.e.,10largest-amplitudefrequencybinsofFFTarepreserved),thefunctionwillproducetheÞguresshowninFigures4-6. 0 100 200 300 400 500 600 700 800 900 100 0 0 0 .2 0 .4 0 .6 0 .8 1 1 .2 Figure4:Analysisandsynthesiswindowsusedinthefunction. 100 200 300 400 500 600 700 800 900 1000 1.5 1 0.5 0 0.5 1 1.5x 104 alkup. puhe (must), analyysiikkuna (sin) ja synteesiikkuna (pun) Figure5:Originalspeech(black),analysiswindow(blue),synthesiswindow(red). 0 2000 4000 6000 8000 10000 1200 0  1.5 1  0.5 0 0.5 1 1.5x 104 Figure6:Originalspeech(black)andcodedspeech(red).