Proc1999IEEEWorkshoponApplicationsofSignalProcessingtoAudioandAcousticsNewPaltzNewYorkOct17201999presentedthesinelaw6as r2whereistheperceivedangleofavirt ID: 521027
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Proc.1999IEEEWorkshoponApplicationsofSignalProcessingtoAudioandAcoustics,NewPaltz,NewYork,Oct.17-20,1999UNIFORMSPREADINGOFAMPLITUDEPANNEDVIRTUALSOURCESVillePulkkiLaboratoryofAcousticsandAudioSignalProcessingHelsinkiUniversityofTechnologyP.O.Box3000,FIN-02015HUT,FinlandVille.Pulkki@hut.fiABSTRACTTheperceivedspatialspreadofamplitudepannedvirtualsourcesisdependentonthenumberofloudspeakersthatareusedtopro-ducethem.Whenpair-wiseortriplet-wisepanningisapplied,thenumberofactiveloudspeakersvariesasafunctionofthepanningdirection.Thismaycauseunwantedchangesinspatialspreadandcolorationofavirtualsourceifitismovedinthesoundstage.Inthispaperamethodispresentedtomakethedirectionalspreadofamplitudepannedvirtualsourcesindependentoftheirpanningdirection.Thisisaccomplishedbypanningthesoundsignaltomultipledirectionsneareachothersimultaneously.Thisformsasinglevirtualsourcewithconstantdirectionalspreadasafunctionofdirection.1.INTRODUCTIONInmanytheatersandauditoriumsthereexistsloudspeakersystemsthatincludealargenumberofloudspeakers.Audiosystemswithmultipleloudspeakersarealsobecomingmorecommonindomes-ticuse.Indomesticusethespeakersaremostoftenplacedtoahorizontalplanearoundthelistener(two-dimensionalspeakerse-tups).Intheaterstherearealsosystemsinwhichalsoelevatedordescendedloudspeakersexist(three-dimensionalsetups).Virtualsourcescanbepositionedtosuchloudspeakersystemsusingvariousmethods.Intwo-dimensionalsetupsthepanningismostoftenperformedusingpair-wisepanningmethods[1].Pair-wisepanningcanbegeneralizedtotriplet-wisepanningforthree-dimensionalloudspeakersetups[2].Pair-wisepanningandtriplet-wisepanningyieldsanacceptablevirtualsourcequalityinrela-tivelylargelisteningarea.However,thevirtualsourcequalityisdependentonpanningdirectionbecausethenumberofloudspeak-ersemanatingthesamesoundsignalvariesindifferentdirections.Thismaybeperceivedinconvenientwhenmovingvirtualsoundsourcesareapplied.Inmatrixingsoundreproductiontechniques,likeAmbisonics[3],soundsignalsareencodedanalogicallytofewaudiochannels.Inthedecodingstageloudspeakersignalsaredecodedusingsomematrixingoperations.Inthesetechniquesthesamesoundsignalisexistentinallloudspeakers,whichmaydegradethevirtualsourcequality.However,whenmovingsoundsourcesareapplied,thenumberofloudspeakersproducingavirtualsourceisnotdepen-dentonpanningdirection,thusthedirectionalspreaddoesnotvaryprominently.Basicallythematrixingsystemsandpair-wiseortriplet-wisepanningmethodsarequitesimilartechniques.Inbothmethodsasoundsignalisappliedtoanumberofloudspeakerswithdifferentamplitudes.Thegoalofthisstudyistoformmethodsforvirtualsourcepositioningthatwouldbesomethinginbetweenthematrix-ingtechniquesandpair-wiseortriplet-wisepanning.Thispaperisorganizedasfollows:Atrstsomebasicsofspatialhearingandamplitudepanningarereviewed.Themethodforspreadingamplitude-pannedvirtualsourcesisthenpresented.Thedirectionalspreadofpair-wisepannedvirtualsourcesandspreadedvirtualsourcesarecomputedusingabinauralmodel.2.SPATIALHEARINGSpatialanddirectionalhearinghasbeenstudiedintensively;foroverviews,seee.g.[4].TheduplextheoryofsoundlocalizationstatesthatthetwomaincuesofsoundsourcelocalizationaretheinterauraltimedifferenceITDandtheinterauralleveldifferenceILDwhichareduetowavepropagationtimedifference(primarilybelow1.5kHz)andtheshadowingeffectbythehead(primarilyabove1.5kHz),respectively.Bothcuesdependonfrequency.Inthemedianplanewherethedistancestobothearsareequal,theITDandILDvaluesareclosetozero.Othereffects,suchasspectralcuesandheadmovements,areconsideredtocarryeleva-tionandfront-backinformationinthemedianplane.Spatialdis-criminationisdifcultalsoinsocalledconesofconfusionwhereILDandITDvaryonlyslightlyduetotheunsymmetryofthehead.Aconeofconfusioncanbeapproximatedwithaconewhichhassymmetryaxisinthelinepassingthroughlistener'sears.Ifthecuesofanauditoryobjectareconicting,thelistenermayperceivetheobjectinmultipledirectionssimultaneously.Thedirectionalspreaddenoteshowwelltheauditoryobjectissituatedinonedirection:whatsmallerdirectionalspread,thatmorepoint-likeauditoryobject.3.AMPLITUDEPANNINGAmplitudepanning[5]ismostoftenappliedtotwoloudspeak-erswhichareinastandardstereophoniclisteningconguration,asdepictedinFig.1.Loudspeakers1and2areplacedinfrontofthelistenerwithapertureof .Asignalisappliedtoeachloudspeakerwithdifferentamplitudes,thiscanbeformulatedas \n \r \n \r (1)where \n isthesignaltobeappliedtoloudspeaker,isthegainfactorofthecorrespondingchannel,and\nisthetimeparam-eter.Thesoundsignalsarrivetolistener'sbothearsfrombothloud-speakers.Ifthewavepropagationtimedifferenceistakenintoac-count,buttheshadowingeffectoftheheadisneglected,wemayW99-1 Proc.1999IEEEWorkshoponApplicationsofSignalProcessingtoAudioandAcoustics,NewPaltz,NewYork,Oct.17-20,1999presentedthesinelaw[6]as !#"%$ !#"%$&\r('*)+,('.-/,(2)where$istheperceivedangleofavirtualsourceand$&istheloudspeakerbaseangle,asinFig.1.Theequationisvalidonlywhenthefrequencyisbelow600Hzandwhenthelistener'sheadispointingdirectlyforward.Intheequationitisalsoassumedthattheelevationis.Theequationdoesnotsetlimitationsto$,butinmostcasesititsvalueissettosatisfy0$01$&.If0$02$&theamplitudepanningwillproduceantiphaseloudspeakersignalswhichmaydistortthevirtualsource[4].0j-0j12jxya)sourcevirtualFigure1:Astandardstereophoniclisteningconguration.Thevirtualsourcecanbepositionedbetweentheloudspeakers.Ifthelistenerisfacingtowardsthevirtualsource,thetangentlawismorecorrect[7]345"%$34"%$&\r('*)+,('.-/,76(3)Thisequationhasthesamelimitationsasthesinelaw.Theperceptionofthevirtualsourcecanbemodeledbycon-structingthesoundsignalenteringlistener'searsusingmeasuredHRTFsandlisteningsetupmodel[8].Thefrequency-dependentILDandITDcanbethencalculatedusingabinauralauditorymodel.Thevirtualsourcequalitiescanthenbemonitoredbycom-paringtheITDsandILDsofrealandvirtualsourceswitheachother.Further,theITDandILDcanbeexpressedindirectionan-gles,accordingtoindividualtablelookup,whichenablescompa-rationofsoundobjectdirectionperceptionbetweenindividuals.Ithasbeenshownthatthemodelisabletopredictmanyphenomenaexistinginspatialreproduction[11].3.1.Pair-wiseamplitudepanningWhenthenumberofloudspeakersexceedstwo,pair-wisepanningmethodscanbeused.Thesoundsignalispannedtotheadjacentloudspeakerpairbetweenwhichthevirtualsourcedirectionlies.Thevirtualsourceisproducedusingoneortwoloudspeakers.Ifthevirtualsourceispannedcoincidentwithaloudspeaker,onlythatparticularloudspeakeremanatesthesoundsignal.Whenthesoundsignalispannedtoasingleloudspeaker,itisactuallynotavirtualsource,butarealsource.Thismeansthatitsdirectionalspreadisaslowasitcanbe.Whenthevirtualsourceispannedtotwoloudspeakers,thedirectionalspreadishigher,itcanbelocalizederroneouslyanditmaybecolored.Thedirectionalspreadofanauditoryobjectmaybeestimatedbysimulatingthelisteningconditionandbycalculatingthemainlocalizationcues.Theaveragedirectionalspread8perceivedbyanindividuallis-tenermaybeestimatedas8\r:9ILD0#0;)ILD0#0-ITD0=0;)ITD0=0(4)where9ILDand9ITDrepresentafrequency-dependentsaliencefunctionofILDandITD,respectively.Variable;denotestheme-dianvalueofILDandITD,whichrepresentsthecenterdirectionofthesoundobjectaroundwhichthespectralspreadappears.ITDandILDareexpressedasazimuthanglesat42ERB(equivalentrectangularbandwidth)channels.-10010203040506000.511.522.533.544.555.5Panning angle / degreesDirectional spread / degreesFigure2:Simulateddirectionalspreadofpair-wiseamplitudepannedandmultiple-directionamplitudepannedvirtualsources.Solid:pair-wisepanning.Two-directionpannedvirtualsources:dashed-spreadangle,dash-dotted-spreadangleé.5loud-speakers,directions)@?,)é,,é,and?wereused.2-DVBAP,0#00#0\r-10010203040506000.20.40.60.81angle / degreesgain factor valuels 0°ls 30°ls 90°Figure3:Thegainfactorsofloudspeakersatdirection,éand?asfunctionofpanningangle.Solid:onepanningdirection.Twopanningdirections:dashed-spreadangle,dash-dotted-spreadangleé.5loudspeakers,directions)@?,)é,,é,and?wereused.2-DVBAP,0#00#0\rA.Inthisstudyaroughapproximationwasusedofthesaliencesofdirectionalcues.TheITDsaliencefunction9ITDwasmodeledW99-2 Proc.1999IEEEWorkshoponApplicationsofSignalProcessingtoAudioandAcoustics,NewPaltz,NewYork,Oct.17-20,1999withafunctionwithvalue1.0atlowfrequenciesand0.1athighfrequencies.TheILDsaliencefunction9ILDhadvalue0atlowfrequenciesand0.4athighfrequencies.Betweenfrequencies400Hzand2000Hzthesalienceschangedtheirvalueslinearly.A5-loudspeakersystemwithspeakerdirections,�,?,)@?,and)�wassimulated,andapair-wisepannedvirtualsourcewithpinknoisewasappliedtoit.Thedirectionalspreadwascomputedbetween)Band ,asshowninFig.2.Thedirectionalspreadwascalculatedfor5individuals,andtheaveragevalueoverindividualswassettobethedirectionalspreadestimate.TheHRTFsofindividualshavebeenmeasuredbyWightmanandKistler[9].Inthegureitcanbeseenthatthedirectionalspreadhaslocalminimacoincidentwithloudspeakerdirections.Betweentheloud-speakersthevirtualsourceisspreadprominently.Thissimulationresultcorrespondswelltoknownbehavioramplitude-pannedvir-tualsources.ThecorrespondinggainfactorsareshowninFig.3.3.2.Triplet-wisepanningIntriplet-wisepanning,thesoundsignalisappliedtomaximallythreeloudspeakersattime.Theloudspeakersformatrianglewhenviewedfromthelistener'sposition,asinFig.4.Thisenablesthree-dimensionalpositioningofvirtualsources.Three-dimensionalvec-torbaseamplitudepanning(VBAP)isamethodforpositioningvirtualsourcestoarbitrarydirectionsinsidearbitraryloudspeakertriplets[2].lllnkmpchannel mvirtualsourcechannel nchannel kFigure4:Three-dimensionalvectorbaseamplitudepanning.Inthree-dimensionalVBAPaloudspeakertripletisformu-latedwithvectors.Theunit-lengthvectorsC DC EandCGFpointfromlisteningpositiontotheloudspeakers.Thedirectionofthevirtualsourceispresentedwithunit-lengthvectorH.VectorHisexpressedasalinearweightedsumoftheloudspeakervectorsH\rDCD-ECE-FCF6(5)HereD,E,andFarecalledgainfactorsofrespectiveloud-speakers.ThegainfactorscanbesolvedasI\rHKJLNM'DOEFwhereI\rQPDEFRSJandLDTEF\rQPC DUC EVCGFR.Thecalculatedfactorsareusedinamplitudepanningasgainfactorsofthesignalsap-pliedtorespectiveloudspeakersaftersuitablenormalization,e.g.0#0I*0#0\r.Whenthenumberofloudspeakersisgreaterthanthree,theloudspeakersetupisdividedtotrianglesformingatriangleset.Anautomatictriangleformingalgorithmhasbeenpresentedin[10].Duringthepanningprocessasingletrianglefromthesetischosentobeusedinpanning.Theselectioncanbemadebycalculat-ingthegainfactorsineachloudspeakertriangleinthetrianglesetandselectingthetrianglethatproducednon-negativefactors.Ifthetrianglesinthesetarenon-overlapping,theselectionisunam-biguous.VBAPcanbealsoformulatedintwodimensions,inthisformulationitcanbeappliedalsotopair-wiseamplitudepanning.2-DVBAPisareformulationoftangentlaw(Eq.3)[2].3-DVBAPhasasimilarfeaturewithpair-wiseamplitudepan-ninghad,thedirectionalspreadisdependentonthepanningdirec-tion.Thechangeofdirectionalspreadcanbeevenhigherbecausethenumberofloudspeakersemanatingsamesoundsignalvariesfromonetothree.4.UNIFORMSPREADINGOFAMPLITUDE-PANNEDVIRTUALSOURCESIthasnowbeshownthatthedirectionalspreadofpair-wiseandtriplet-wisevirtualsourcesdependsonpanningdirection.Meth-odsformakingthedirectionalspreadofavirtualsourceconstantarenowconsidered.Thebestwaywouldbe,ofcourse,tomakethevirtualsourceaspoint-likeaspossible.Thereexistssomeat-temptstothis[11].However,reducingthedirectionalspreadde-mandscomputationalresources,andthespreadcaninveryfewcasesremovedtotally.Otherwaytosolvetheproblemistoincreasethedirectionalspreadindirectionswheretheloudspeakersareinordertocreatearoughlyconstantdirectionalspread.Thedirectionalspreadcanbeincreasedbyapplyingthesamesoundsignaltomorethanonephysicalloudspeakerateachtime.However,thevirtualsourcequalityondirectionsbetweentheloudspeakersshouldnotbede-gradedmore.Thiscanbeimplementedwithamethodinwhichthesoundsignalispannedsimultaneouslytomultiplepanningdirectionsnearthewantedvirtualsourcedirection.Despiteofthemultiplepan-ningdirections,thelistenerwillstillperceiveasinglevirtualsource.Theaveragedirectionofthepanningdirectionsisconsideredasthepanningdirection,wherethevirtualsourceiswantedtoap-pear.Themethodiscalledmultiple-directionamplitudepanning(MDAP).Thelargestanglebetweenthemultiplepanningdirec-tionsiscalledthespreadangle.Whenthemultiplepanningdirectionsarelocatedinsidethesameloudspeakerset,MDAPisequivalenttotraditionalampli-tudepanningwithasinglevirtualsource,sincethesoundsignalsarepannedtosameloudspeakers.ThisimpliesthatMDAPdoesnotdegradefurtherthevirtualsourcequalityindirectionswherethevirtualsourcequalityisatitsworstintraditionalamplitudepanning.ThedifferencebetweentraditionalamplitudepanningandMDAPappearswhenthereexistloudspeakersbetweenthepan-ningdirectionsinMDAP.Thesoundsignalsarethenpannedtodifferentloudspeakersets,whichaffectsthegainfactorsandin-creasestheamountofusedloudspeakers.Thisspreadsthevirtualsource.TheamountofspreadingcanbeselectedbyadjustingthespreadangleofMDAP.Whenthevirtualsourceisdesiredtobespreadintwo-dimensionalspeakersetups,theeffectcanbeachievedusingtwopanningdirections,asinFig.5.IftheloudspeakersarenotspreadW99-3 Proc.1999IEEEWorkshoponApplicationsofSignalProcessingtoAudioandAcoustics,NewPaltz,NewYork,Oct.17-20,1999evenly,theremightbesituationsinwhichthereexistmorethanonespeakerbetweenpanningdirectionsofonevirtualsource,whichmaycausethatsomeofthespeakersbetweenthepanningdirec-tionsmaynotemanatesoundatall.Thiscanbeavoidedbyapply-ingmorepanningdirectionstoMDAP.ggg= 0.2= 0.96= 0.121pp321Figure5:Spreadingthevirtualsourceusingtwopanningdirec-tions.Figure6:Spreadingthevirtualsourcein3-DloudspeakersetupsusingthreepanningdirectionsIn3-Dloudspeakersetups,iftwopanningdirectionsareusedinMDAP,thesoundsignalisappliedatleasttotwoloudspeak-ersattime.Ifthesoundisdesiredtobeappliedatleasttothreeloudspeakersattime,threepanningdirectionsareneededasisil-lustratedinFig.6.ThedirectionalspreadofvirtualsourcescreatedwithMDAPwith2panningdirectionswithspreadanglesor�areshowninFig.2.ThevirtualsourcescreatedwithMDAPdonothavelocalminimaondirectionscoincidentwithloudspeakers,aspair-wise-pannedvirtualsourceshave.ItcanalsobeseenthattheamountofdirectionalspreadincreaseswhenthespreadangleofMDAPisincreased.ThedirectionalspreadisalsoroughlyconstantoverpanningdirectionwithvirtualsourcescreatedwithMDAP.TheresultcorrespondswelltoinformallisteningtestsinwhichitwasfoundthatthedirectionalspreadofvirtualsourcescreatedwithMDAPdidnotvanishondirectionscoincidentwithloudspeakers.ThecorrespondinggainfactorsareshowninFig.3Inmatrixingsystemsthereproducedsoundsignalisappliedtovirtuallyallloudspeakersatonetime.ThiscanbesimulatedwithMDAPbyapplyingthesoundsignaltoneededamountofdirectionsandbygainingtheinputsignalproperlyindifferentdi-rections.5.CONCLUSIONSThepair-wiseandtriplet-wiseamplitudepannedvirtualsourcescanbespreadbypanningthesamesoundsignaltomultipledi-rections.Thistechniquesiscalledmultiple-directionamplitudepanning(MDAP).WhenapplyingMDAP,thesoundsignalneveremanatesfromonlyoneloudspeaker.Thedirectionalspreadisincreasedondirectionscoincidentwithloudspeakers,butthedi-rectionalspreadbetweenloudspeakersremainsonsamevalueasinpair-wiseortriplet-wisepanning.Theamountofdirectionalspreadofthevirtualsourcecanbecontrolledbyadjustingthepan-ningdirections.Thepanningdirectionsetscanbecomposedinsuchamannerthatthespreadofvirtualsourcesisnotdependentonpanningdirection.Thedirectionalspreadwassimulatedusingabinauralmodel,andexaminedwithinformallisteningtests.6.ACKNOWLEDGMENTTheworkofMr.PulkkihasbeensupportedbytheGraduateSchoolinElectronics,TelecommunicationsandAutomation(GETA).TheauthorwouldliketothankDr.FredWightmanandDr.DorisKistleratUniversityofWisconsin,MadisonformakingtheHRTFmea-surementsavailabletoscienticcommunity.7.REFERENCES[1]J.Chowning,Thesimulationofmovingsoundsources,J.AudioEng.Soc.,vol.19,no.1,pp.26,1971.[2]V.Pulkki,Virtualsourcepositioningusingvectorbaseam-plitudepanning,J.AudioEng.Soc.,vol.45,no.6,pp.456466,1997.[3]M.A.Gerzon,Periphony:With-heightsoundreproduc-tion,J.AudioEng.Soc.,vol.21,no.1,pp.210,1972.[4]J.Blauert,SpatialHearing,Revisededition,TheMITPress,Cambridge,Massachusetts,1997.[5]A.D.Blumlein,,U.K.Patent394,325,1931,ReprintedinStereophonicTechniques,AudioEng.Soc.,NY,1986.[6]B.B.Bauer,Phasoranalysisofsomestereophonicphenom-ena,J.Acoust.Soc.Am.,vol.33,no.11,pp.15361539,November1961.[7]B.Bernfeld,Attemptsforbetterunderstandingofthedi-rectionalstereophoniclisteningmechanism,in44thCon-ventionoftheAudioEngineeringSociety,Rotterdam,TheNetherlands,February1973.[8]V.Pulkki,M.Karjalainen,andJ.Huopaniemi,Analyzingvirtualsourceattributesusingabinauralmodel,J.AudioEng.Soc.,vol.47,no.4,1999.[9]F.L.WightmanandD.J.Kistler,HRTFmeasurements,http://www.waisman.wisc.edu/hdrl/,1998.[10]V.PulkkiandTapioLokki,Creatingauditorydisplaystomultipleloudspeakersusingvbap:Acasestudywithdivaproject,inInternationalConferenceonAuditoryDisplay,Glasgow,England,1998,ICAD.[11]V.Pulkki,M.Karjalainen,andV.V¨alim¨aki,Localization,coloration,andenhancementofamplitudepannedvirtualsources,inTheProceedingsoftheAES16thInternationalConference,1999,pp.257278.W99-4