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AudioEngineeringSocietyConventionPaperPresentedatthe118thConvention2005May28–31Barcelona,SpainThisconventionpaperhasbeenreproducedfromtheauthor’sadvancemanuscript,withoutediting,corrections,orconsiderationbytheReviewBoard.TheAEStakesnoresponsibilityforthecontents.AdditionalpapersmaybeobtainedbysendingrequestandremittancetoAudioEngineeringSociety,60East42Street,NewYork,NewYork10165-2520,USA;alsosee www.aes.org.Allrightsreserved.Reproductionofthispaper,oranyportionthereof,isnotpermittedwithoutdirectpermissionfromtheJournaloftheAudioEngineeringSociety DetectionofsubwooferdependingoncrossoverfrequencyandspatialanglebetweensubwooferandmainspeakerAnttiKelloniemi,JukkaAhonen,OlliPaajanen,andVillePulkkiHUT,Telecommunicationssoftwareandmultimedialaboratory,Espoo,FinlandHUT,Laboratoryofacousticsandaudiosignalprocessing,Espoo,FinlandCorrespondenceshouldbeaddressedtoAnttiKelloniemi(antti.kelloniemi@hut.fiABSTRACTSincethedirectionofsoundisnotperceivedatverylowfrequencies,itisfeasibletouseonlyonesubwooferforlowfrequencyreproductioninmulti-channelaudiosetups.Alisteningtestwasconductedto“ndthecrossoverfrequencywherethelistenersbegintodetectthesubwooferpresence.Thetestwasarrangedinasymmetricallisteningroomusingfourpairsofspeakers,arrangedsymmetricallyinfouranglestothefrontofthelistenertoequalizethetimbresaswellaspossibleinreverberantconditions.Thedetectionjudgementwasdoneusingaversionofthetwoalternativesforcedchoice(TAFC)adaptivemethod,withwhichthe75%pointofthepsychometricfunctionwasfound.Withtheusedsoundsamplesthecrossoverfrequencycouldbesettoabout120Hzbeforethesubwooferbecamedetectable.Nocorrelationwasfoundbetweenthehighestacceptablecrossoverfrequencyandlisteninganglewhentheangleexceeded30INTRODUCTIONTheaccuracyofdirectionperceptionofsoundsourcedependsonfrequency[1].Atthelowestfrequenciesthedirectioncannotbejudgedatall,sosubwoofersarecommonlyusedforsoundreproductionatforex-ampleinhometheatresetups.Subwooferisusedtoreproducelowfrequenciesofallloudspeakersuptoacertaincrossoverfrequency,whichimpliesthatthemainandsurroundspeakerscanbemadesmaller,astheirlowfrequencycutocanbehigher.Theopti-mallocationandcrossoverfrequencyforsubwooferhavebeendiscussedinearlierresearchasdiscussedinSection2,buttheirdependencyoneachotherisnotcompletelyunderstood.Inthispaper,listeningtestsdescribedinSection3wereconductedto“ndoutthedependencyofthedetectionofsubwoofer 6431 Kelloniemietal.Detectionofsubwoofer presenceonthecrossoverfrequencyandonthehor-izontalanglebetweenthemainspeakerandthesub-woofer.Itwasassumedthatwhenthehorizontalangleislargerbetweenmainspeakerandsubwooferitwouldbeeasiertodetectthesubwooferpresence.TestresultsarepresentedinSection4.BACKGROUNDTheuseofasubwooferaspartoftheloudspeakersetinsoundreproductionhasbeentestedandthe-oreticallyanalysedearlierbyseveralauthors[2,3,4,5,6,7].Itisgenerallyknownthatwhenweraisethecrossoverfrequencybetweenmainspeak-ersandsubwooferormovethesubwooferawayfromthemainsoundsourcelocation,itgetseasiertolo-calizethesubwooferasasourceofthelowfrequencycontent.Themaximumcrossoverfrequencyapplica-blehasbeenevaluatedtobesomewherebetween200Hz[2]and100Hz[3].Evenlowercrossoverfrequen-ciesbelow85Hzhavebeenused,noticingthatthenthepositioningoflow-frequencysourcesinalisten-ingroomgetsnoncritical[5].Also,thelocationofsubwooferaectsitsdetectioninmanyways.Ifthedistancebetweenmainspeakerandlistenerdepartsprominentlyfromthedistancebetweensubwooferandlistener,timedelaydierencesmaybeperceived[2].Alsothelocationsofthesubwooferandlistenerrelativetothemaximumandminimumlocationsofstandingwavesexcitedatthemodalfrequenciesoftheroomaecttheperceivedloudnessofthesub-wooferandtheeasinessofdetectingit[4,6,7].Intheearlierlisteningteststhesubwooferlocationhasbeenkeptconstantorthelocationshavebeenchosenfromasmallsetmainlyclosetothewalls,whenparameterssuchasrelativeloudness,delayorcrossoverfrequencyhavebeenchanged[2,3,5,6].Theresponsesfromthemainspeakersandthesub-woofertothelisteningpositionshavebeendierentandthustheresultscannotbegeneralizedastheydependmuchoneachroomandsetup.LISTENINGTESTS3.1ApproachInourtestwewantedtoknowifthehorizontalanglebetweenthemainsoundsourceandthesubwooferwouldbeacriticalfactoraectingthehighestap-plicablecrossoverfrequency.Fornotlosingtheef-fectsofreverberationandroommodes,wechosenottoconductthetestinananechoicroom.Thiswasdone,becausewebelievethatresultsinananechoicroomwouldbeverydierentfromtheonesapplica-bleinnormallisteningroomsituations.Thesamespeakermodelwasusedasthemainspeakerandthesubwooferinasymmetricalsetup.Thiswaythetim-bredierencewithinthetwospeakersineachpairwasminimized.Asthelisteningwasnotconductedinanechoicconditions,thereexistsdierencesbe-tweenloudspeakersindierentpairsduetodierentcouplingtotheroomacoustics.Theroomresponseofeachspeakerwasmeasuredandtheresultingmag-nitudespectracanbeseeninFig.2.Inthefre-quencyresponseplotsitisseenthattheresponsesinapairaresimilarwhereaslargedierencescanbefoundbetweeneachpairofspeakers,forexampleatthelowestroommodefrequencyof63Hz.Sig-ni“cantdierencesarealsonotedinthemagnitudespectraofthetwospeakersatlisteningangleof30Thesedierenceswereexpectedtohaveeectonsubwooferdetection,whichinanechoicconditionswouldhaveappearedaslogicaldependencyofthecrossoverfrequencyonthelisteningangle.Alisteningtestwasdesigned,inwhichthelistenersreportonesamplepairoutoftwo,wheretheydetectifthesubwooferisused.Alisteningpanelof18subjectswasused.Allofthemhadexperienceinplayinganinstrumentorincriticallistening.Halfofthelistenershadbeensubjectsinformallisteningtestsbefore.3.2MethodThetestwasconductedusingaversionoftwoalter-nativesforcedchoice(TAFC)method,whichadaptstothe75%pointofthepsychometricfunctionasshownbyKaernbach[8]andwhichisnowdescribed.Thetestsampleswereplayedintwopairs.Oneofthepairswasalwaysthereferencesampleplayedtwicefromthemainspeaker(AA)whiletheotherpairhadthereferencesampleandthesamplesplitbetweenthemainspeakerandthesubwoofer(AB).Theorderofthepairsandthesampleswithinapairwasalteredrandomly.Thelistenerhadtode-cide,whetherthesplitsamplewasinthe“rstorinthesecondpair.Asde“nedbytheadaptiveTAFCmethod,ifthelistenerfoundthecorrectsamplepair,thecrossoverfrequencywasdecreasedbyonestep.Incaseofincorrectresponse,crossoverfrequencywasincreasedbythreesteps.Thesamesamplewas 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