Lateralization of complex binaural stimuli: A weighted-image
model
RichardM. SternandAndrewS. Zeiberg
DepartmentofElectricaland ComputerEngineering
andBiomedicalEngineering
Program,
Carnegie
MellonUniversity,
Pittsburgh,
Pennsylvania
15213
Constantine
Trahiotis
Center
for Neurological
Sciences
andDepartment
ofSurgery
{Otolaryngology),
University
of Connecticut
HealthCenter.Farmington,Connecticut
06032
(Received31 August1987;acceptedfor publication18March 1988)
This articledescribes
a new modelthat predictsthe subjective
lateralpositionof bandpass
stimuli.It is assumed,as in othermodels,that stimuliare bandpass
filteredand rectified,and
that therectifiedoutputsof filterswith matchingcenterfrequencies
undergointerauralcross
correlation.The modelspecifies
and utilizesthe shapeand locationof assumedpatternsof
neuralactivitythat describethe cross-correlation
function.Individualmodesof thisfunction
receivegreaterweightingif theyarestraighter(describingconsistent
interauraldelayover
frequency)and/or morecentral(describing
interauraldelaysof smallermagnitude).This
weightingof straightness
and centralityis usedby the modelto predictthe perceivedlaterality
of severaltypesof low-frequency
bandpass
stimuliwith interauraltime delaysand/or phase
shifts,includingbandpass
noise,amplitude-modulated
stimuliwith time-delayedenvelopes,
andbandpass-filtered
clicks.This modelis comparedto othertheoriesthat describe
lateralizationin termsof the relativecontributions
of informationin the envelopes
and fine
structures of binaural stimuli.
PACS numbers:
43.66.Ba,43.66.Qp,43.66.Pn,43.66.Nm [ WAY]
INTRODUCTION
stimuli,we foundthat obviousextensions
acrossfrequency
The purposeof thisarticleis to describesomeattributes of theoriessuchas the position-variable
model(Stem and
of binauralprocessing
that help to describethe subjective Colbum, 1978) could not describeall of the observeddata.
lateralposition
of certaincomplex
stimuli.We p.resent
a Additional constraintswere necessary.Specifically,it becrudeblack-boxmodelthat expresses
theseattributesin a
cameclearthat it wasnecessary
to emphasize
thoseinternal
quantitativefashion.
delaysin the model'sfrequency-timedescriptionof interRecently,many experimenters
haveobtainedinterest- aural stimulus correlation for which the information is most
ingnewdataconcerning
thelateralizationof high-frequency consistentacrossfrequencies.
In order to expressthis conandcomplexbinauralstimuli.For example,Henning( 1974,
ceptin a quantitativefashionand to furtherexploreits sa1980, 1983), McFadden and Pasanen (1976), and Nuetzel
lieneefor experimentalstudies,we havedevelopeda new
and Halter ( 1976, 1981) haveall demonstrated,usinginterblack-boxmodel, called the weighted-image
model. This
aural discriminationexperimentsand forced-choice
lateramodelis not as detailedas the position-variable
model,nor
lity judgments,that the lateralpositionof a high-frequency doesit directlyexpress
itspredictions
in termsof thephysiobinaural stimulusis affectedby the interaural time delay
logical signalprocessingoccurringat the auditory periph(ITD) of the envelopeof that stimulus,providedthat the
ery. However,the weighted-image
modeldoesappearto be
signalsto the two earsoccupycomparablespectralregions. usefulfor developinginsightinto how complexbinaural
More recently,Bernsteinand Trahiotis (1985a,b) and Trasoundsare processed,
andit is mucheasierto obtainpredichiotisandBernstein( 1986) havedirectlymeasuredthe pertionsfrom this modelthan it is from the position-variable
model.
ceivedlateralityof suchstimulianddemonstratedthat ITDs
of the envelopecan affect the laterality of low-frequency as
well as high-frequencystimuli.
Therenowappearto besufficientnewdatato enablethe
characterization of the results in terms of formal models of
binauralinteractionin an interestingfashion.While a numberof modelshavepreviouslybeendeveloped
to describethe
lateralpositionof binauralstimuli (e.g., Sayersand Cherry,
1957; Stern and Colburn, 1978; Lindemann, 1986), none
directly addresseshow information is combinedacrossdifferentfrequencies.
While attemptingto constructa general
modelthat describes
the subjective
lateralpositionof such
156
J. Acoust.
Soc.Am.84 (1),July1988
In the next section, we review some recent data that
motivatedusto reconsider
the integrationof interauraltiming informationacrossfrequencies.In Sec.II, we describe
the assumptions
that specifythe weighted-image
model.In
Sec.III, we comparethe predictionsof this model to some
recent experimentalresults.In Sec. IV, we discussthese
comparisonsof predictionsand data, and we consideralso
similaritiesand differencesbetweenpredictionsin models
basedon consistencyof interaural time differencesacross
frequencyand modelsbasedon salienceof envelopeinformation of complexstimuli.
0001-4966/88/070156-10500.80 ¸ 1988Acoustical
SocietyofAmerica
156
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.j
I. MOTIVATION
FOR THE MODEL
auditory processing
can be modeled(at least in part) by
passing
signalsto eachear througha bankof parallelbandIt
lateralpositionof the imageof a low-frequency
bandpass passfilters,eachwitha slightlydifferentcenterfrequency.
that theauditorysystemperforms
noisewasdramaticallyaffected
bychanges
in thebandwidth isusuallyfurtherassumed
somesort of interauralcrosscorrelationon the outputsof
of the stimulus.For example,considerthe resultsin Fig. 1,
the bandpassfilters.Figure 2 is a plot of the locationsof the
whichshowshow bandwidthaffectsthe lateralpositionof a
maxima of the cross-correlation function of a broadband
bandof noisepresentedwith a centerfrequencyof 500 Hz
noise
with a 1500-•sITD, aftersuchbandpass
filtering.The
andan ITD of 1500/•s.Thesedata,whicharepart of a larger
horizontal
axis
represents
interaural
delay
(•-)
and is the
studythat is currentlybeingpreparedfor publication(Traargument
of
the
cross-correlation
function.
The
vertical
axis
hiotisand Stern, 1988), were obtainedusingmethodsdeindicates
the
center
frequencies
of
the
bandpass
filter
(f).
scribed in detail in Bernstein and Trahiotis (1985a). Position is expressedin terms of the interaural intensity The frequencyof 500 Hz is indicatedby the horizontal
Recently,TrahiotisandBernstein(1986) notedthat the
difference (IID)
of a secondnarrow band of noisecalled the
pointer.Listenersadjustedthe IID of the pointersothat its
positionmatchedthat of the stimulusof interest.Note that
the soundis perceivedtowardonesideof the headwith narrow bandwidths, but moves to the other side of the head as
the bandwidthis increasedto only 400 Hz.
In retrospect,it is easyto understandwhy thisphenom-
broken line.
If the bandwidth of a 500-Hz stimuluswere sufficiently
broad, the ITD would be readily identifiablebecausethe
locusof the peaksis a straightand verticalline at only the
value of the interauraldelay parameter•- corresponding
to
that ITD (1500/•s in this case). This "straightness"could
very well be the cue usedto recognizethat the interaural
delayof the stimulusis exactly 1500/•s. Sincereal sounds
emittedby point sourcesproduceITDs that are consistent
enon is observed.For very narrow bandwidths,the noise
sourcecloselyresembles
a puretoneof 500 Hz. Considera
the"straighter"a particularline
500-Hz tonepresentedwith the signalto the left ear time overa rangeof frequencies,
or
trajectory
of
maxima,
the
morethat trajectoryis likely to
delayedrelativeto thesignalto the right earby 1500/•s.This
represent
the
actual
ITD
of
the
stimulus.On theotherhand,
stimulusis equivalentto onein which the signalto the left
if
the
signal
is
very
narrow
in
bandwidth,
the auditorysysearisleadingthesignalto therightearby 500/•s,because
the
tem
is
unable
to
distinguish
between
the
various
peaksbeperiodera 500-Hztoneis2000/zs.Consequently,
theimage
cause
there
is
not
enough
range
of
frequencies
to
estimate
of thebinauralsoundis perceivedtowardthe left sideof the
adequately
the
"straightness"
of
any
trajectory.
Under
these
head. As bandwidth is increased,however, the signal becircumstances,
we
believe
that
the
auditory
system
tends
to
comeslessand lesstonelike.In the limiting case,oneis prelateralize the sound toward the side of the head of the basis of
sentedwith broadbandnoisewith the signalto the right ear
leadingthesignalto theleft earby 1500/zs,andthissignal the trajectorythat is closestto thef axis,i.e., themost"central" locus of maxima. We believe that the more central trawould certainlybe lateralizedtoward the right (or "leading") sideof the head.This raisesthe questionof howthe jectoriesare weightedmoreheavilybecausethereare more
unitswith smallinternalinauditorysystemis able to determinethat the signalto the binauralcoincidence-counting
teraural
delays
than
there
are
neural
unitswith largerinterrightearisleadingthesignalto theleft earby 1500/•swhen
nal
delays.
This
is
a
common
assumption
in binauralmodels
thesignalis sufficiently
broadin bandwidth,eventhoughit
(e.g.,SayersandCherry,1957;Colburn,1977) andwasused
is "fooled" when the bandwidth is smaller.
in a remarkablyinsightfulqualitativeattemptto
Theperception
of thesestimulicanbeeasilyunderstood by Jeffress
explain
essentially
identicalauditoryphenomenain 1972
in termsof howtheauditorysystemislikely to processthem.
(Jeffress,
1972,
pp.
357-358).
Jeffress
focuseduponcentraMost theoriesof binauralinteractionassumethat peripheral
lity anddid not discuss
straightness
nor howbothcentrality
• 40
o0
so
lO
,oo/
-lO
•
_so......
Bandwidth
(Hz)
FIG. 1. Pointerlid neededto matchthe positionof bandpasstargetswith
centertYequency
500Hz and ITD 1500,usasa functionof thebandwidthof
the target (unpublisheddata of Trahiotisand Bernstein).
157
-4000
-2000
2000
4000
Interaural Delay x
•2o
J. Acoust.Sec. Am., Vol. 84, No. 1, July 1988
FIG. 2. Locationof the peaksof the cross-correlation
functionfollowing
peripheralbandpassfilteringfor broadbandnoisewith an 1TD of 1500,us.
The verticalaxisindicatesthecenterfrequencyof thebandpass
filters,while
the horizontalaxisindicatesthe argumentof the cross-correlationfunction.
Stern eta/.: A weighted-imagemodel
157
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js
100o
andstraightness
couldbemanipulated
sothat theirrespective effectsand interactionscouldbe discoveredand quantified. Nevertheless,
Jeffress'insightsare impressive,and it
seemsremarkableto us that his lucid statementsdo not ap-
pearto havestimulated
studies
oflateralization
asa function
of the bandwidth of stimulation.
In manycases(includingthe500-Hznoisewitha 1500#s ITD), eitherstraightness
or centrality
considered
in isolation would causethe sound to be lateralized toward differ-
250
----
ent sidesof the head.We believethat, in thesecases,lateral
......
position
istheresultof sometypeof resolution
of theseconflicting piecesof information(perhapsnot unlike the
,
"trade"
ofinteraural
timing
andintensity
information
that -4000
,c= 1500gs, 4•= 0ø
x= 1000gs, 4•=90ø
'c= 500 Izs,e = 180ø
• = 0.0 izs,4•= 270o
o•
-2000
2000
4000
Interaural Delay • (gs)
characterizes
the lateralizationof simplestimuliwith small
interaural differences).
FIG. 3. Lociof thepeaksof thecross-correlation
function
fornoisewith
of ITD andIPD chosen
toproducemaximaat 1500/.rs
In order to examinethe extent to which straightness severalcombinations
playsa rolein thelateralization
of complexstimuli,it isuse-
and 500 Hz in each'case.
ful to considersomenew data that describethe joint depen-
denceof the lateralpositionof 500-Hz bandpass
noiseon
ITD and interauralphasedifference(IPD). Thesestimuli
areparticularlyusefulbecause
appropriate
combinations
of
ITD and IPD enablethe experimenterto manipulatethe
interauralcorrelationof a binauralbandpassnoisesuchthat
straightness
andcentralitycanbeindependently
specified
at
a particularfrequencyof interest.Specifically,
considera
bandpass
noisepresented
with an ITD of Ts andan IPD of
•bs.After thesignals
undergoperipheral
bandpass
filtering,
the maximaof the cross-correlation
functionat frequencyf
will occur at
r= T• + (4s/2rrf)(k/f),
toriesat 1500/isdecreases
astheIPD isincreased
from0øto
270 ø.
Resultsof a lateralizationexperimentalusing these
stimulifor onesubjectareshownin Fig. 4. Note thatthedata
for the IPD of 0øare similarto thosein Fig. 1 (althoughthe
imageappearsto traversethe midlineat a narrowerbandwidth), and that, as the IPD is increasedfrom 0ø to 270ø,
thereis an increasing
tendencyfor the imagesof the noises
with broader bandwidths to remain on the same side of the
headas the imagesof the narrow-bandnoise.It is easyto
understandthesedata in termsof the competitionbetween
straightness
andcentralityasdiscussed
above.Specifically,
all narrow-band stimuli are lateralized on the left side of the
wherek isaninteger.Hence,a maximumof thecross-corre- head(whichcorresponds
to negativevaluesof the vertical
lationfunctionwill appearat r equalssomearbitrary Ta at
coordinatein Fig. 4) because
the trajectoryat - 500tts (at
frequencyfif valuesof Tsand•b•arechosensuchthat
500Hz) ismuchmorecentralthanthetrajectoryat 1500tts.
Ts = Td -- (•/2rrf)
-- (k/f).
(1)
With an IPD of 0ø,asbandwidth is increased,we believethat
The parameter•b•controlsthestraightness
of thetrajectory theimageof thenoisetendsto movetowardtherightsideof
it becomes
increasingly
clearthat thereisa
with k equalto 0, as •b•equals0 rad producesa trajectory theheadbecause
straight
trajectory
at
1500/is
which
represent
the "true"
thatisperfectlystraightfor r equalsTa = T• ( asin Fig. 2).
ITD.
As
the
IPD
is
increased
to
270
ø
(and
the
ITD is reIf, on the other hand,• equalsrr rad, and if Ts is selected
duced
appropriately),
the
trajectory
that
passes
through
according
to Eq. ( 1), thecorrelationfunctionwill includea
1500/rs
at
500
Hz
becomes
increasingly
less
effective
in
trajectoryof maximathatalsopasses
throughr equalsTa at
frequency
f, but that trajectorywill beless"straight."
Usingagainthe pointing.procedure
of Bernstein
and
Trahiotis
(1985a),
we
measured
the
subjective
lateral
position
ofbandpass
noises
with
acenter
frequency
of500
Hzas • 1o
a
function
ofthestimulus
bandwidth
forcombinations
of
ITD and IPD. Measurements were obtained for four differ-
•.
t, x=1500•,
•---•
o- -- o
a ..... a
x = 1000 •zs,e = 90'
x=500•s,
x = 0.0 •s,
ent
values
ofIPD:
0',90
ø,180
ø,and
270
ø.The
ITDineach.• 5
case
wasequal
to[1500/zs-(•bs/2rr
1000f)](with• in
rad andfin kHz), so that maxima of the cross-correlation
functionat 500Hz wouldalwaysoccurat valuesof r equalto
1500, -- 500,3500, -- 2500•s, etc.Within a narrowregion
around500 Hz, the trajectoriesof maximaof the cross-correlation function exhibit equal centrality but different
straightness
for thefourcombinations
of ITD andIPD considered.
Trajectories
of themaximaof thecorrelation
functions for thesestimuli are sketchedin Fig. 3 for the four
valuesof IPD usedin theexperiment.Note that all trajectoriesintersectat 500 Hz andthat the straightness
of the trajec158
J. Acoust.Sec. Am., Vol. 84, No. 1, July 1988
o
/•./
.'/ ,
•o
_. •
, .--9
-
400
FIG. 4. Perceivedpositionof bandpass
targetswith centerfrequency500
Hz, presented
with combinations
of ITD and IPD producingdifferent
straightness
but similarcentralityat 500 Hz (seetext).
Stern ota/.: A weighted-imagomodel
158
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.j
"pulling"the imageof the noisetowardthe right sidebecauseit becomesincreasingly
lessstraight,while simultaneouslythe trajectoryaround -500 its becomesmore
straight(Fig. 3). Note that thestimuluswith an IPD of 270ø
and an ITD of 0 its producesa patternof crosscorrelation
for which both straightnessand centrality would tend to
causethe imageto be lateralizedtowardthe left sideof the
head(as is seenin thedataof Fig. 4).
Beforebeginningour work on the model describedin
the next section,we first comparedpredictionsof the posi-
frequency-dependent
cross-correlation
function (such as
thoseshownin Fig. 2) and how thesemaxima vary as a
functionof frequency.[ In contrast,themodelsof Sayersand
Cherry ( 1957); Stem and Colburn ( 1978); and Lindemann
(1986) all describelateralizationin termsof operationson
theentirefrequency-dependent
crosscorrelationof thestim-
tion-variable model of Stem and Colburn (1978) to these
correlationfunctionof thebinauralstimuli.For simpletimedelayednoise,thelociof thesemaximaform hyperbolictrajectoriesin ther-f planethat arespacedapartby r = 1/f for
a givenf The relativeweightof eachtrajectoryisassumed
to
dependon its straightness
and centrality.The straightness
componentof the weightingfunctionis designed
to weigh
moreheavilythosetrajectoriesthat aremorestraight(parallel to thef axis) and, hence,are morelikely to representa
true ITD of a realstimulusthat isconsistent
overfrequency.
The centralitycomponentof theweightingfactorsenhances
the contributionof trajectorieslocatedalongvaluesof internal delay (the r axis) for which there are presumedto be a
greaternumberof neuralunitsavailable.This emphasizes
the contributionsof trajectoriesof values of r that are
smallerin magnitude.Note that, if the stimulusis a pure
tone, all of the trajectoriesof maxima of the cross-correlation functionare straightand vertical,and, consequently,
theweightingof thetrajectoriesisonlyaffectedby theirrelativecentrality.[ Tonalstimuliproducetrajectories
with nonzeroextentalongthef axisbecause
of theimperfectfrequency resolutionof the filters.The spacingof the maxima is
determinedby thefrequencyof thestimulus(ratherthanthe
centerfrequencyof thefilter) aslongasthebandwidthof the
stimulus is lessthan the filter bandwidth.] Therefore, the
predictionsof the weighted-image
modelfor tonesare similar to the predictionsof the position-variable
model,except
that theweighted-image
modelcomputes
thecentroidof the
maxima of the cross-correlation
function, while the position-variablemodel computesthe centroid of the entire
data.That modelassumes
that the lateralpositionof binaural stimuliis predictedfrom thecentroidof a functionrelated to the interaural cross correlation of the stimuli after fil-
teringand rectificationassumedin almostall modelsof the
auditoryperiphery.(The specificfunctionthat describes
interaural timing informationis expressedin termsof the re-
sponse
of hypothetical
auditory-nerve
fibersto thestimuli.)
The position-variable
modelincludesa functionthat implicitly weightscomponents
of the cross-correlation
function
that exhibitgreater"centrality."However,thereis no feature of that modelthat providesgreaterweightingfor componentsof the functionthat arestraighteroverfrequency.
Usingthe position-variable
model,we obtainedpredictionsfor thenarrow-bandstimuliof Fig. 4 by computingthe
interauralcross-correlation
functionof the stimuliafterperipheralprocessing.
Predictionswere obtainedutilizing several implementations
of the model;eachversionwasmotivatedby practicalaswell astheoreticallybasedfactors.We
exploredthe effectsof varyingthenatureof threefeaturesof
the model:the characteristics
of the bandpassfilters and
nonlinearrectifierin themodelof peripheralprocessing,
and
the more central function that describes the distribution of
units that reflectinterauralcoincidences
of neural activity.
Predictionsdo appearto be affectedby the particularfunctionsthat are usedto characterizesuchelementsof the position-variable model, and these issueswill be discussedat
lengthin a subsequent
article (Shearand Stern,1988).
The aboveeffortsnotwithstanding,
we feelthat thecomplexityof the position-variable
modeland its implementation can obscuresomeof the fundamentalaspectsof the
stimuliandhowtheyaffectthe overalltrendsof predictions
of anymodel.Consequently,
wefocusedupona "weightedimagemodel"that formalizesthe notionsof "straightness"
and"centrality"andusesthemto moreeasilyobtainquantitative predictionsof the laterality of complexstimuli. We
now describe this model in detail.
ulus.]
Predictionsof the weighted-image
model are derived
from a weightedlinearcombinationof the centroidsalong
the r axis of the maxima of the internal interaural
cross-
cross-correlation function.
Morespecifically,
the•weighted-image
modelgenerates
a variabledesignatedby P, which is obtainedby a linear
combinationof individualimages
In the aboveexpression/z
i is the locationalongthe r axis,
averagedoverfrequency,of the ith trajectoryof maximaof
the cross-correlation function
II. THE WEIGHTED-IMAGE
MODEL
The weighted-image
modelwasdevelopedto refineour
understanding
of theconcepts
of straightness
andcentrality
that werequalitativelydescribedabove,and to explorethe
extentto whichtheycouldaccountfor severalbinauralphenomena.Because
wewishedto explorea numberof phenomenafor whichthe auditory-nerveresponse
is not well specified, this model was formulated in a way that would provide
roughpredictions
quickly,with lessconcernfor thedetailsof
physiological
processing.
Towardthisend,predictions
of the
weighted-image
modelare basedonly to the maximaof the
159
J. Acoust.Soc. Am., Vol. 84, No. 1, July 1988
/.t,= • r(i,f• )p(r(i,f•),f•)q(f• )
k
wherer(hfk ) is thelocationalongthe taxis of the ith maximum
of the cross-correlation
frequency fn.
The
function
at characteristic
frequency-dependentfunction
p (r (i, fn ), fk ) indicatesthe relative numberof neural units
at interaural delay r(i, fn ). The function q(fk ), which is
sketchedin Fig. 5, is a frequency-weighting
functionevalu-
ated at frequencyf• and as obtainedby a polynomialapStern ot aL: A weighted-imagemodel
159
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js
The form of thisfunctionis basedon that of thep(r)
• o.o
used by Colburn (1977) and Stern and Colburn (1978),
exceptthat it becomes
a narrowerfunctionof r for frequenciesabove300Hz. (This frequencydependence
wasincluded for reasonsrelatedto predictions
for higherfrequency
stimulithat are not discussed
in the presentarticle.) The
amplitudeof the functionis scaledto maintainconstantarea
in thetailsofp (r, f ) alongther axisat all frequencies.
The functionq(f) usedin the weighted-image
model
wasa best-fitthird-orderpolynomialapproximationto the
frequency-weighting
functionimpliedby the data of Raatgever( 1980,p. 48). For frequencies
at or below 1200Hz,
thisparametricapproximation
is
• -4.o
CubicRegression
-8.0
-10.0
......
200
0
400
600
800
1000
1200
Frequency, Hz
q(f) = 10- (b,(•ooos•
+ b2(•ooos•
2+ b,t•ooos•)/•o,
FIG. 5. An empiricalfrequency
weightingfunctionfor thesalience
of components
of binauralstimuli.Data wereobtainedby Raatgever(1980) and
werefit by a cubicpolynomial
approximation.
The frequency
weighting
functionis assumed
to bea constantfor frequencies
above1200Hz.
wheref is in kHz and
b• = ( - 9.383)(10-•),
b• = (1.126)(10-4),
proximationto empiricaldata of Raatgever(1980). [The
functions
p (r, f ) andq( f ) arespecified
below.] The computationof/-ti weighsmoreheavilythe contributionof frequencies
aroundthe dominantregionof 600 Hz [through
thecontribution
ofq(f) ], andit weighsmoreheavilyvalues
off that aresmallerin magnitude[ throughthecontribution
ofp(r,f) ]. The summations
in Eq. (3) are evaluatedover
logarithmicallyspacedvaluesoffk.
The weightingcoefficient•oi for the ith trajectoryis
specified
by the equation
b3= ( - 3.992)(I0-•).
Raatgever's
resultsdo notextendto frequencies
above1200
Hz, so,at thesefrequencies,
we assumethat q(f) is a constantequalto
q(f) = 10- (b,(1200)
+ b2(12007
+ b•(1200)•)/10
Theparameter
Koin Eq. (4) determines
therelativeweighting of straightness
andcentralityin the theoreticalpredictionswithstraightness
contributing
to thepredictions
more
if Kois smallerin magnitude.
The predictions
of thisarticle
wereobtainedusinga valueof 0.035for Ko,whichseemsto
•o•= a• + Ko
p(v(i,fk),fk)q(fk)log
, (4)
bestdescribe
thedataof Fig. 4. In general,weexpectthatthe
bestvalueofKowouldvaryfromsubjectto subject,sincethe
wherep(r, f) and q(f) are definedas above,and the conand centralitycuesare
stantsf• andf• refer to the upperand lowerfrequencies, relativesalienceof the straightness
likely
to
differ
for
different
individuals.
We are currently
respectively,
overwhichthe computationis evaluated.The
examining
the
extent
to
which
subject-to-subject
variability
parameter
a• describes
thestraightness
or curvature
of the
in
a
number
of
additional
low-frequency
lateralization
reith trajectoryand is obtainedusingthe formula
sultscanbeaccounted
forbyvaryingtheparameter
Koin the
k
Here,a• canbethought
ofasthefrequency-weighted
"variance"about• alongtheaxisof the pointsthat comprisethe
ith trajectoryof maximaof the cross-correlation
functionin
the r-f plane.Again,we notethat, if the stimuliare pure
tones,
thestraightness
para•ter • equals
0, andthevarioustrajectories
contributeto P [ throughp (r(i, f• ), f ) ] exactlyastheydo in the postion-variable
model.
We usedthe followingfunctionto describethe greater
weighted-image
model.
It isdifficultto succinctly
characterize
thesensitivity
of
thepredictions
to theexactformofthefunctionsp
(r, f) and
q(f) becausethe effectsof the two functionsinteractwith
eachotherin a complexfashion.Nevertheless,
we are convincedthat,eventhoughtheexactnumericalpredictions
of
the model dependon the specificform that is chosenfor
thesetwo functions,the form of thesepredictions(and
thereforetheextentto whichtheyqualitativelydescribe
the
form of the observeddata) will remainthe samefor any
reasonable
pulseshapes.
weighting of more central maxima of the cross-correlation
III. COMPARISONS
functionimposedbyp (r, f ):
DATA
'r(f),
ly(f)rl•0.15 ms,
p(r,f) = y(f)exp(- []y(f)rl-0.15]/0.6L
otherwise,
wherethefrequency-dependent
parametery(f) isequalto
f<0.3
Y(f)=[],
(f/0.3)
2,f)0.3,
wheref is in kHz.
160
d.Acoust.
Soc.Am.,Vol.84, No.1, July1988
OF THE MODEL TO EXPERIMENTAL
In this section,we presentand discuss
comparisons
of
thepredictions
of theweighted-image
modelto theresultsof
severalexperimental
studies.
At present,thesecomparisons
arelimited to low frequencies
becausewe believethat lateralizationabove1500-2000Hz is affectedby the well-known
inabilityof the peripheralauditorysystemto track the fine
structureof thesehigherfrequencystimuli.We believethat
the trade-offbetweenstraightness
andcentralityproposed
Sterneta/.: A weighted-image
model
160
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.j
aboveoperates
in the samefashionat higherfrequencies,
eventhoughprocessing
mustbebasedonlyon the ITDs of
theenvelopes
ofthesestimuli.However,
quantitative
predictionsfor thesestimuliwouldrequirea muchmoredetailed
specification
of howtheyareprocessed
physiologically
than
theverysimpledescription
of thepeaksof thecross-correlationfunctionthatisthebasisfor theweighted-image
model.
In general,predictions
wereobtainedby weightingthe
contributions
of 21 trajectories
of maximaof thecross-correlationfunction.Thislargenumberof trajectories
isrequired
B. Laterality of amplitude-modulated narrow-band
stimuli
Bernsteinand Trahiotis (1985a,b) recentlymeasured
the lateralityof sinusoidally
amplitude-modulated
(SAM)
low-frequency
tones.The signalsto the two earsin these
experiments
were
SL(t) = [ 1 + COS(tomt
) ]COS(to•t)
(6a)
and
Sn(t) = [ 1 + cos(to,.
(t -- r,. ))]cos(too
(t - •'½))(6b)
by thegradualdecrease
in themagnitude
ofp (r,f) as I•-I
increases.
Computations
wereevaluated
at 80 frequenciesfk or, equivalently,
in eachtrajectory,whichwerelogarithmically
spacedover
SL(t) = cos(oct)q- • cos[(tocq-to,.)t ]
therangeof interest..
A. Joint dependenceof lateralityof bandpassnoise on
interauraltime delay and interaural phase difference
Predictions
of theweighted-image
modelfor thedataof
Fig. 4 areprovidedin Fig. 6, plottedwith anarbitrarylinear
scaling
of theverticalaxis.ASdiscussed
in Sec.I, thesepredictionsand data are easily understoodin terms of the
straightness
and centralityof the maximaof the interaural
+ «cos[(toc-- to,•)t ]
S(t) = cos[toe(t-
+ cos{(toc
+ to,")
X [t -- ((toc•-½
+ to",
rr•)/(too+ to,.))]}
+ i cos{(toc
)
X [t -- ((toJ'c-- to•r• )/(toc-- to•))]},
cross-correlation
function.For verynarrowbandwidths,the
stimuliaresimilarto 500-HztoneswithanITD of - 500bts
and they are lateralizedtoward the left sideof the head. As
the bandwidthof the stimuliis increased,
a rivalry becomes
established
between
thetrajectoryat •' = q- 1500/•s(which
isstraighter),andthetrajectorypassing
throughr = - 500
/•s (whichismorecentral,or closerto thef axis).Whenthe
IPD equals0', the straightertrajectoryat 1500btsis much
more dominant.The stimuli with IPDs of 90ø,180ø,and 270*
producecross-correlation
functionswith trajectoriesthat
passthrough•- = 1500/•s at 500 Hz with progressively
decreasingstraightness.
As a result,themodelpredictsthat the
trajectoryat q- 1500$tsis weightedlessheavily(for these
other valuesof IPD), decreasing
the extentto which the
image:is lateralizedtoward the right sideof the headfor a
givenbandwidth.Thesetrends,of course,are alsoobserved
in thedata,althoughtherearesomequantitative
differences
betweenpredictions
and data (suchas the frequencyat
whichthe 1500-1ts
curvecrosses
the horizontalaxis).
(7a)
and
(7b)
wherecoc is the carrier frequencyand to., is the modulator
frequency.Bernsteinand Trahiotisconsidered
two typesof
ITD: waveformdelay (in which both the finestructureand
low-frequencyenvelopewere delayed equally; i.e., v½
equaledr., ) and modulatordelay (in whichonly the envelopecontainedan ITD andthecarrierremainedinteraurally
in phase,i.e.,r c equaled0). Figure7 showsanaverage(over
three subjects)of the lateral postionof 500-Hz tones,and
SAM toneswith modulationfrequencies
of 25 and 50 Hz.
For a smallnumberof ITDs, data pointsare availablefor
only two of the threesubjects.Missingdata pointsfrom a
given subjectwere estimatedby linearly interpolating
betweenadjacentdata pointsfor that subject,weightedaccordingto differences
of the ITDs.
As seenin Eqs. (7a) and (7b), sinusoidally
amplitudemodulatedtonesconsistof threesinusoids(oneat the carrier
frequencyand one eachat the carrierfrequencyplusand
minusthemodulatorfrequency).Althoughthesestimuliare
easyto describemathematically,it is dincult to predictaccuratelythe physiological
response
that they produce.Specifically, the preciseinteraural cross-correlationfunction
that wouldbeobserved
for SAM tonesdepends
on theexact
bandwidthof the peripheralauditoryfilters,the amountof
two-tonesuppression
producedby the stimuli,and otherdetailsof physiological
processing
that arenotspecified
explicitly in the simpleweighted-image
model.In orderto obtain
a basicunderstanding
of howthe factorsof straightness
and
centralitycomeinto play for the data of BernsteinandTrahiotiswithoutfurthercomplicatingthe model,we obtained
predictionsfor a simpletypeof stimulusthat iscloselyrelatedto the SAM tone.Specifically,
we convertedthe linespectrum of the SAM tonesto a continuousbandpass
spectrum
with interauralphaseshiftsthat wereequalat the frequencies of the carrier and of the two sidebands and that were
FIG. 6. Predictions
of theweighted-image
modelfor thedataof Fig. 4.
161
d. Acoust.Sec. Am., Vol. 84, No. 1, July 1988
linearly interpolatedbetweenthese frequencies.In other
words,the IPD of the stimuliat any frequencybetweenthe
Stern ota/.: A weighted-imagemodel
161
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js
• 800
600
500
\".. 5oo
40O
-5
o
-10
o
500-Hz tone
[3---13 Modulator
Frequency
,a,---,,• Modulator
Frequency•/'
.4000
= 50 Hz
-15
-2000
200•
2000
4000
Interaural Delay •
FIG. 7. Experimental
measurements
of positionasa functionof waveform
ITD for 500-Hz toneswith and withoutamplitudemodulation,averaged
over three subjects.Data are replottedfrom Bernsteinand Trahiotis
FIG. 9. Loci of the peaksof the cross-correlation
functionfor 500-Hz amplitude-modulatednarrow-bandnoisewith a bandwidth of 50 Hz and a
waveformITD of 700its.
(1985a).
of maximaspanonly a very narrowbandwidth,and lateralization mustbe dominatedby the relativecentralityof the
two sidebands was
4Eo= coc
(re - r,• ) +
trajectories.
The mostcentraltrajectoryisat r = 700$tsfor
an
ITD
of
700/•s
(Fig. 9), andit passes
throughr = - 700
This means that maxima of the cross-correlation function at
/•s for an ITD of 1300its (Fig. 10). As the frequencyof
frequencyfwill appearat
modulationof the SAM tonesincreases,
the trajectoriesof
r=rm + (f•/f)(r•
-rm) + (k/f•),
(8)
maximaof thecross-correlation
functionspananincreasingwheref is in Hz, fc equalsco•/2rr,andk is an integer.
ly widerrangeof frequency,
and theweighted-image
model
Figure 8 containspredictionsof the weighted-image predictsthat the trajectoriesthat are straightershouldbe
modelfor thedataof Fig. 7. Boththeobserved
andpredicted weightedincreasinglymore heavily.For the stimuluswith
positionsare roughlysinusoidal
functionsof the waveform the 700-/_rs
waveformdelay,the morecentraltrajectoryat
delay.More interestingly,
thefrequencyof modulationhasa
700/•s is alsothe straighterone,and hencelateralposition
muchgreatereffecton perceivedlateralpositionat ITDs of
shouldremainrelativelyunchangedas the frequencyof
approximately
1300/•sthanit doesat ITDs of approximate- modulationincreases.
Whenthe waveformITD is 1300
ly 700/.rs,and a similareffectis seenin the predictionsas however,the trajectoryat 1300/•sis the straightest.
Therewell.
fore, as the frequencyof modulationincreases,the lateral
Once more, consideration of the loci of the maxima of
positionis predictedto changeas the trajectoryat 1300
the interauralcrosscorrelationof the stimuli providesan
becomesweightedincreasinglymore heavily becauseit is
intuitivelyappealingexplanationfor thegreaterdependence straighterthanthe morecentraltrajectoryat - 700
of positionon modulationfrequencyfor ITDs near 1300
Applicationof the straightness
andcentralityconcepts
comparedto 700$ts.Figures9 and 10 showthe locationsof
for theoriginalSAM tonedatawouldalsoproducepredicthe peaksof the crosscorrelationfor the idealizedstimuli
tionsthatexhibitthemajortrendsseenin Fig. 8 if anapprothat wereusedto obtainthe theoreticalpredictions,
present- priate descriptionof the physiologicalprocessing
of SAM
ed with waveformdelaysof 700 and 1300/•s, respectively. tones were available. This can be asserted with confidence
When the frequencyof modulationis small,the trajectories
•,800
• 600
1500
:25Hz
.:2000
•. .... /•'
.... Modulat=
5;r•;oquency
V
FIG. 8. Predictions
of weighted-image
modelfor the dataof Fig. 7. The
verticalaxishasbeenlinearlyscaledby an arbitraryconstant.
162
d. Acoust.Sec.Am.,Vol.84, No.1,July1988
400
-4000
-2000
200
2000
4000
Interaural Delay • (its)
FIG. 10.Loci of the peaksof thecross-correlation
functionfor 500-Hz amplitude-modulated
narrow-bandnoisewith a bandwidthof 50 Hz and a
waveformITD of 1300/•s.
Sterneta/.: A weighted-image
model
162
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.j
because
SAM stimuliwith waveformdelays(like all other
stimuli)alwaysproduce
a straighttrajectoryat thevalueoff
corresponding
to the ITD, regardless
of thespecifics
of the
model.The other trajectorieswould take on a form that is
morecomplexthanthelocishownin Figs.9 and10,butthey
1o•
• 60
will berelatively
lessstraightin all cases.
In summary,
predictionswill be dominatedby centralityconsiderations
at
small:modulation
frequencies,
butstraightness
becomes
an
increasingly
importantfactorasthe modulationfrequency
increases.
Tl•e predictionsin Fig. 8 for 500-Hz tones(the solid
curve),canalsobecomparedto earlierdataobtainedby Sayers( 1[}64),DomnitzandColburn( 1977), andYost ( 1981),
whichdescribe
the positionof tonalstimuliasa functionof
ITD (or IPD) usingdifferentexperimentalprocedures.
Thesepredictions
areanexcellent
description
of thedataof
DomnitzandColburn.Theyalsoprovidea gooddescription
of thedataof SayersandYostexceptforstimuliwithITDs of
abouthalftheperiodof thetone(whichcorrespond
to 180ø
IPDs). The datafor thesestimulifromthe variousexperimentsdiffer:Sayers'resultsindicatethat subjects
hearthese
stimuliat eachof thetwoearsandoccasionally
at thecenter
•. 20
FIG. 11.Lateralization
performance
with60-and200-/zs
groupdelaysasa
function
of thecenterfrequency
of an800-Hz-wide
transient
signal.
Trahiotisexperiments).Therefore,themaximaof thecrosscorrelationfunctionfor thesestimuliare alsodescribedby
Eq. (8) with the parameterr• setequalto zero.
Figure 11containsresultsobtainedby Henning(1983)
for 800-Hz-wide
of the head, Yost's observerstended to lateralize thesestimu-
li consistentlyto one sideof the head, and Domnitz and
Colburn'ssubjects
described
imageswith centersthat were
at the,center
of thehead.While manyof thesedifferences
in
thedataaredue,in part,to differences
in experimental
methodsand responseprocedures,it is clear that tonal stimuli
with 180*IPDs arequitelablieanddifficultto lateralizein a
consistent
fashion.The weighted-image
model(like theposition-variable
model) predictsthat IPDs of 180'will producean imagethat is at the centerof the head,becauseits
predictionsare basedon a eentroidcomputation.At other
ITDs, the data from thesethreestudiesare in reasonably
goodagreementwith eachother,with the dataof Bernstein
and Trahiotis (1985a,b), and with the predictionsof the
weighted-image
model.
c. Lateralizationof low-frequencytransientspresented
with group delay
Becauseof difficultiesin characterizingthe auditory
processingof SAM tones (including thosecited above),
Henning(1983) performed
a seriesof lateralization
experimentsusingbriefbandpass
transientsignalsfor whichITDs
in the"envelope"andfinestructurecouldbeseparately
ma-
thesedata is that the transientsare clearlylateralizedto one
sideof the headfor low frequencies,
to the othersideof the
headat somewhathigherfrequencies,and at the middle of
the headat the highestfrequencies
examined.
Figure12showstheoretical
predictions
of theweightedimagemodelfor thedataplottedin Fig. 1I. The predictions
exhibitmanyof thesignificant
featuresof thedata,including
the movementof the imagefrom onesideof the headto the
otherascenterfrequencyincreases
from400 to 1000Hz. An
examinationof the trajectoriesof the maximaof the crosscorrelationfunctionsof Henning'sstimuli indicatedthat
theseresultscannotbe explainedin termsof competition
betweenstraightness
and centrality.Henning (1983) suggestedthat the data shownin Fig. 11 reflectthe dominance
•
these
experiments
is
&.(t)-2Aø
sin[(cøaw/2)(t)]
sin[co•(t)],
(9a)
rr
t
s•(t)-- 2Ao
sin[
(co.w/2)
(t--At•)]
•'
t -- Atg•
Xsin[co•
(t-- Argo)
- At•co•
],
(9b)
where
ro•w
isthe
bandwidth
ofthe
signal
and
ro•
isthe
carrierfrequency.
WhenAtg•= - Atc, thebinauralsignalis
saidto exhibitgroupdelaybut notphasedelay(a condition
that isequivalentto themodulatorITD of theBernsteinand
163
J. Acoust.Soc.Am.,Vol. 84, No. 1, July1988
transients as a function of
centerfrequency.Henning'ssubjectsreportedwhetherthe
stimuliwereperceived
to theleftor to therightof thesubjective midline,and resultsare plottedin termsof the percentageof"correct"or consistent
lateralizations.
If theperceptual image is unimodal, then this percentageshouldbe
monotonically
relatedto theexpected
positionpredictedby
theweighted-image
model.The mostoutstanding
featureof
nipulated.
Using
Henning's
notation,
thesignal
toone
earin
and the signalto the other ear is
narrow-band
Group
delay
=200
gs
•\•----Group
delay=
x••quenc
(Hz)
FIG. 12.Predictionsof theweighted-image
modelfor the dataof Fig. 11.
SternoraL: A weighted-image
model
163
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js
ofstimulus
components
nearabout700Hz forthelateralization of complexstimuli.This "dominantregion"effecthas
beenexploredby Raatgever(1980) andothers,andit is reflectedin the model by the frequency-weighting
function
q( f ) (Fig. 5). In orderto explorefurthertheimportanceof
straightness
andthe dominant-frequency
effectin the lateralizationdata of Fig. 11, we obtainedtwo additionalsetsof
predictions
ofthe modelfor thesestimuli.First,weremoved
the straightness
weightingfrom the predictionsby setting
thestraightness
parameter
tr• equalto zero.Second,
weremovedthe effectsof the dominantfrequencyregionby settingthefrequency-weighting
functionto a constantindependent of frequency.These predictionsconfirm Henning's
hypothesis
in that the shapeof the predictionswasaffected
by removingthe frequency-weighting
functionbut not by
removingthe straightness-weighting
parameter.
analyzingpredictionsof the weighted-imagemodel even
thoughit hastheshortcomings
citedabove.For example,we
foundthat the tradebetweenstraightness
and centralityin
the modelplaysa very important role in understandingthe
lateralizationof bandpass
noiseas a functionof bandwidth
(Fig. 4) andlow-frequency
SAM tonesasa functionof modulationfrequency(Fig. 7). On theotherhand,straightness
doesnot greatlyaffectlateralizationin othercasessuchas
experiments
usingtonal stimuli,and the lateralityof lowfrequency
transients
presented
with puregroupdelays(Fig.
11).
Presently,webelievethat thebestresearchstrategyisto
incorporatethe bestfeaturesof the weighted-image
model
into a morephysiologically
plausiblemodelin orderto adequately describethesecomplexstimuli. We are currently
attemptingto modifytheposition-variable
model(Sternand
Colburn, 1978) to incorporatean attributesimilarto the
straightness
of the trajectories
in the weighted-image
model.
IV. DISCUSSION
A. Limitations of the weighted-image model
B. Envelope detection or consistency over frequency?
Althoughwe believethat the basicconceptualframework of the weighted-image
modelis valid and useful,it is
clear to us that many detailsneedto be worked out more
carefully.For example,whilewe estimatedthe straightness
of eachtrajectoryfor thetheoreticalpredictions
by computingitssecondcentralmomentalongthe v axis(i.e., its "variance"), thereare a numberof otherequallyplausiblemeasuresthat needto be explored.Presently,we are especially
concernedwith trying to understandhow the relative
weightingof the centroidsof the maximashouldbe deter-
Many recentdiscussions
of the processing
of complex
andhigh-frequency
binauralstimulihavefocusedon therelativesalience
of timinginformationthat canbeprovidedby
the envelopes
ascomparedto thefinestructureof the stimu-
mined.
In addition,the weighted-image
modelin its present
form has somefundamentalweaknesses.
The mostsignificant structural
weakness of the model is that it describes
mechanisms
of lateralizationin termsof operationson trajectoriesof maxima of the cross-correlation
functionwithout specifyinghow the systemis ableto identifythesemaxima and clusterthem into discretetrajectories.While some
stimuli (suchasbroadbandnoisepresentedwith an ITD of
the entire waveform) exhibit cross-correlation functions
with clearly identifiedtrajectoriesof maxima in the •--f
plane, other stimuli (such as SAM toneswith modulator
delaysequalto half the periodof the carrier component)
producecross-correlation
functionsthat appearto splitand
merge at variousfrequencies.The weighted-imagemodel
cannotbe easilyappliedto suchstimuli.Other stimulisuch
as SAM toneswith high carrier frequenciesproducecrosscorrelationfunctionswith many small local maxima and
minima, and somecriteria must be establishedfor identify-
ing whichare the "important"maxima.Finally, we again
note that the auditory systembecomesunableto track the
fine structureof stimulias frequencyincreases
about 1600
Hz. As a result, many of the maxima and minima of the
interauralcross-correlation
functionswill becomelesspronouncedas timing information about the fine structuredi-
minishes.
In orderforthemodelto describe
theperception
of
thesestimuli,it mustbemodifiedsothatit canspecifywhen
thesepeaksbecometoosmallto affectperception.
We believewe havegaineda greatdeal of insightby
164
J. Acoust.Soc. Am., Vol. 84, No. 1, July 1988
lus. Some researchers discuss information obtained from the
envelopein termsof groupdelay,or the localslopeof the
phasespectrum.(Variationsof thefinestructurecanbediscussed
in termsof phasedelay,which,at a givenfrequency,
isequalto the IPD dividedby thefrequency.)It is reasonable,then,to thinkof thesalience
of timinginformationavailablein the envelopes
of complexstimuliin termsof the extent to which groupdelayis consistent
over a rangeof
frequencies.
Ifa particularstimulushasa groupdelaythatis
consistent
overfrequency,that groupdelaywill correspond
to an interauralphasedifference
that increases
linearlywith
frequency.This, of course,is exactlytheconditionencountered if one has a stimulus with an ITD that is consistent over
frequency,
whichproduces
a stimuluswith at leastoneperfectlystraighttrajectory.In otherwords,thosestimulithat
producetrajectories
thatarestraightin thev-f planearealso
exactlythosestimulithat tendto exhibitpronounced
envelopeswithinterauraltiminginformationthatcanbeusedfor
localization.As a stimulusconditionis manipulated
in such
a way asto decrease
the amountof straightness,
the salience
of the envelopeis also likely to decrease.As a result, one
cannotdistinguish
on thebasisof thesedataandpredictions
alongwhetherthephenomena
aremediatedbyprocessing
of
interauraldelaysof theenvelopes
of thestimuli(in thestrict
sense),or by the competitionbetweenthe straightnessof the
trajectoriesof the cross-correlationfunction versusthe centrality of the variousmodesin that function.
We generallybelievethat consideration
of the straightnessversusthe centrality of the modesof the interaural
cross-correlation
functionis a moreintuitivelypleasingway
to think of how we processbinauralsoundsthan comparisonsof the ITDs of the envelopeversusthe finestructureof
the stimuli,or comparisons
betweeninterauralgroupdelay
versusphasedelay.First, theoriesbasedon emphasis
of the
straight componentsof the cross-correlationfunction are
Stern eta/.: A weighted-imagemodel
164
ownloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.j
basedona patternrecognition
concept,
thatof searching
for Bernstein,L. R., and Trahiotis, C. (1985a). "Lateralization of Low-frequency,ComplexWaveforms:The Use of Envelope-based
Temporal
the ITD that is mostlikely to be generated
by a physical
Disparities,"J. Acoust.Soc.Am. 77, 1868-1880.
soundsource.Second,we believethat the straightness--cen- Bernstein,
L. R., andTrahiotis,C. (1985b)."Lateralization
of Sinusoidally
trality tradedescribes
thelateralizationphenomena
equally
Amplitude-modulated
Tones:Effectsof SpectralLocusandTemporal
Variation," 1. Acoust. Soc.Am. 78, 514--523.
wellat highfrequencies
(at whichtiminginformationin the
envelopes
is generallyassumed
to mediatelateralization)as Colbum,H. S. (1977). "Theoryof BinauralInteractionBasedon Auditory-nerveData. II. Detectionof Tonesin Noise,"J. Acoust.Soc.Am.
it doesfor stimuliat low frequencies
(at whichtiminginfor61, 525-533.
mation in the fine structureof a soundhad beenpreviously
assumedto mediate lateralization). As discussedabove, en-
Colbum, H. S., and Durlach, N. I. (1978}. "Models of Binaural Interac-
tion,"in Handbookof Perception,
Vol.IF, Hearing,editedby E. C. Car-
terette and M.P. Friedman (Academic, New York).
velopesofhigh-frequency
stimulipossess
ITDs thatarecon- Domnitz,
R. H., and Colbum, H. S. (1977). "Lateral Position and Intersistentover a range of frequencies.The weighted-image
aural Discrimination," J. Aconst. Soc. Am. 61, 1586-1598.
modelis not very well suitedto describethe lateralizationof
Henning,G. B. (1974}. "Detectabilityof Interaural Delay in High-frequencyComplexWaveforms,"J. Acoust.Soc.Am. 55, 84.-90.
thesehigherfrequencystimulibecause
it cannotneglectthe
ontheLateralization
of Comcycle-by-cycle
informationthat theycontain.We are confi- Henning,G. B. (1980}. "SomeObservations
plexWaveforms,"J. Acoust.Soc.Am. 68, 446-453.
dentthat a morephysiologically
plausiblemodelthat incor- Henning,G. B. (1983). "Lateralizationof Low-frequencyTransients,"
Hear. Res. 9, 153-172.
poratestheconcepts
of straightness
andcentralityshouldbe
Jeffress,
L. A. (1972}. "Binaural Signal Detection:Vector Theory," in
ableto describethesehigh-frequency
data.
Foundations
of Modern,•uditoryTheory,g'ol.11,editedby J. V. Tobias
V. SUMMARY
AND CONCLUSIONS
In this article we examined the results of several studies
of thesubjective
lateralityof low-frequency
complexbinaural sounds.We foundthat manyof the phenomenaconsideredcanbepredicted
by a verysimplemodelthatisbasedon
the centroidsof the trajectories
of the maximaof the interaural cross-correlation
function of the stimuli after peripheralbandpass
filtering.In orderfor themodelto predict
the data, it mustweighmore heavilythe contributions
of
thoseregionsof thecross-correlation
functionfor whichthe
ITD of thestimulusisconsistent
overa rangeof frequencies.
We believethatthispropertyofthe modelandthedataarea
consequence
of a naturaltendencyof theauditorysystemto
attemptto form perceptualimagesunderassumptions
that
the soundsourceis physiologically
realizable.Becauseof
thiswebelievethatit ismoreappropriate
to modelthelateralizationof complexbinauralstimuliin termsof theconsistencyof the interauralcuespresentedover a rangeof frequencies
thanin termsof physicalattributessuchasphase
delayversusgroupdelay.
(Academic, New York ).
Lindemann, W. (1986). "Extension of a Binaural Cross-correlationModel
by ContralateralInhibition.I. Simulationof Lateralizationfor Stationary Signals,"I. Acoust.Soc.Am. 80, 1608-1622.,
McFadden,D., and Pasanen,E. O. (1976}. "Lateralizationat High-frequencies
Basedon InterauralTime Differences,"
J. Acoust.Soc.Am. 59,
634-639.
Nuetzel, J. M., and Halter, E. R. {1981}. "Discrimination of Interaural
Delaysin ComplexWaveforms:SpectralEffects,"I. Acoust.Soc.Am.
69, Ill2-1118.
Nuetzei,J. M., and Halter, E. R. (1976). "Lateralizationof Complex
Waveforms:Effectsof Fine Structure,Amplitude,and Duration," J.
Aeoust. Soc. Am. 60, 1339-1346.
Raatgever,
J. (1980). "On theBinauralProcessing
of Stimuliwith Different Interaural Phase Relations," Doctoral dissertation, Technisehe
Hogesehool
Delft, The Netherlands.
Sayers,B. McA. (1964). "Acoustic-Image
Lateralization
Judgements
with
Binaural Tones," J. Acoust. Soc.Am. 36, 923-926.
Sayers,B. McA., andCherry,E. C. (1957). "Mechanismof BinauralFusionin theHearingof Speech,"
.I. Acoust.Soc.Am. 29, 973-987.
Schiano,J. L., Trahiotis, C., and Bernstein,L. R. (1986). "Lateralizafion of
Low-frequency
TonesandNarrowBandsof Noise,"J. Acoust.Soc.Am.
79, 1563-1570.
Shear,G. D., and Stern, R. M. (1988}. "Lateralization of Broadbandand
Complex Stimuli: Predictionsof the Position-VariableModel," J.
Acoust.Soc.Am. (in preparation).
Stem, R. M., Jr., and Colbum, H. S. (1978). "Theory of BinauralInteraction Basedon Auditory-NerveData. IV. A Model for SubjectiveLateral
Position," J. Acoust. Soc. Am. 64, 127-140.
ACKNOWLEDGMENTS
This workwassupported
by the NationalInstitutesof
Health (Grants NS14908, GM07477, and NS20174). We
thank G. D. Shear for providingthe experimentaldata
shownin Fig. 4. We alsothank L. R. Bernsteinand G. D.
Shearfor manystimulatingdiscussions
abouttheseandother phenomena.
165
J. Acoust.Soc.Am.,Vol. 84, No. 1, July1988
Trahiotis, C., and Bernstein,L. R. (1986). "Lateralization of Bandsof
NoiseandSinusoidally
Amplitude-Modulated
Tones:Effects
ofSpectral
Locus and Bandwidth," J. Acoust. Soc. Am. 79, 1950-1957.
Trahiotis, C., and Stem, R. M., Jr. (1988). "Lateralization of Bands of
Noise: Effects of Bandwidth and Differences of Interaural Time and
Phase,"J. Acoust.Soc.Am. (in preparation).
Yost, W. A. (1981}. "Lateral Position-ofSinusoldsPresentedwith Inter-
auralTemporalandIntensiveDifferences,"
J. Acoust.Soc.Am. 70, 397409.
Sternetal.: A weighted-image
model
165
Downloaded 25 May 2010 to 128.2.130.32. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js