It is well established that the interaural time differen~ITD! and the interaural level difference~ILD ! provide theprimary cues for the horizontal localization of a sousource, whereas the monaural spectral modifications induced by the pinna provide the primary cues for vertilocalization ~Middlebrooks and Green, 1991; Carlile, 199Blauert, 1997; Wightman and Kistler, 1997!. Pinna effectsstart to appear at frequencies around 3 kHz, where the wlength becomes comparable to the pinna size, with thecalled ‘‘pinna notch’’ appearing within the octave from 612 kHz ~Shaw, 1997!. This supports the general belief ththe source must have substantial high-frequency energya fairly wide band for accurate judgment of elevation~Rof-fler and Butler, 1967; Gardner and Gardner, 1973; But1986; Asano, Suzuki, and Sone, 1990!.
The role of the torso in localization is less well undestood. The fact that the torso disturbs incident sound waat low frequencies has been recognized for a long time~Han-son, 1944; Kuhn and Guernsey, 1983!. However, the effectsof the torso are relatively weak, and experiments to estabthe perceptual importance of low-frequency cues have pduced mixed results. For example, Theile and Spikof~1982! concluded from their experiments that the torso donot provide significant cues for front/back discriminatioHowever, while agreeing that high-frequency spectral care needed for front/back discrimination, Asanoet al. ~1990!
1110 J. Acoust. Soc. Am. 109 (3), March 2001 0001-4966/2001/10
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observed that front/back discrimination is significantly improved when the subjects are provided with the correct lofrequency spectrum.
The effect of the torso on vertical localization in thmedian plane was first systematically investigated by Ganer ~1973!, who observed that—although the subjectisense of source location was greatly diminished when hfrequencies were removed—it was possible for some sjects to localize sounds from loudspeakers located in theterior median plane, despite the fact that the source hadspectral energy above 4 kHz. Gardner also measuredhead-related transfer function~HRTF! of a mannequin, bothwith and without pinna occlusion and with and withouttorso. By comparing the change in the response at118°elevation to that at218° elevation, he concluded that thpinna had no influence below 3.5 kHz, but that the tointroduced important ‘‘clues of a secondary nature’’ betwe0.7 and 3.5 kHz. However, he cautioned that the mere pence of elevation-dependent low-frequency spectral featdoes not mean that they can be exploited by the audisystem. Searleet al. ~1976! identified six localization cues intheir statistical model of human sound localization, and uGardner’s data to estimate the variance due to the torsoflection or ‘‘shoulder bounce.’’ They concluded that thshoulder bounce provided by far the weakest elevation c
Kuhn ~1987! used a KEMAR mannequin with and without pinnae and torso in a study of the behavior of the HR
for all elevations in the median plane. He showed that mdian plane directivity is governed by specular reflection frothe torso at frequencies below 2 kHz and by complex pinphenomena for frequencies above 4 kHz. However, the qtion of whether or not the low-frequency features provideffective elevation cues was not addressed.1
Going outside the median plane, Genuit and Pla~1981! showed that the torso introduced both direction- adistance-dependent effects on the HRTF that are limitedthe spectral range below 3 kHz, and Genuit~1984! subse-quently included separate torso and shoulder submodehis structural HRTF model. Brown and Duda~1998! ob-served torso reflections in head-related impulse respo~HRIR! data, and also included a ‘‘shoulder echo’’ in thestructural HRTF model. However, that component was omted during their formal tests of the model because informlistening experiments had indicated that the simulated toreflections did not have a significant effect on perceivedevation in the median plane.
This paper reports on psychoacoustic experiments windividualized HRTFs that show that there are significaelevation cues for sources having little high-frequencyergy, but the source must be away from the median plaSome of the experiments used measured HRTFs, and oused a simplified low-frequency HRTF model. The methoused for the psychoacoustic experiments are describeSec. II. The experimental results obtained with measuHRTFs are reported, analyzed, and discussed in Sec. III.tion IV presents an analysis of the low-frequency characistics of HRTF that demonstrates that the pinnae do not ctribute to the HRTF at frequencies below 3 kHz. Simpgeometric models of the head and torso of each subjectthen developed and analyzed to establish that the headtorso are the determinant contributors to the HRTFs atfrequencies. Finally in Sec. V, the results of psychoacouexperiments with synthetic approximations and simple mels of the head and torso are reported that confirm the ctributions of head and torso to the perceived elevation.
II. METHODS
A. HRTF measurements
The HRTFs employed in this study were measured usthe blocked-ear-canal technique~Møller, 1992; Algazi, Av-endano, and Thompson, 1999!. The probe tubes of two Etymotic Research ER-7C microphones were attached to plaear plugs, which were then inserted into the subject’scanals. The subjects were seated and, to minimize hmovements, were asked to control their head positionviewing their reflection in a mirror; however, they were notherwise physically constrained. The impulse responwere obtained using Golay codes~Crystal River EngineeringSnapshot™ system!, played through Bose Acoustimass™Cube speakers. The speakers were mounted on a 1-m-rhoop that was rotated about the subject’s interaural axis.sampling rate for the measurements was 44.1 kHz. Tomove most room reflections, the resulting impulse respon
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were windowed and truncated to a duration of 4.5 ms, awere equalized to compensate for the loudspeaker andcrophone transfer functions.
The geometry of the HRTF measurement apparaleads naturally to use of the interaural–polar spherical codinate system shown in Fig. 1. The origin of this sphericoordinate system is at the interaural midpoint, which is ually somewhat below and behind the center of the head.azimuth angleu is measured between the median plane anray from the origin to the source. An azimuth angle of190°corresponds to the right side of the subject, and290° to theleft, with u50° defining the median plane. The elevatioanglef is the polar rotation angle, withf50° defining theanterior horizontal half-plane. The elevation sequence290°,0°, 90°, 180°, and 270° corresponds, respectively, to lotions below, in front of, above, in back of, and below thsubject.2
The HRTFs were measured at 1250 locations in spawith elevation increments ofDf55.625° for a range245°<f<231° and at 25 different azimuth angles with5° spacing in the front, increasing towards the interaupoles~Algazi et al., 1999!.
To a first degree of approximation, in this coordinasystem the ITD depends on azimuth alone~Searleet al.,1976; Wightman and Kistler, 1997!. A surface of constantinteraural–polar azimuth is often called a ‘‘cone of confsion.’’ Thus, in principle, knowledge of the ITD would allowone to estimate the azimuth, and hence to constrain the ltion of the source to a particular cone of confusion. Foconstant range, the source moves around a ‘‘circle of consion’’ which corresponds to the trajectory described by oof the loudspeakers as the hoop rotates.
B. Subjects
Six subjects were tested, four males and two femaranging in age from 20 to 42 years. None of the subjects wrelated to the research and all had normal hearing. All sjects were students or staff members at UC Davis, andno previous experience with listening tests.
C. Experiments
The experiments involved listening to simulated or vtual auditory sources through headphones. The headphstimuli were produced by convolving a test signal with tleft and right impulse responses for each position tested,the subjects were asked to report the perceived elevatio
Localization accuracy was measured on the left sidethe subject in 16 different situations, one for each of tpossible combinations of the following three factors:
The aim of the experiments was to compare the accurof the elevations reported by the subjects for full-bandwidsound sources with that for low-pass-filtered, limitebandwidth sources. In an ‘‘absolute-judgment’’ approathe subject listened to a presentation of a test signal and
1111Algazi et al.: Low-frequency elevation localization
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a graphical interface to select any point on a circle that bcorresponded to the perceived elevation. To familiarize sjects with the procedure, test sessions were precededbrief description of the coordinate system and a presentaof a subset of the stimuli. Subjects were asked to think ofcircle as a projection of the circle of confusion onto a plaTo visualize this mapping, circles of confusion were costructed on the surface of a three-dimensional image osphere, and subjects could immediately relate the circlethe trajectories of the loudspeakers at the time when tHRTFs were measured. To provide familiarization with tprocedure, each subject was allowed a brief time periodwhich she or he could follow a marker on the circle and hthe corresponding stimulus. Front and back locations wtested separately and the subject always knew which cotion prevailed.3
Each of the 16 situations was tested separately. Forample, a particular test might be for a low-pass-filtersource at245° azimuth located in the front. For each teone of 12 elevation angles was randomly selected, subjethe constraint that each angle would eventually be repe10 times. This gave a total ofn5120 responses per te
FIG. 1. The interaural–polar coordinate system. A surface of constanteraural azimuthu is a cone of confusion, while a surface of constant intaural elevationf is a half-plane through the interaural axis.
1112 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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situation. When the source was in the front, the elevatangles ranged from245° to 78.75° in 11.25° steps. Subjecwere allowed to respond with an elevation anywheretween290° and 90°. The mirror image locations were uswhen the source was in back: 225° to 101.25° in211.25°steps, and subjects could respond anywhere between 90270°. Each test situation required approximately 15 mincomplete, with all 16 situations tested in about 4 h. Toduce fatigue, experiments were split into sessions of 2each, performed on different days.
D. Stimuli
The 22-kHz test signal was a sequence of two Gausnoise bursts, sampled at 44.1 kHz and independently geated on each presentation. Each noise burst had a duratio500 ms, with a 250-ms silent period between bursts. Indition, to increase the effective number of localizatio‘‘looks’’ ~Buell and Hafter, 1988!, each noise burst wa100% amplitude modulated with a 40-Hz sinusoid, phasedbegin and end with zero slope. Thus, each noise burstessentially 20 bursts of 25-ms duration each. The 3-kHzsignal was obtained by filtering the wideband signal with40th-order Butterworth low-pass filter having a 3-kHz cutofrequency. The convolution of the test signals with tHRTFs was done numerically inMATLAB . In addition, theresulting signals were filtered by a headphone compensafilter designed following Møller’s procedure~Møller, 1992!.The resulting sound files were played back through AK240-DF headphones using a PC equipped with a TurBeach Tahiti sound board. Although the energy in the tsignal was constant, the variation of the HRTF with elevtion produced a corresponding small variation in loudnewith an average SPL of 73 dB. Finally, the electrical signdriving the headphones were analyzed with a spectrum alyzer to verify that nonlinearities or noise in the processiand the hardware were not introducing spurious higfrequency signals.
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FIG. 2. Scatterplots for judged sourcelevation versus actual elevation foSubject S6 for a 22-kHz-bandwidthsource at four different azimuths. Inthe top row the sound source was ithe front hemisphere, while in the bottom row it was in back. Each plotshows data for 10 judgments at eacof 12 different elevations, togethewith the sample correlation coeffi-cient. The performance is comparabfor all azimuths and hemispheres.
1112Algazi et al.: Low-frequency elevation localization
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FIG. 3. Scatterplots as in Fig. 2, buwith the signal low-pass filtered to remove frequency components abovekHz. Performance in the median plan(u50°) is severely degraded. As thmagnitude of the azimuth increasethe performance improves, particularlfor sources in the back hemisphere.
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III. EXPERIMENTS WITH MEASURED HRTFS
Scatterplots of experimental results for a typical subj~S6! using full-bandwidth and 3-kHz low-pass stimuli ashown in Figs. 2 and 3. The eight situations shown in Figare for the 22-kHz-bandwidth source at the four differeazimuths. All eight cases are quite comparable, showingthe accuracy of judging elevation was not particularly sentive to whether the source was in the median plane or onof the cones of confusion, or whether the source was in fror in back. By contrast, Fig. 3 shows that when the mamum signal frequency was reduced to 3 kHz, performawas very poor in the median plane, but improved at otazimuths. Figure 4 shows similar 3-kHz bandwidth resufor another subject~S1!. Once again, the subject performevery poorly in the median plane, and was more accuratthe back than in front away from the median plane. Wh
1113 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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wideband results confirm that high frequencies are the mcontributors to elevation perception, it is surprising thaway from the median plane, one can still judge elevatwith a low-bandwidth source.
The effect of reducing the bandwidth can be measuby the change in the sample correlation coefficient. For Sject S6 we observe that the degradation in the median pwas about 90% in both hemispheres. The performancebetter for azimuths away from the median plane and wbetter in back than in front. Figure 5 shows that this genetrend was exhibited by the majority of the subjects testThis figure compares side-by-side the sample correlationefficients for full-bandwidth stimuli and for 3-kHz low-passtimuli for all subjects and all azimuths. The average corlation coefficientr for all subjects is summarized in Tablefor both wideband and low-pass tests.
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FIG. 4. Scatterplots as in Fig. 3, bufor Subject S1. The performance igenerally similar. In both cases, performance in the median plane is severely degraded, but a good correlation appears for sources away from thmedian plane and in back.
1113Algazi et al.: Low-frequency elevation localization
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FIG. 5. Comparison of low-pass anfull-bandwidth correlation coefficientsfor all subjects. Black: full bandwidth;gray: 3-kHz low pass. Values ofuruabove 0.18 are statistically significanat the 95% level.
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A standard significance test for the sample correlatcoefficientr is the Fisherz statistic,z50.5 ln(11r)/(12r); ifthe true correlation coefficient isr and if the sample sizen isgreater than 10, this statistic is approximately normally dtributed with mean 0.5 ln(11r)/(12r) and variance 1/(n23) ~Cramer, 1946!. For our data, wheren5120, any cor-relation whose magnitude is less than 0.18 is not statisticsignificant at the 95% confidence level.
Analysis of the performance of individual subjecshows that the correlation was always statistically significfor the full-bandwidth source for all subjects. When the snal was low-pass filtered and the source was in the meplane, the correlation was not significant for most subjeand the degradation in performance was highest. Whensource was away from the median plane, the performaimproved, as shown in Fig. 5 and Table I, and was best inback.
Inspection of the scatterplots in Figs. 3 and 4 reveasignificant amount of bias in the subjects’ estimates. Tomore specific, most of the time the subjects estimatedvirtual source location to be lower than it actually was. Asmeasure of accuracy, the correlation coefficient is invarito bias, but the rms error includes it.4 Table II shows both thebias and the rms error~in degrees!, averaged over all sixsubjects for each experimental condition. The rms errorrandom guessing between290° and190° is 51.96°, and therms values for low-pass stimuli in front or in the mediaplane indicate performance at the chance level. Howelower rms errors are achieved when the source is away fthe median plane and in back. Because bias contributednificantly to the rms error, we believe that the correlaticoefficient is a better indicator that low-frequency informtion is providing an elevation cue.
Finally, we observe that the results were subject depdent. At the extremes, one subject performed poorly in bthe wideband and low-pass tests, while another subject hsurprisingly good performance in all the low-pass tests,at 245° and265° in the back had an increase in rms er
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from 20° to 23°~less than 20%! when the bandwidth wasreduced from 22 to 3 kHz.
IV. LOW-FREQUENCY HRTF ANALYSIS
The perceptual experiments in the previous section cfirmed the existence of low-frequency elevation cues. Tphysical sources of these cues are reflected in featpresent in the HRTFs. Given the frequency range in whthese features appear, it is natural to assume that theycaused by larger body structures such as the torso and hwhose dimensions are comparable to the wavelengthquestion. Although Gardner~1973! and Kuhn~1987! showedthat the effects of the pinnae on the spectrum become noable above 3.5 kHz, it was important to establish that thwere negligible below 3 kHz.
The hypothesis that the low-frequency elevation cuwere not due to the pinnae was tested in three ways:
~1! By analyzing and identifying features of measurHRTFs obtained by including or removing differenbody parts~pinnae or torso!;
~2! By synthesizing HRTFs based on simple torso and hmodels and comparing such synthetic HRTFs to msurements; and
~3! By psychoacoustic tests of perceived elevation for ctomized approximations to the HRTFs that are bassolely on the geometry of the torso and of the head.
Several sets of HRTFs obtained by including or remoing the pinnae and torso of a KEMAR mannequin were alyzed. The goal was to separate the effects of the differanatomical structures and to isolate their partial contributito the low-frequency portion of the HRTFs. Strictly speaing, these contributions cannot be isolated this way, becathe combination of structures does not imply the superption of their acoustic fields. However, the effects of the torhead, and pinnae are sufficiently separated in time,quency, and spatial location that they can be observed
TABLE I. Average correlation coefficientr for four different azimuths. F5front and B5back.
selecting the domain in which their individual influencdominate.
A. HRTF data
Three sets of HRTFs of a KEMAR mannequin weobtained by including or removing different anatomicstructures. The data sets were collected according tocombinations shown in Table III.
The HRTFs of two human subjects were also measuFor each subject, two HRTFs were measured, a stanHRTF and a ‘‘pinna-less’’ HRTF, obtained by suppressithe effects of the subjects’ pinnae. This was achieved byuse of a rubber swimming cap that covered the outer eAdhesive tape was placed on the pinna regions to fursmooth the surface. Microphone probe tubes were placethe outside surface of the tape at positions correspondinthe ear canals. All measurements were made at the sspatial locations and with the techniques described in Sec
B. Contribution of the pinnae
The contribution of the pinnae to the HRTFs at lofrequencies can readily be evaluated on a KEMAR manquin with removable pinnae. Figure 6 illustrates the elevatdependence of the KEMAR HRTF with and without pinnaThe measurements were made for the ipsilateral ear ocone of confusion atu5245°. The squared magnitudesthe HRTFs were smoothed with simple auditory filters (Q58) and the results were displayed as images. In theseage displays, the HRTF data at a particular elevationdisplayed along a vertical line, where the gray scale indicapower in decibels. Because 90° elevation is in the cenfront/back differences are revealed as lack of bilateral symetry in the images.
Clearly, the pinnae have a major effect on the spectrabove 3 kHz, but relatively little effect below 3 kHz. Belo3 kHz, the average difference between the spectra withwithout pinnae is 0.86 dB. Thus, the pinnae do not appeacontribute significant monaural cues below 3 kHz. Howevin both cases, one can see elevation-dependent, arch-shnotches in the spectrum that extend as low as 700 Hz. Thare potential sources of elevation information that are clenot due to the pinnae.
The contribution of the pinnae to binaural ILD cueslow frequencies was also evaluated. The ILD was compuas the difference between the right and the left dB valuethe smoothed HRTF spectra. For frequencies below 3 kHcomparison of the ILDs of data set 1~both pinnae and torsopresent! and data set 2~pinnae removed! in the cone of con-fusion atu5245° is shown in Figs. 7~a! and~b!. The mag-nitude of the ILD is shown in a gray scale as a function
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elevation and frequency. We also evaluated the ILD for thuman subjects. In Figs. 7~c! and ~d! we show the ILDs forthe one of these subjects. For the KEMAR mannequin afor both of the two human subjects, the contribution of tpinnae to the low-frequency ILD was insignificant.
The essential identity of the pinnae/no-pinnae ILDs pafor frequencies below 3 kHz was observed for all azimuand for all subjects. This is in agreement with the obsertion of Kuhn ~see Fig. 14 in Kuhn, 1977!, who attributed theILD variations he observed in this frequency range totorso.
C. Contribution of the torso
Now that it has been established that the effect of pinis negligible below 3 kHz, what remains to be clarified is tnature of the separate head and torso contributions tolow-frequency cues. To this end we make use of the msurements in data set 2~pinnae removed!. The removal of thepinnae reduces the complexity of the HRIRs, particularlythe contralateral side, and simplifies identification of thead and torso contributions.
Figure 8 shows both the HRIR and the HRTF of KEMAR for an azimuth angle of245° with torso but no pinnae~data set 2!. Both ipsilateral and contralateral responsesdisplayed as functions of elevation and of time or frequenThe ipsilateral HRTF image is clearly brighter than the cotralateral image, which is a consequence of the ILD at245°azimuth. Notice that the ipsilateral HRTF data~the lower-leftpanel! are actually the same as in the right panel in Fig.the difference in visual appearance is due to a combinatio~a! a linear instead of a logarithmic frequency scale, and~b!a gray scale that encompasses both the high-amplitudelateral data and the low-amplitude contralateral data.
The HRIR images shown in Fig. 8~a! expose features othe HRTF that are hard to see in the frequency domain,they deserve a more detailed description. In either imageimpulse response at a particular elevation is displayed alvertical line. To reduce the effect of the ILD on ‘‘washinout’’ the contralateral image, the impulse responses wscaled so that the maximum magnitude was unity for bthe ipsilateral and the contralateral ear. As the color barthe right indicates, bright values are positive and dark valare negative. The gray band at the very top of either im
TABLE III. KEMAR HRTF data sets.
Set Pinnae Torso
1 Yes Yes2 No Yes3 No No
1115Algazi et al.: Low-frequency elevation localization
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corresponds to the zero value before the impulse respstarts. The strong white band or ridge near the top cosponds to the initial peak of the response. This peakactually ‘‘clipped’’ to allow the weaker parts of the impulsto be visible. This initial ridge is horizontal in the ipsilaterimage because the time of arrival was the same for all eletions. The initial ridge occurs about 0.4 ms later in the cotralateral image than in the ipsilateral image, correspondto the ITD at245° azimuth. Note that the ITD is actually noconstant, but varies by about60.1 ms; this phenomenon idiscussed further in Sec. IV E.
The initial pulse is followed by a series of subsequepulses. We focus on the response of the ipsilateral~upper-left panel of Fig. 8! because it is simpler than thresponse of the contralateral ear. Probably the most pronent feature is the pair of V-shaped ridges, one that is stger in the front and one that is stronger in the back. Fromway that these delays increase and then decrease with etion, we infer that the reflections come from below the eaThe delays are maximum for sound source locations abthe subject~at aboutf590°!. The maximum delay of abou1 ms corresponds to a distance of 33 cm, which is rougtwice the distance from the ear canal to the shoulder. Ththe pattern of delays suggests that the reflections are indue to a specular reflection from the torso. This was furtverified using data set 3, where removal of the torso resuin a loss of these reflections~compare the upper-right paneof Fig. 8 and the upper-middle panel of Fig. 9!.
In the frequency domain the torso reflections act acomb filter, introducing roughly bilaterally symmetric, arcshaped periodic notches in the spectrum that are particuclear for the ipsilateral ear@see Fig. 8~b!#. The frequencies awhich the notches occur are inversely related to the deland thus produce a pattern that varies with elevation.lowest notch frequency corresponds to the longest delay.
FIG. 6. Comparison of HRTF spectra. The left panel shows the specwith the pinnae attached, and the right panel shows the effect of remothe pinnae. The data are for the left ear atu5245°, so that these areipsilateral data. The measurements were smoothed by a constant-Q aufilter (Q58). The gray scale indicates the magnitude of the smoothed stra in decibels. The elevation-dependent arch-shaped patterns thapresent in both cases are due to head and torso effects. Notice thatextend down to fairly low frequencies~below 3 kHz!.
1116 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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lays longer than a sixth of a millisecond will produce onemore notches below 3 kHz and will contribute to the lowfrequency ILD of Fig. 7. Although the complexity of response of the contralateral ear makes it somewhat difficusee, analysis of data set 3 in the frequency domain confirmthat removing the torso indeed eliminated the large ar
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FIG. 7. Comparison of ILDs with and without pinnae.~a! KEMAR withpinnae;~b! KEMAR without pinnae;~c! Subject SA1;~d! Subject SA1 withpinnae ‘‘removed.’’ Data shown foru5245° and frequencies below 3 kHz
FIG. 8. ~a! HRIRs and~b! magnitude HRTFs for KEMAR with no pinnaeThe responses are shown for the cone of confusion atu5245° and fre-quencies up to 15 kHz. In the time-domain plots the amplitude of the HRhas been scaled to enhance the gray-scale image.
1116Algazi et al.: Low-frequency elevation localization
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shaped notches@compare the lower-right panel of Fig. 8~b!and the lower-middle panel of Fig. 9~b!#.
The contralateral impulse response in the right paneFig. 8~a! exhibits similar but weaker torso reflections, witheir corresponding notches in frequency domain. The ctralateral response displays other features, not explainetorso reflections, that become visible because of the relaweakness of the direct sound and torso reflections. Thfeatures are considered further in Sec. IV E.
Next, we develop a simple geometrical model for ttorso that accounts for the delayed reflections.
D. Geometric model of the torso
Although the human torso does not have a regular shit can be approximated by a simple ellipsoid, illustratedFig. A1 in the Appendix. The choice of an ellipsoid is bason analytical simplicity and its small number of parametewhich can be related to and estimated from anthropom~height, width, depth!. An algorithm for computing the delayD(u,f) of the torso reflection relative to the initial pulsea function of azimuth, elevation, and the geometrical paraeters is outlined in the Appendix.
This algorithm was used to compute the delays usanthropometric measurements for three subjects~KEMARand two humans!. Considering the simplicity of the modethe resulting delays were remarkably close to the measdata. Figure 10 compares the delays produced by the magainst the delays measured from the corresponding Hdata~data set 2—with torso but without pinnae!. The threesubjects exhibited different torso reflection patterns thatpended on body dimensions, and the anthropometry-bageometric model was able to account for these differenFigure 10 shows that the behavior of the model followsmeasured data closely.
E. Contribution of the head
Given its size, the head is the other anatomical structhat may contribute elevation-dependent features at low
FIG. 9. ~a! Right HRIR data for the KEMAR head with no pinnae and ntorso.~b! Magnitude of the HRTF. Three azimuths on the contralateral sare shown.
1117 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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quencies. To isolate the effect of the head, we use measments with both the pinnae and torso removed. The resulipsilateral response is rather featureless, because the enof the direct sound is large relative to the energy of tsecondary waves that are diffracted around the head~Aven-dano, Duda, and Algazi, 1999!. Thus, here we focus on thcontralateral response.
Figure 9 displays contralateral HRTF data in data se~both pinnae and torso removed! for three different azimuths~225°, 245°, and265°!. The impulse response exhibitsprominent X-shaped pattern, particularly away from the mdian plane@see Fig. 9~a!#. A simplified explanation is that theincident sound wave travels to the contralateral ear bypaths, one around the front of the head and the other arothe back~Duda and Martens, 1998!; the upper or primarypart of the X-shaped pattern arises from the shorter path,the lower or secondary part from the longer path.
As we noted earlier, the onset of the primary wave vies slightly as a function of elevation, indicating some elevtion asymmetry. This asymmetry has been discussedDuda, Avendano, and Algazi~1999!, where it was observedthat the ITD on a cone of confusion is actually not constabut can vary by as much as 0.12 ms as a function of eletion. For a spherical head, the HRTF can be computedactly from the head radius and the angle of incidence,angle between the source and the position of the ear c~Duda and Martens, 1998!. If the ear canals are diametricallopposed, the primary and secondary waves would each hthe same delay for all elevations on a cone of confusion,no X-shaped pattern would be seen. However, an X-sha
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FIG. 10. Comparison of the delayD from the model~dashed! and themeasured subject data~solid!: ~a! KEMAR; ~b! Subject 1; and~c! Subject 2.The delays are shown as functions of elevation for five azimuths in ecase.
1117Algazi et al.: Low-frequency elevation localization
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pattern appears if the ears are displaced. Several researhave noted that human ears typically lie behind and bethe horizontal axis~Genuit, 1984; Blauert, 1997!. Becausethe interaural axis defines the axis of rotation, this displament causes the angle of incidence to change as the somoves around the cone of confusion, with larger chanoccurring towards the contralateral hemisphere. Althouother factors, such as the nonspherical shape of the headaffect the time delay~Dudaet al., 1999!, the ear location isparticularly important.
F. Geometric model of the head
A simple spherical-head-with-offset-ears model is nused to account for the features observed in Fig. 9. Withmodel, both the ILD and the ITD vary on a cone of confsion. The HRTF for the sphere is obtained from Rayleiginfinite series solution to the equations for the diffractionsound by a sphere~Duda and Martens, 1998!. To computethe transfer function from the source to the ear, three qutities are needed: the distancer to the source, the angle oincidencec, and the head radiusa1 @see Fig. 11~a!#. Thedistance to the source was 1 m for our experimental dataThe angle of incidencec is the angle between the vectors tothe source and the vectore to the ear: c5cos21@(sTe)/isi iei#, where sT is the transpose ofs and r5i si is the length ofs ~see Fig. 11!. The only anthropomet-ric data needed are the head radiusa1 and the vectore,which is determined by the offsets of the ear downa2 , andbacka3 .
A comparison between the spherical head model wsize and offset parameters extracted from KEMAR~a1
58.5 cm,a253 cm, anda350.5 cm! and the data in data se3 ~both pinnae and torso removed! reveals that the sphericahead-with-offset-ears model provides a good approximato the elevation-dependent patterns in both the frequencythe time domain~cf. Figs. 9 and 12!. Notice that theX-shaped pattern due to the elevation-dependent onsetsecondary waves is introduced by the ear offset. Aspected, some discrepancies remain, because neither a hhead nor KEMAR’s head is really spherical, and effectsthe neck have not been modeled. However, the belevation-dependent features introduced by the head apto be captured.
FIG. 11. Geometry for the head model. Here,s is a vector from the centerof the head to the sound source,e is a vector from the center of the heathrough the entrance of the ear canal, andc is the angle between them. Thanthropometric parameters are the head radiusa1 , the downward offset ofthe eara2 , and the backward offset of the eara3 .
1118 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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V. EXPERIMENTS WITH A HEAD-AND-TORSOAPPROXIMATION
In Sec. IV, we demonstrated that a simple geometrihead-and-torso~HAT! model accounts for the behavior othe low-frequency experimental HRTFs. In this section,report on psychophysical experiments employing a classspherical-head model and an empirical torso-delay moAlthough this HAT approximation does not capture all tdetails of the experimental HRTFs at low frequencies, itcorporates the principal subject-dependent effects ofhead, shoulders, and torso. Thus, the purpose of theseexperiments is to assess the elevation cues that are convby simple geometrical features, individualized for each sject.
The spherical-head model was computed frominfinite-series solution to the problem of the scatteringacoustic waves from a point source by a rigid sphere~Dudaand Martens, 1998!. The resulting HRTFHs( iv,r ,c,a1) de-pends on the angular frequencyv, the distancer from thecenter of the head to the source, the incidence anglec be-tween the ear and the source, and the radiusa1 of the sphere.The HAT model approximates the complete HRTF by asuming that the wave incident on the head is the sum odirect wave and a weaker torso reflection that arrives aftedelay D(u,f) that depends on azimuthu and elevationf.For simplicity, it was assumed that the direct wave andtorso reflection arrive from the same direction, so thatHAT HRTF can be written as
HHAT~ iv!5a@11reivD~u,f!#Hs~ iv,r ,c,a1!,
wherer is the torso reflection coefficient, anda51/(11r)is a scale factor that guarantees thatHHAT(0)51.5
The resultingHHAT was individualized for each of thesix subjects by making separate estimates for the varparameters. For all subjects, we usedr 51 m, because thawas the range for the measured data, and for simplicityassumed thatr51/3, independent of direction or frequency6
The head radiusa1 and the ear locations~which are needed
FIG. 12. ~a! The HRIR and~b! the magnitude of the HRTF for the heamodel at three different azimuths on the contralateral side. A comparwith Fig. 9 shows a good general correspondence with the measured d
1118Algazi et al.: Low-frequency elevation localization
7
1119 J. Acoust. S
TABLE IV. Average correlation coefficientr for four different azimuths. F5front and B5back.
to calculate the incidence anglec! were individualized foreach subject by optimizing a least-squares fit to experimtally measured ITD data estimated from individual HRimages like those shown in Fig. 8. We could have usedellipsoidal torso model to compute the delayD(u,f) of thetorso reflection, but, as Fig. 10 illustrates, that would haintroduced some additional error into the HAT approximtion. Instead, we chose to determine the torso delays fmeasurements taken from individual HRIR images.
The experiments conducted with the HAT approximtion used the signals and methods described in Sec. IIbefore, a 3-kHz stimulus was produced by filtering the widband, amplitude-modulated noise signal with a 40th-orButterworth filter having a 3-kHz cutoff frequency. Thlow-pass signal was then convolved with the locatiodependent HAT HRTF approximation. Localization accracy was measured in eight different situations, for azimanglesu of 0°, 225°, 245°, 265°, using a source locatioeither in front or in back. The results for the HAT approxmation could therefore be compared directly to the resobtained for each subject’s measured HRTF with the sa3-kHz low-pass stimulus.
As a whole, the results of these experiments withHAT approximation complement and confirm the results otained with measured HRTFs. The results are summarizeTable IV, which adds to Table I the correlation coefficiefor all eight conditions for the HAT approximation, averagover the six subjects used in the study. We note that the Happroximation and the measured HRTF gave quite simresults. Performance in the median plane was very poor,
oc. Am., Vol. 109, No. 3, March 2001
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the larger correlations occurred away from the median pland in the back.
However, examination of the details of individual resureveals some interesting differences. For all subjects,HAT approximation provided a more consistent elevaticue than the measured HRTFs. However, for some subjthe correspondence between intended and perceived etions was poorer when the HAT approximation was usThese observations are exemplified by the experimentalof Subject S6~Figs. 3 and 13! and Subject S1~Figs. 4 and14!. These figures show that the HAT approximation ledsubstantially less scatter of reported elevations for eachget elevation than when the measured HRTF was used. Hever, with the HAT model, target elevations between 90° a140° were not well discriminated, with the mean beiaround 160° regardless of target elevation, while targetevations greater than 140° were more consistently andrectly reported. Thus, the linear correspondence betweenget and reported elevations that the correlation coefficmeasures is only a partial characterization of the differenbetween the results for the measured HRTF and for the Happroximation.
VI. DISCUSSION AND CONCLUSIONS
The experimental results reported have clearly estlished the existence of low-frequency cues for elevation tare significant away from the median plane. The analysisthe HRTFs has shown that the HRTF features below 3 kare primarily due to the torso reflection and head diffractio
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FIG. 13. Scatterplots for the HATmodel, 3-kHz bandwidth, Subject S6A comparison with Fig. 3 where themeasured HRTF was used shows vesimilar results. The ability to localizein back actually appears to be bettethan the performance with the measured HRTF. However, at azimuths o225° and 245°, the HAT modelseems to lead to more of a bimoda~low/high! response.
1119Algazi et al.: Low-frequency elevation localization
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FIG. 14. Scatterplots for the HATmodel, 3-kHz bandwidth, Subject S1A comparison with Fig. 4 where themeasured HRTF was used shows vesimilar results. The greatest differencoccurs at large azimuth in front, whervery few low elevations were reportedwith the measured HRTF. Howeverelsewhere the results are quite comprable.
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while the pinnae do not contribute significantly at these lfrequencies. The torso reflection effects are stronger onipsilateral side, while the head diffraction effects are stronon the contralateral side where the direct sound is attenuby the head. Further, it was shown that simple geomemodels for the head and the torso provide strong corrobtion of the physical basis for low-frequency elevation cuThe parameters of these models can be estimated fromthropometry to account for individual differences. A simphead-and-torso~HAT! geometric model was used to synthsize approximate HRTFs. Below 3 kHz, the synthetic HRwas basically similar to the measured HRTF. Psychoacouexperiments were conducted with an individualized HAT aproximation of low-frequency HRTF data. It was observthat the approximate HRTFs provided low-frequency eletion cues that were just as effective as those provided bymeasured HRTFs.
This study did not systematically examine other possisources of low-frequency elevation cues. We now discthese briefly and speculate on their importance on the bof the results of this work. First, the changes of the ITD welevation that were discussed in Sec. IV E could provideevation cues. However, these ITD deviations are significin only a fairly small range of spatial locations, and could nby themselves explain the full range of low-frequency effeobserved. Second, timbre and loudness are monaural speproperties that vary with elevation. Based on the resultsported for the median plane in this and previous studthese physical variations are clearly ineffective as lofrequency elevation cues. Finally, there are other larger atomical structures~such as the legs! that effect the HRTF atlow frequencies. Although not included in this paper, othHRIR measurements with seated subjects reveal knee retions at low elevations and in the front, but they vanishedabout 235° and occurred only in the front where lowfrequency elevation cues are weak. Thus, we believeknee reflections can at best provide very limited elevatcues. An interesting unanswered question is the genera
1120 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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fect of posture or of head rotation on low-frequency elevtion cues.
The existence of low-frequency cues has implicatiofor the binaural simulation of virtual sources. Spherical hemodels are commonly used to estimate the low-frequebehavior of the HRTF; this work suggests that the torso pvides additional cues that also should be taken into accoFinally, recognition of the presence of low-frequency cuprovides a possible opportunity for enhancing elevation cfor listeners with hearing loss at higher frequencies.
ACKNOWLEDGMENTS
The authors would like to thank Dennis Thompson fhis help with much of the experimental work, and the Ediand anonymous reviewers for their very thorough, thougful, and helpful suggestions. Support of the research wprovided by the University of California DiMI University-Industry collaborative program, by the Creative AdvancTechnology Center, by Aureal, by the Interval Research Cporation and by the Hewlett-Packard Research LaboratoSupport was also provided by the National Science Fountion under Grants No. NSF IRI-96-19339 and NSF ITR-086075. Any opinions, findings, and conclusions or recomendations expressed in this material are those ofauthors and do not necessarily reflect the view of the Ntional Science Foundation.
APPENDIX: THE ELLIPSOIDAL TORSO MODEL
This Appendix explains the algorithm used to computhe time delayD(u,f) for the torso reflection as a functioof the azimuthu and elevationf of the sound source. Thegeometry for the ellipsoidal torso model is shown in Fig. Awhich identifies the following anthropometric parameters
1120Algazi et al.: Low-frequency elevation localization
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a4—distance from the center of the head to the top oftorso;
a5—displacement of the head in front of the torso;a6—torso half-height;a7—torso half-width;a8—torso half-depth.
In contrast to the spherical-head model, we do nottempt to solve the wave equation for the ellipsoid, for whithere is no simple analytical solution. Instead, we assuthat the ellipsoid is a rigid surface and a specular reflectorsound with suitably short wavelengths. This approach istified by the data, which exhibit a strong isolated reflectidue to the torso. Thus, a ray-tracing algorithm is usedcompute the time delayD(u,f) of the torso reflection.
The algorithm can be outlined as follows. Given a sousource at the points, the problem is to compute the pointpon the surface of the ellipsoid where the reflection will occand usep to calculate the difference in path lengths to tearse for the direct and the reflected sound waves. The cculation makes use of the vectorv5 s2 p from the reflectionpoint p to the sources. Once p is determined, the torsoreflection delay is obtained by first computing the differenbetween the path length for the direct and the reflected sofrom the source to the center of the head,d5i pi1i vi2i si , wherei pi is the length ofp. A correction based onWoodworth’s formula~Blauert, 1997! is then applied to ac-count for the additional distance of each component toear positione. The total delay is obtained asD(u,f)5(d1dr1ds)/c wherec is the speed of sound in air~340 m/s!anddr andds are the corrections for the diffraction arounthe head for the reflection and the source, respectively.example, the correction for the direct sound can be compuas ds5a1 sin(cs2p/2), wherecs is the angle between thsource vectors and the ear vectore. This formula givespositive values for angles of incidence greater than 90°,negative otherwise. The same formula is applied to corthe path length of the reflection.
The main problem is to compute the reflection pointpon the surface of the ellipsoid for a given source locations.
FIG. A1. Anthropometry for the torso model and related geometry.
1121 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
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Our approach is to work backwards, stepping systematicacross the surface of the ellipsoid at pointspi to find thesource directionsi that would cause a reflection at that poinFor a given p5 pi we apply Snell’s law to determine thdirectionu of the incident sound vectorv5au. To obtainuwe first compute the normal to the ellipsoid surface¹g atpoint p, where the equation for the ellipsoid is written as
g~x1 ,x2 ,x3!5S x1
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u5 p22pT¹g
i¹gi2 ¹g.
Once the direction vectoru is found, the source location cabe obtained by noting thats5 p1au. To computea we usethe constraint that the range of the source is known. Incase we assume that all source locations are on the surfaa sphere with radiusr 51 m ~which is the case in our measurements!. Thus, the constraint can be written asi p1 vi5i p1aui51, and the value ofa is computed as the positive root of
a52 pTu6A~ pTu!22i ui2~ i pi221!
i ui2 .
With values of vectorsp, v, ands, we can now compute thetorso delayD(u,f).
This procedure yields the values of the torso delaysource locations which do not lie on a regular spatial gand that usually do not coincide with our measurempoints. We solve this final problem by applying an interplation procedure based on a spherical harmonic expansi
1Only static localization cues are considered in this paper. Low-frequedynamic cues are also important. Perrett and Noble~1997! verifiedWallach’s hypothesis that horizontal head rotation can be used to resfront/back confusion as well as to determine the magnitude of the elevaangle. Moreover, they showed that this dynamic cue requires the presof acoustic energy below 2 kHz. They observed in passing that, althohorizontal head rotation cannot resolve an up/down ambiguity in elevattheir subjects were nonetheless able to tell if the source was above or bthe horizontal plane; they speculated that spectral cues created by the sders and torso were responsible.
2Note that these angles are different from the angles in a conventivertical–polar coordinate system. In particular, a surface of consinteraural–polar azimuth is a horizontal cone, while a surface of consvertical–polar azimuth is a vertical plane. The advantages of interaupolar coordinates were pointed out by Searleet al. ~1976!, and they havealso been used by Morimoto and Aokata~1984! and by Middlebrooks~1999!. However, these authors have named the angles differenMorimoto and Aokata call 90°-u the ‘‘lateral angle’’ andf the ‘‘risingangle,’’ while Middlebrooks callsu the ‘‘lateral angle’’ andf the ‘‘polarangle.’’ At the risk of some confusion, we have chosen to retain convtional terminology.
3As expected, front/back confusion was greater for low-pass stimuli than
1121Algazi et al.: Low-frequency elevation localization
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full-bandwidth stimuli~see Carlile and Pralong, 1994!. For some subjectsthe location of the low-pass-filtered sound always appeared to be inback.
4Some caution must be exercised in computing statistics for directionalbecause of the 360° ambiguity~Mardia, 1972! and the possibility of up/down as well as front/back confusion~Wenzel et al., 1993!. However,because we separated front and back stimuli, and because the reportewere confined to a semicircle, we computed the bias and rms error uthe target and reported angles as if they were rectangular coordinateparticular, the bias was computed as the average signed error, and therror as the square root of the average of the squared error. The propresence of up/down confusion makes the resulting values a bit moresimistic than necessary, but does not change the conclusion that the anerrors are large.
5Mathematically, the HRTF is defined as the ratio of two transfer functioone from the source to the ear with the subject present, and the otherthe source to the location of the center of the head under free-field cotions. For an infinitely distant source, these transfer functions become itical at very low frequencies, and the HRTF approaches 1~unity DC gain!.However, at close ranges, the inverse square law results in a highegain for the ipsilateral ear and a lower DC gain for the contralateral~Duda and Martens, 1998!. In our HAT model, these small differences aignored.
6Avendano, Algazi, and Duda~1999! describe a more elaborate torso modin which the reflection coefficient varied with azimuth, elevation, and fquency. The torso model used in this paper seems to produce similaevation perceptions, and was chosen for its simplicity.
Algazi, V. R., Avendano, C., and Thompson, D.~1999!. ‘‘Dependence ofsubject and measurement position in binaural signal acquisition,’’ J. AuEng. Soc.47~11!, 937–947.
Asano, F., Suzuki, Y., and Sone, T.~1990!. ‘‘Role of spectral cues in me-dian plane localization,’’ J. Acoust. Soc. Am.88, 159–168.
Avendano, C., Algazi, V. R., and Duda, R. O.~1999!. ‘‘A head-and-torsomodel for low-frequency binaural elevation effects,’’ in Proceedings of1999 IEEE Workshop on Applications of Signal Processing to Audio aAcoustics, New Paltz, NY, pp. 179–182.
Avendano, C., Duda, R. O., and Algazi, V. R.~1999!. ‘‘Modeling the con-tralateral HRTF,’’ inProceedings of the AES 16th Conference on SpaSound Reproduction~Rovaniemi, Finland!, pp. 313–318.
Blauert, J. P.~1997!. Spatial Hearing~revised edition! ~MIT Press, Cam-bridge, MA!.
Brown, C. P., and Duda, R. O.~1998!. ‘‘A structural model for binauralsound synthesis,’’ IEEE Trans. Speech Audio Process.6~5!, 476–488.
Buell, T. N., and Hafter, E. R.~1988!. ‘‘Discrimination of interaural differ-ences of time in the envelopes of high-frequency signals: Integratimes,’’ J. Acoust. Soc. Am.84, 2063–2066.
Butler, R. A. ~1986!. ‘‘The bandwidth effect on monaural and binaurlocalization,’’ Hear. Res.21, 67–73.
Carlile, S., and Pralong, D.~1994!. ‘‘The location-dependent nature of peceptually salient features of the human head-related transfer functionsAcoust. Soc. Am.95, 3445–3459.
Carlile, S., editor~1996!. Virtual Auditory Space: Generation and Applications ~R. G. Landes, Austin, TX!.
Cramer, H.~1946!. Mathematical Methods of Statistics~Princeton Univer-sity Press, Princeton, NJ!, pp. 397–400.
Duda, R. O., and Martens, W. L.~1998!. ‘‘Range dependence of the response of a spherical head model,’’ J. Acoust. Soc. Am.104, 3048–3058.
Duda, R. O., Avendano, C., and Algazi, V. R.~1999!. ‘‘An adaptable ellip-
1122 J. Acoust. Soc. Am., Vol. 109, No. 3, March 2001
he
ta
datangIn
rmsblees-ular
,mi-n-
Cr
-el-
io
d
l
n
J.
soidal head model for the interaural time difference,’’ in Proceedingsthe IEEE International Conference on Acoustics Speech and Signalcessing ICASSP’99, II-965–968.
Gardner, M. B., and Gardner, R. S.~1973!. ‘‘Problem of localization in themedian plane: Effect of pinna cavity occlusion,’’ J. Acoust. Soc. Am.53,400–408.
Gardner, M. B.~1973!. ‘‘Some monaural and binaural facets of mediaplane localization,’’ J. Acoust. Soc. Am.54, 1489–1495.
Genuit, K., and Platte, H. J.~1981!. ‘‘Untersuchungen zur Realisation einerichtungsgetreuen U¨ bertragung mit elektroakustischen Mitteln~Investiga-tions on the implementation of directionally faithful transmission by eletroacoustical means!,’’ Fortschritte der Akustik,FASE/DAGA ’81, Berlin~VDE-Verlag, Berlin!, pp. 629–632.
Genuit, K. ~1984!. ‘‘Ein Modell zur Beschreibung von Außenohru¨bertra-gungseigenschaften~A model for the description of the outer-ear transffunction!,’’ Doctoral dissertation, Dept. of Elec. Engr., RheinischWestfalischen Technichen Hochschule Aachen, Aachen, Germany.
Hanson, W. W.~1944!. ‘‘The baffle effect of the human body on the response of a hearing aid,’’ J. Acoust. Soc. Am.16, 60–62.
Kuhn, G. F.~1977!. ‘‘Model for the interaural time differences in the azmuthal plane,’’ J. Acoust. Soc. Am.62, 157–167.
Kuhn, G. F., and Guernsey, R. M.~1983!. ‘‘Sound pressure distributionabout the human head and torso,’’ J. Acoust. Soc. Am.73, 95–105.
Kuhn, G. F. ~1987!. ‘‘Physical acoustics and measurements pertainingdirectional hearing,’’ inDirectional Hearing, edited by W. A. Yost and G.Gourevitch~Springer, New York!, pp. 3–25.
Mardia, K. V. ~1972!. Statistics of Directional Data~Academic, London!.Middlebrooks, J. C., and Green, D. M.~1991!. ‘‘Sound localization by hu-
man listeners,’’ Annu. Rev. Psychol.42, 135–159.Middlebrooks, J. C.~1999!. ‘‘Virtual localization improved by scaling non-
individualized external-ear transfer functions in frequency,’’ J. AcouSoc. Am.106, 1493–1510.
Møller, H. ~1992!. ‘‘Fundamentals of binaural technology,’’ Appl. Acous36~5!, 171–218.
Morimoto, M., and Aokata, H.~1984!. ‘‘Localization cues of sound sourcein the upper hemisphere,’’ J. Acoust. Soc. Jpn.~E! 5~3!, 165–173.
Perrett, S., and Noble, W.~1997!. ‘‘The effect of head rotations on verticaplane sound localization,’’ J. Acoust. Soc. Am.102, 2325–2332.
Roffler, S. K., and Butler, R. A.~1967!. ‘‘Factors that influence the local-ization of sound in the vertical plane,’’ J. Acoust. Soc. Am.43, 1255–1259.
Searle, C. L., Braida, L. D., Davis, M. F., and Colburn, H. S.~1976!.‘‘Model for auditory localization,’’ J. Acoust. Soc. Am.60, 1164–1175.
Shaw, E. A. G.~1997!. ‘‘Acoustical features of the human external ear,’’ iBinaural and Spatial Hearing in Real and Virtual Environments, edited byR. H. Gilkey and T. R. Anderson~Erlbaum, Mahwah, NJ!, pp. 25–47.
Theile, G., and Spikofski, G.~1982!. ‘‘Die Bedeutung des menschlicheRumpfes fu¨r die Lokalisation in der Medianbene~The importance of thehuman torso for localization in the median plane!,’’ Fortschritte der Akus-tik, FASE/DAGA ’82, Gottingen ~DPG-Verlag, Bad Honnef!, pp. 1181–1186.
Wenzel, E. M., Arruda, M., Kistler, D. J., and Wightman, F. L.~1993!.‘‘Localization using nonindividualized head-related transfer functions,’’Acoust. Soc. Am.94, 111–123.
Wightman, F. L., and Kistler, D. L.~1997!. ‘‘Factors effecting the relativesalience of sound localization cues,’’ inBinaural and Spatial Hearing inReal and Virtual Environments, edited by R. H. Gilkey and T. R. Anderson ~Erlbaum, Mahwah, NJ!, pp. 1–23.
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