Download Individual differences in external-ear transfer

Individual differences in external-ear transfer functions of cats
Li Xua) and John C. Middlebrooksb)
Kresge Hearing Research Institute, University of Michigan, 1301 East Ann Street, Ann Arbor,
Michigan 48109-0506
共Received 6 July 1999; accepted for publication 7 December 1999兲
Knowledge of the direction-dependent filter characteristics of the external ears is useful for the study
of spatial hearing in experimental animals. The present study examined individual differences in the
directional components of external-ear transfer functions 共directional transfer functions, DTFs兲
among 24 anesthetized cats. Ears were fixed in a frontal position. Inter-cat differences in DTFs were
quantified across a mid-frequency range from 8 to 16 kHz and across 30 locations in the horizontal
plane and vertical midline. Across cats, DTFs showed similar direction dependence, but tended to
differ in regard to the center frequencies of spectral features, such as spectral peaks and notches.
Certain mid-frequency notches, for instance, varied in frequency across cats by nearly a factor of 2.
Scaling of DTFs in frequency could reduce the overall differences between pairs of cats. Scale
factors that minimized inter-cat differences ranged as high as 1.57 and correlated moderately with
cats’ body weights. Nevertheless, appreciable individual differences remained after frequency
scaling. Inter-cat differences in DTFs were substantially larger than differences that resulted from
variability in positioning the ears. The results suggest some guidelines regarding the conditions
under which it is acceptable to apply DTF measurements from one cat to another. © 2000
Acoustical Society of America. 关S0001-4966共00兲02903-9兴
PACS numbers: 43.64.Ha, 43.66.Pn, 43.66.Qp 关BLM兴
INTRODUCTION
As a sound passes from a free-field source to the ear
canal, its spectrum is transformed by interaction with the
head and external ear. The transfer function is commonly
known as the head-related transfer function 共HRTF兲 共Butler,
1987; Morimoto and Ando, 1980; Wightman and Kistler,
1989a兲. The HRTF varies with the angle of incidence of
sound, so the spectrum of the sound in the ear canal carries
directional information.
Domestic cats are widely used as experimental animals
for studies of spatial hearing, both for cortical physiology
共Brugge et al., 1994, 1996, 1998; Imig et al., 1990; Middlebrooks and Pettigrew, 1981; Middlebrooks et al., 1998; Rajan et al., 1990; Xu et al., 1998, 1999兲 and for psychophysics
共Casseday and Neff, 1973; Jenkins and Masterton, 1982;
Huang and May, 1996; May and Huang, 1996; Populin and
Yin, 1998兲. Knowledge of cats’ HRTFs can guide physiological study of specific spatial cues 共e.g., Rose et al., 1966兲
and can inspire models of spatial sensitivity 共e.g., Middlebrooks, 1987; Rice et al., 1992兲. In several recent studies, cat
HRTFs have been used for synthesis of a virtual auditory
space 共Brugge et al., 1994, 1996, 1998; Chan et al., 1993;
Delgutte et al., 1999; Nelken et al., 1997; Reale et al.,
1996兲.
Human HRTFs show prominent differences among listeners 共Mehrgardt and Mellert, 1977; Middlebrooks, 1999a;
Shaw, 1966; Wightman and Kistler, 1989a兲. The functional
significance of such individual differences is demonstrated
by studies of virtual sound localization. When human subjects listen through HRTFs recorded from other subjects,
a兲
Electronic mail: [email protected]
Electronic mail: [email protected]
b兲
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they show substantial errors in localization 共Middlebrooks,
1999b; Wenzel et al., 1993兲. This raises concern about the
validity of generalizing HRTFs measured from any particular
cat to a variety of other cats.
The present study characterized the individual differences in cat HRTFs across a sample of 24 cats. Particular
attention was paid to the directional components of HRTFs,
which are known as directional transfer functions 共DTFs;
Middlebrooks and Green, 1990兲. The results showed that the
amount of individual differences in cat DTFs is comparable
to, if not larger than, that of inter-subject differences in human DTFs. The individual differences could be reduced by
frequency scaling, and the scale factors were related to the
body weights of the animals. That indicates that there existed
a relationship between the physical sizes of the animals and
the frequencies of the prominent spectral features in the
external-ear transfer functions.
I. METHOD
A. Animal preparation
Twenty-four purpose-bred adult cats 共11 females and 13
males兲 were used in this study. Three of them were supplied
by Sinclair Research Center, MO, and the rest were supplied
by Harlan Industrials, Inc., IN. Weights ranged from 2.4 to
6.1 kg. For the 21 cats obtained from Harlan Industrials, Inc.,
three shared a father, six pairs shared fathers, and the remaining six cats were not related directly. Measurements of the
head-related transfer function were preceded by single-unit
recording in the right auditory cortex 共Furukawa et al., 2000;
Middlebrooks et al., 1998; Xu et al., 1998, 1999兲. Each cat
was anesthetized for surgery with isoflurane, then was transferred to ␣-chloralose for single-unit recording followed by
acoustic measurement. A stainless-steel fixture was attached
0001-4966/2000/107(3)/1451/9/$17.00
© 2000 Acoustical Society of America
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to the frontal bones with screws and dental cement. A midline scalp incision was made, the temporalis muscle was retracted on the right side, and a recording chamber was positioned over the right auditory cortex. Portions of scalp and
temporalis muscle were removed to accommodate the recording chamber, and the scalp incision was closed to minimize distortion of the ears. The presence of the skull opening
and recording chamber almost certainly influenced details of
external-ear transfer functions. Nevertheless, essentially the
same opening and chamber were present in all animals, so
there should have been minimal influence on the inter-cat
differences. Also, inter-cat differences that varied with body
weight and gender 共Sec. II C兲 would not have been affected
by the recording chamber.
The animal was transferred to the center of a soundattenuating chamber with the cat’s interaural axis centered in
the sound chamber. The body of the cat was supported in a
canvas sling, and its head was supported from behind by a
bar attached to the skull fixture. Under anesthesia, the relaxed pinna position tended to be lateral and downward in
comparison to the pinna position of an alert cat. Care was
taken to restore the normal-appearing position of the pinnae.
Both ears were supported by a pair of curved wire supports
so that the pinnae resumed a symmetrical forward position
that resembled the pinna position adopted by a cat attending
to a frontal sound.
B. Experiment setup and acoustic system
Experiments were conducted in a sound-attenuating
chamber that was lined with acoustical foam 共Illbruck兲 to
suppress reflections of sounds at frequencies ⬎500 Hz.
Sound stimuli were presented from loudspeakers 共Pioneer
model TS-879 two-way coaxials兲 mounted on two circular
hoops, 1.2 m in radius, one in the horizontal plane and one in
the vertical midline plane. On the horizontal hoop, 18 loudspeakers spaced by 20 degrees covered 360 degrees. On the
vertical hoop, 14 loudspeakers spaced by 20 degrees ranged
from 60 degrees below the frontal horizon, up and over the
top, to 20 degrees below the rear horizon. Vertical locations
were labeled continuously in 20-degree steps from ⫺60 to
⫹200 degrees. Since the vertical and horizontal hoops shared
speakers at 0 and 180 degrees, the total number of locations
was 30. Experiments were controlled with an Intel-based
personal computer. Acoustic stimuli were synthesized digitally, using equipment from Tucker-Davis Technologies. The
sampling rate for audio output was 100 kHz, with 16-bit
resolution.
C. Measurements of transfer functions
A 12-in. probe microphone 共Larson-Davis model 2540兲
was used for the acoustic measurements. The stainless-steel
probe tube that connected to the 21-in. microphone had an
inner diameter of 3.2 mm and an outer diameter of 4.0 mm.
The probe tube was inserted approximately 2 mm into the
ear canal through a vertical incision at the posterior base of
the pinna. The probe stimuli delivered from each of the 30
loudspeakers were pairs of Golay codes 共Foster, 1986; Golay, 1961; Zhou et al., 1992兲 that were 81.92 ms in duration.
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Recordings from the microphone were amplified, then were
digitized at a rate of 100 kHz, yielding a spectral resolution
of 12.2 Hz from 0 to 50 kHz.
Before each experiment, the frequency responses of the
loudspeakers were measured using the Golay stimuli and the
1
2-in. microphone positioned in the center of the sound chamber in the absence of the animal. The influence of the frequency responses of the loudspeakers was eliminated by dividing them from the ear-canal spectra. The resulting transfer
functions were head-related transfer functions 共HRTFs兲. A
similar procedure has been used in previous studies of cats’
external-ear transfer functions 共Musicant et al., 1990; Rice
et al., 1992兲. In the present study, our analysis was based on
the direction-specific components of the HRTFs, referred to
as directional transfer functions 共DTFs兲. The DTF for each
sound source location was obtained by dividing the HRTF
for each location by the root-mean-squared HRTF averaged
across all 30 locations 共Middlebrooks and Green, 1990;
Middlebrooks, 1999a兲. In control experiments performed in
three cats, recordings from the probe microphone in the ear
canal were made simultaneously with recordings from a
Knowles miniature microphone 共model 1934兲 that was
placed at a deeper position in the ear canal. Consistent with
such dual-microphone recordings in humans 共Middlebrooks
et al., 1989; Middlebrooks and Green, 1990兲, HRTFs measured at the two sites were quite different, whereas DTFs
computed for the two recording sites were nearly identical.
D. Data analysis
We convolved each DTF in the linear frequency scale
with a bank of bandpass filters to obtain samples spaced
equally on a logarithmic scale 共Middlebrooks, 1999a兲. The
purposes of this procedure were 共1兲 to roughly equalize the
number of samples per perceptual critical band and 共2兲 to
facilitate scaling of DTFs in frequency. The filter bank consisted of 118 triangular filters. The 3-dB bandwidth of the
filters was 0.0571 oct, filter slopes were 105 dB per oct, and
the center frequencies were spaced in equal intervals of
0.0286 oct from 3 to 30 kHz. The interval of 0.0286 oct was
chosen to give intervals of 2% in frequency. As a consequence of bandpass filtering, the very sharp peaks or notches
in the DTFs were blunted, which resembled the perceptual
consequence of filtering by the cochlea 共Glasberg and
Moore, 1990兲.
Individual differences between DTFs were quantified by
a metric that will be referred to as the inter-subject spectral
difference. That metric was computed across the 36 filterbank components from 8 to 16 kHz. That mid-frequency
band was chosen because it contains prominent directiondependent spectral features 共Musicant et al., 1990; Neti
et al., 1992; Rice et al., 1992兲 and because our preliminary
tests indicated that it captured the most systematic differences in the DTFs among cats. Behavioral studies have demonstrated that cats can accurately localize noise that is limited to mid-frequencies 共Huang and May, 1996兲, and we
have shown that mid frequency sounds have the strongest
influence on cat neuronal signaling of sound locations 共Xu
et al., 1999兲. The spectral difference was computed as follows. For each pair of cats, the dB amplitudes of the 36
L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
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components of DTFs were subtracted, component by component, to form a difference spectrum for each source direction.
Then, the variance across the 36 components of the difference spectrum was computed. Finally, the variance was averaged across the 30 tested directions for each pair of cats.
We quantified systematic frequency differences between
the DTFs of pairs of cats by using a frequency-scaling procedure 共Middlebrooks, 1999a兲. That procedure served as a
tool to quantify frequency disparities between DTFs and to
evaluate the relationship between the physical sizes of the
animals and the spectral features of their DTFs. For each pair
of cats, the set of 30 DTFs from one cat was scaled upward
by 2%, alternating with downward 2% scaling of the other
cat’s set of DTFs. Amplitudes of the DTFs were not adjusted. After each scaling, the spectral difference was computed between 8 and 16 kHz. This procedure was repeated
until the scale factor was found that produced the minimum
spectral difference between any given pair of cats. That was
termed the optimal scale factor. The percent reduction in the
inter-subject spectral differences as a result of optimal frequency scaling was also computed.
II. RESULTS
A. General properties of cat DTFs
For the 24 cats used in the present study, DTFs were
measured from all 24 left ears and 22 of the right ears. For
the 22 cats in which both ears were measured, the spectral
differences in DTFs between left and right ears averaged
11.3 dB2. The right ear was somewhat more distorted than
the left by the right-sided skull opening and recording chamber 共see Sec. I兲. That asymmetry presumably contributed to
the left/right spectral differences. Our subsequent data analysis was based on recordings from the 24 left ears. Figure 1共a兲
shows 14 DTFs of one cat 共cat 19兲 before they were processed with the bandpass filter bank. Filtering with the bandpass filter bank resulted in significant smoothing of the spectra and yet preserved the major spectral features 关thick line in
Fig. 1共b兲兴. One of the prominent features in the cat DTFs was
the mid-frequency notches, as has been emphasized in previous studies of cat HRTFs 共Musicant et al., 1990; Rice
et al., 1992兲. Generally, the notch center frequencies tended
to increase systematically as source elevation increased. The
trend often was violated, however, for DTFs at lowest elevations. Also, the DTFs at the highest locations 共⫹80 and
⫹100 degrees兲 in about half of the cats failed to show any
obvious spectral features such as notches or peaks.
Changes in the position of a cat’s ears can produce systematic changes in HRTFs 共Middlebrooks and Knudsen,
1987; Young et al., 1996兲. When we compared DTFs among
different cats, we attempted to position the ears in a
‘‘normal-appearing’’ forward position that was consistent
across all subjects. In six cats, we tested the reliability with
which a consistent ear position could be attained. In each of
the six cats, the ears and the probe microphone were positioned twice, once by each of two investigators, and two sets
of DTF measurements were made. Figure 1共b兲 共thin and
thick lines兲 shows examples of DTFs measured by two different experimenters. The two measurements matched each
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FIG. 1. Directional transfer functions 共DTFs兲 from the left ear of one cat
共cat 19兲 for the 14 elevation locations in the vertical midline plane. 共a兲
Unfiltered DTFs. 共b兲 Two sets of measurements processed by a bank of
bandpass filters 共see Sec. I for details兲. Thick lines are from the same set of
measurements as shown in 共a兲. Thin lines are after a second experimenter
repositioned the probe tube microphone and the pinnae.
other fairly well at all locations and across frequencies. The
spectral difference between the two measurements computed
across all 30 locations was 3.25 dB2. The spectral differences
of the two replicated measurements in the other five cats
were 0.56, 2.83, 3.04, 5.80, and 7.10 dB2. These spectral
differences are considerably smaller than the spectral differences between pairs of cats 共detailed later in Fig. 4兲. In another subset of three cats, we deliberately changed the pinna
to extreme forward and backward positions beyond those
that could normally be obtained in a behaving cat. This was
done by pulling a thin string attached to the tip of the pinna
and by pushing or retracting the wire support of the pinna.
We found that the spectral differences between those extreme pinna positions averaged 14.19 dB2 (n⫽9, i.e., three
cats times three possible combinations of pinna positions兲,
which was smaller than the mean spectral differences between pairs of cats 共detailed later in Fig. 4兲. Young et al.
共1996兲 tested the influence of more moderate change of ear
position on spectral notches of cat HRTFs. Data illustrated in
their figure 6 showed that inter-cat differences were substantially larger than differences resulting from changes in ear
position. Therefore, we were confident that the individual
differences in cat DTFs were not solely due to the differences in ear position.
L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
1453
FIG. 2. The DTFs from five cats for
selected locations. The upper left
panel represents DTFs for a location in
the horizontal plane 40 degrees ipsilateral to the ear that contained the microphone, and the other five panels
represent DTFs for ⫺40- to 120degree elevations in 40-degree steps in
the vertical midline plane as labeled
above the DTFs. Arrows indicate the
spectral notches defined in the text. In
all panels, DTFs from the five cats are
ordered based on the spectral notch
frequencies in the DTFs for ⫹40degree elevation. The same order is
given by a rank of body weights of the
cats; that is, DTFs for the lightest cat
are placed on the top and those for the
heaviest cat at the bottom. Cats 8, 12,
15, 1, and 11 had body weights of 2.5,
2.9, 3.6, 4.0, and 6.1 kg, respectively.
B. Individual differences
Despite some similarity in the general features of the
DTFs from different cats, we observed substantial individual
differences in the DTFs. Figure 2 plots DTFs from five cats
at six locations. The upper left panel represents DTFs at
ipsilateral 40 degrees on the horizontal plane. The rest of the
panels represent DTFs from five midline elevation locations
at ⫺40 to ⫹120 degrees in 40-degree steps. Arrows in those
panels indicate mid-frequency notches in the DTFs. A spectral notch was defined here as a spectral minimum in the
frequency range between 5 and 20 kHz, bounded on either
side by slopes that were ⭓5 dB high. The DTFs plotted in
each panel are ordered based on the spectral notch frequen-
cies defined at ⫹40 degrees elevation, and the order of cats is
the same across all panels. The inter-subject differences in
the DTFs included differences in the detailed shape of each
DTF and in the frequencies of the prominent spectral features such as spectral notches and peaks.
The prominent mid-frequency spectral notches highlight
the individual differences among cat DTFs. Figure 3 summarizes the inter-subject differences in the spectral notch center
frequencies in the DTFs of the 14 elevation locations. Figure
3共a兲 plots the center frequencies of notches for the five cats
whose DTFs are shown in Fig. 2. Each line represents data
from one of the cats. The lines are broken at locations at
which no spectral notches could be identified. In frontal lo-
FIG. 3. Individual differences in the
spectral notch center frequencies of
the DTFs. 共a兲 Each line plots for one
of the five cats shown in Fig. 2 the
spectral notch frequencies in the DTFs
for the 14 elevation locations. 共b兲 The
box plot summarizes the distribution
of spectral notch frequencies in the 14
elevation DTFs of all 24 cats. At each
elevation, the mean is represented by
the small square and the minimum and
maximum are represented by the asterisks. The three vertical bars represent
the 25, 50 and 75 percentiles and the
ends of the two horizontal bars represent the 5 and 95 percentiles of the
distribution. The number to the right
indicates the number of cats at each
elevation at which mid-frequency
notches could be identified.
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L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
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FIG. 4. Distributions of inter-subject spectral differences in DTFs before 共a兲
and after 共b兲 frequency scaling. Values were computed for all 276 possible
pairwise combination of 24 cats.
cations, notch frequencies increased systematically as source
elevation increased from ⫺20 to ⫹80 degrees. In rear locations, notch frequencies also increased as sources moved up
from the rear horizon. Individual differences in the notch
frequencies of cat DTFs were apparent. The lines were
roughly parallel to each other, at least for frontal locations,
suggesting that the set of all DTFs from one cat could be
aligned with that of another cat by scaling in frequency.
The distributions of the individual differences in spectral
notch frequency among the sample of 24 cats are illustrated
in Fig. 3共b兲 in a box-plot format. In this format, the mean
notch frequency at each location is represented by the small
square and the minimum and maximum values are represented by the asterisks. The three vertical lines represent 25,
50, and 75 percentiles and the ends of the two horizontal bars
represent 5 and 95 percentiles of the distribution, respectively. The number of cats in which mid-frequency notches
could be identified varied from elevation to elevation. Those
numbers are given in a column on the right side of Fig. 3共b兲.
There was a clear trend that the spectral notch center frequencies varied systematically with the frontal midline elevation. Nevertheless, the inter-subject differences in the
spectral notch frequencies could be as large as 1 oct for most
locations in elevation. The variation was especially large in
the rear locations. The smallest range of notch frequencies
was found at 0 degrees elevation at which they varied over
only 0.60 oct in our sample of 24 cats. The extent of the
individual differences in the spectral notch frequencies can
also be appreciated from another perspective. If one makes a
vertical line in Fig. 3共b兲 anywhere between 10 and 12 kHz, it
passes within the distribution of notch frequencies at all el1455
J. Acoust. Soc. Am., Vol. 107, No. 3, March 2000
FIG. 5. Examples of frequency scaling between a pair of cats 共cat 11 and cat
21兲. 共a兲 The DTFs from cat 11 共thin lines兲 and cat 21 共thick lines兲 for the
eight frontal elevation locations before frequency scaling. 共b兲 At optimal
frequency scaling, DTFs from cat 11 共thin lines兲 were scaled upward by
1.219 and those from cat 21 共thick lines兲 were scaled downward by 1.195, a
combined relative scaling of 1.457. The vertical grid lines indicate the frequency band 共8–16 kHz兲 over which quantitative comparisons were made.
evations. That means that a notch at, say, 11 kHz could signal nearly any location among one or more of the cats in our
sample.
We computed the spectral differences in the DTFs averaged across all 30 locations for each pair of cats. These spectral differences were computed across 36 frequency components from 8 to 16 kHz 共see Sec. I for details兲. The
distribution of the spectral differences across all of the 276
pairwise combination of cats is shown in Fig. 4共a兲. The mean
of the distribution was 17.02 dB2 and the spectral differences
of 9.5% of pairs were ⭓25 dB2.
C. Frequency scaling
The notch data in Fig. 3共a兲 showed that inter-cat differences in notch frequencies tended to be fairly constant across
most locations. That suggests that inter-cat alignment of
spectral features could be improved, and spectral differences
decreased, by scaling the sets of DTFs for each pair of cats
by a single scale factor. That procedure was followed as
described in Sec. I. An example is shown for one pair of cats
in Fig. 5. Panels 共a兲 and 共b兲 show the eight frontal-midline
DTFs of the two cats 共cat 11 and cat 21兲 before and after
frequency scaling. At optimal scaling, the DTFs from cat 11
were scaled upward by 2% ten times and the DTFs from cat
21 were scaled downward nine times, resulting in a total
relative scale factor of 1.457 (1.0210/1.02⫺9 ⫽1.457). Note
that the prominent spectral features 共e.g., notches兲 in the two
sets of DTFs matched well after frequency scaling. The spectral difference of this pair of cats was reduced by 51.3% from
L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
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FIG. 6. Spectral difference as a function of frequency scale factor for the
pair of cats represented in Fig. 5 共cat 11 versus cat 21兲. The optimal scale
factor is indicated by the filled symbol.
34.5 dB2 before scaling to 16.5 dB2 after. Figure 6 shows the
spectral differences for this pair of cats as a function of relative scale factor.
The distribution of spectral differences for the 276 pairs
of cats after scaling is shown in Fig. 4共b兲. The mean was
14.01 dB2. Only one pair showed a spectral difference ⭓25
dB after scaling. Figure 7共a兲 and 共b兲 shows the distributions
of the optimal frequency scale factor and the percent reduction of spectral differences by frequency scaling. For this
illustration, all pairs were ordered such that the optimal scale
factor was ⭓1. The optimal scale factors ranged from 1 to
1.57 with a median of 1.10. The percent reduction in the
inter-subject spectral differences accomplished by frequency
scaling had a median of 11.5%, ranging from 0% to 60.7%.
A substantial amount of spectral difference remained even
after frequency scaling due to nonsystematic differences in
the DTFs among cats that could not be removed by frequency scaling.
The spectral details of a DTF result from the physical
FIG. 7. Distributions of optimal scale factor 共a兲 and percent reduction of
spectral difference by frequency scaling 共b兲. Values were computed for all
276 possible pairwise combination of 24 cats.
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J. Acoust. Soc. Am., Vol. 107, No. 3, March 2000
FIG. 8. Relationship between cat body weight and mean frequency scale
factor. Eleven female and 13 male cats are represented by the circles and
squares, respectively. Solid and dashed lines are linear fits to the data from
female and male cats, respectively.
interaction of an incident sound wave with the head and
pinnae. For that reason, one would expect that the frequencies of spectral features depend on the sizes of the head and
pinnae as well as the shapes of the pinnae. We used the body
weight of each cat as a single number to represent its overall
size. The body weights correlated somewhat with the frequencies of spectral features in the DTFs. For example, for
the DTFs of the five cats shown in Fig. 2, which were sorted
by the notch frequency in the DTF for ⫹40 degrees elevation, the body weights fell in order such that the lightest cat
was represented by the top line and the heaviest cat by the
bottom line. In general, spectral features in the DTFs of a
smaller cat tended to fall in a higher frequency region than
those of a bigger cat 共Fig. 2兲. We summarized the frequencies of spectral features in each cat’s DTFs as the geometric
mean of the optimal scale factor between that cat and every
other cat. Figure 8 plots the mean optimal scale factor for
each cat as a function of its body weight. The circles represent female cats and squares represent male cats. The solid
and dashed lines are linear 共least-square兲 fits for each set of
data. Within each gender, mean scale factor correlated with
body weight. Correlation coefficients 共r兲 were 0.609 for females and 0.806 for males. The correlation was reduced to
0.547 when females and males were combined. The gender
differences were interesting. We measured the pinna sizes in
a few cats and found that female cats tended to have bigger
pinnae compared to male cats of similar body weights. Conversely, given males and females having heads and ears of
similar sizes, the males tended to be more muscular and,
thus, heavier. We speculate that the gender differences would
disappear if we could use the pinna or head size to correlate
with the scale factors. Unfortunately, we did not have ear and
head measurements from every cat. In a recent study of individual differences in human DTFs, we found no indication
L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
1456
of a gender effect that could not be accounted for by the
tendency of females to be smaller than males 共Middlebrooks,
1999a兲. The correlation between the body weights and the
optimal scale factor is further evidence that the inter-cat differences that we observed were not entirely due to different
ear positions among cats.
III. DISCUSSION
The general properties of the directional components of
HRTFs 共i.e., DTFs兲 that we studied were similar to previous
studies of cat HRTFs, but we noted considerable individual
differences in the HRTFs among cats. In the following, we
compare our results to previous studies of cat HRTFs and
discuss the implications of individual differences in HRTFs
for studies of spatial hearing.
A. Comparison with previous studies
Previous descriptions of cat external-ear transfer functions have emphasized characteristics of the direction dependence of the transfer functions that are consistent among
cats. Musicant and colleagues 共1990兲 measured the HRTFs
from six cats for sounds at numerous horizontal and vertical
locations. They observed prominent spectral notches in the
8–18 kHz frequency region. Individual differences were
considered small. Rice and colleagues 共1992兲 confirmed and
extended the observations of the spectral notches in the
HRTFs. They focused on a slightly larger frequency range
共5–18 kHz兲 and proposed a sound-localization scheme based
on the mid-frequency notch frequencies in the two ears.
Again, they emphasized the similarities rather than differences in the HRTFs among the five cats used in that study.
Our measurements of individual DTFs were largely consistent with previous studies in regard to the general location
dependence of spectral features. In general, we found that
spectral features in the mid-frequency region shifted to
higher frequency as sound source moved from lower elevation to higher elevation in the front midline 共Fig. 1兲. The
same was true for rear midline locations, but variability there
was much greater. We sampled lower elevations than in previous studies, i.e., ⫺60 degrees rather than ⫺30 degrees
共Musicant et al., 1990; Rice et al., 1992兲. At ⫺40- and ⫺60degree elevations, mid-frequency notches tended to be wide
and blunt 共Figs. 1 and 2兲. The center frequencies of those
notches tended to shift to higher frequency with decreasing
elevation, which was counter to the trend at elevations
⭓⫺20 degrees. In a behavioral study, May and Huang
共1996兲 tested cat’s head orientation to sounds presented as
low as ⫺45 degrees elevation and found that response errors
increased dramatically compared to those at more centric locations. They attributed these increased errors to the poorer
quality of spectral cues at lower elevations. We note that
most single neurons in the cat superior colliculus show spatial tuning centered above ⫺30 degrees 共Middlebrooks and
Knudsen, 1984兲. Also, coding of low elevations by neurons
in the cat’s auditory cortex tends to be relatively inaccurate
共Xu et al., 1998兲.
In the present study, optimal scale factors served as global measures of inter-cat differences in the frequencies of
spectral features. In the sample of 24 cats, optimal scale fac1457
J. Acoust. Soc. Am., Vol. 107, No. 3, March 2000
tors ranged as high as 1.57 with a median value of 1.10.
Individual spectral notches varied across a larger range, up to
a factor of 2 in some cases 共Fig. 3兲. Although previous studies have measured smaller samples of cats, one can see instances of variation in the frequencies of spectral features. In
the study by Wiener and colleagues 共1966兲, the center frequencies of mid-frequency notches in five cats ranged from
approximately 10 to 13 kHz for sound sources at 0 degrees
azimuth and 0 degrees elevation 共a factor of 1.3; measured
from fig. 6 in Wiener et al., 1966兲. However, in that study,
the authors focused on the low-frequency features of the
external-ear transfer functions and largely ignored the individual differences in frequencies higher than 10 kHz. In the
data illustrated by Musicant and colleagues 共1990兲, three cats
showed similar directional dependence of HRTFs, and it is
difficult to see any differences in frequencies of spectral features. Rice and colleagues 共1992; Fig. 11兲 showed HRTFs
from four cats that appeared very similar. A fifth animal
showed a mid-frequency notch that was displaced upward by
a factor of ⬃1.15, but the authors discussed several experimental factors that might have produced that difference. An
additional cat measured in the same laboratory 共Young et al.,
1996, Fig. 3兲 showed a HRTF for location at 0 degrees azimuth, 0 degrees elevation that was quite similar in shape to
the HRTFs shown in the 1992 report but was displaced upward in frequency by a factor of ⬃1.3. Considering the
smaller sample sizes of previous studies, the magnitude of
inter-cat variation in published data is roughly in line with
the present observations. We consider in the next section
whether that magnitude of variation is likely to be significant
for studies of spatial hearing.
The magnitudes of individual differences in cats are
roughly comparable to those observed in a similar study in
humans 共Middlebrooks, 1999a兲. Optimal scale factors for
DTFs from pairs of humans were somewhat smaller than our
results in cats: humans exhibited a median of 1.06 and maximum of 1.38 compared to median of 1.10 and maximum of
1.57 in cats. The reduction of spectral differences by frequency scaling was more efficient in humans than in cats:
median and maximum percent reductions were 15.5% and
⬃80%, respectively, in humans compared to 11.5% and
60.7% in cats. The lower percentage reduction in cats indicates that efforts to tailor DTFs from one subject for use with
another might be less satisfactory in cats than in humans
共Middlebrooks, 1999b兲. We speculate that inter-cat differences in ear position might contribute spectral differences
that remain after optimal frequency scaling.
B. Implications of individual differences for
physiological studies of spatial hearing
When human subjects listen through headphones to
sounds that have been filtered by HRTFs measured from
their own ears, they report a well localized ‘‘virtual target’’
that appears to originate from the location of the original
free-field source 共Wightman and Kistler, 1989b兲. Virtual localization technology has been applied recently to physiological studies in cats 共Brugge et al., 1994, 1996, 1998;
Chan et al., 1993; Delgutte et al., 1999; Nelken et al., 1997;
Reale et al., 1996兲 and other species 共Hartung and Sterbing,
L. Xu and J. C. Middlebrooks: Individual differences in cat DTFs
1457
1997; Keller et al., 1998兲. This approach offers several advantages, including the potential for independent manipulation of various acoustic parameters and the ability to deliver
spatial cues under conditions in which it would be impossible to achieve high-quality free-field conditions 共i.e., due to
interference from experimental apparatus or due to necessary
surgical distortion of the external ear兲.
When human subjects attempt to localize virtual sources
that have been synthesized using HRTFs measured from
other listeners’ ears 共‘‘nonindividualized’’ HRTFs兲 they
show an increase in localization error, particularly in the vertical and front/back dimensions 共Wenzel et al., 1993兲. Systematic trends in errors can be related to the optimal frequency scale factors between subjects’ own DTFs and the
DTFs from which virtual targets are synthesized 共Middlebrooks, 1999b兲. When small subjects localize targets that are
synthesized from larger subjects’ ears, the most common errors are front/back confusions. When large subjects localize
targets that are synthesized from smaller subjects’ ears, the
most common error is an upward bias in responses. This
increase in localization error resulting from use of nonindividualized DTFs raises concern about the use of nonindividualized DTFs in physiological experiments in cats, since
systematic frequency differences as small as the median
value in our sample of cats 共i.e., 1.10兲 produce conspicuous
localization errors in humans.
Based on the observations in the present study, we can
speculate on some of the likely consequences of using nonindividualized DTFs in cat physiological experiments. We
observed that the general shapes of DTFs and the general
spatial dependence of DTFs are quite similar across cats.
This indicates that basic studies of sensitivity to particular
spectral features and, perhaps, studies of the general characteristics of spatial receptive fields would not suffer from use
of nonindividualized DTFs. Indeed, Reale and colleagues
共1996兲 examined the receptive fields of cortical neurons in a
cat using stimuli synthesized with HRTFs from three other
cats. Receptive fields measured in the three conditions differed at near-threshold stimulus levels but were quite similar
at higher levels. We note, however, that the HRTFs used in
that study were themselves quite similar. In a study in the
guinea-pig inferior colliculus, Hartung and Sterbing 共1997兲
found that receptive fields of units changed substantially
when stimuli synthesized from another guinea pig’s HRTFs
were exchanged for those synthesized from an animal’s own
HRTFs.
Spectral features 共i.e., peaks and notches兲 at particular
frequencies corresponded to different locations in different
cats. Thus, one might expect to encounter errors in experiments in which spatial sensitivity of neurons would be compared to an independent spatial reference, such as when auditory and visual modalities are compared in the superior
colliculus 共e.g., Middlebrooks and Knudsen, 1984; Wallace
et al., 1998兲. Similarly, one might expect to find distortions
in any systematic progression of spatial tuning in such a
midbrain structure, particularly since 共at least in humans兲 use
of nonindividualized DTFs in psychophysical procedures can
result in a high rate of front/back confusions that are greater
than 90 degrees in magnitude.
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J. Acoust. Soc. Am., Vol. 107, No. 3, March 2000
We recently have presented results of a study that examined the locations that are signaled by cortical neurons when
presented with narrow bandpass stimuli 共Xu et al., 1999兲. By
using narrow-band sounds, that study emphasized fine details
of DTFs. Stimuli were presented in a free field, so cats were
exposed to stimuli filtered by their own DTFs. Physiological
results showed a close correspondence with the output of a
model of spectral recognition that was based on DTFs measured from each cat’s own ears. That correspondence would
have been largely obscured had we used nonindividualized
DTFs. Indeed, two sets of DTFs that were used as examples
in the report showed optimal scale factors, one cat to the
other, of only 1.025, yet inter-cat differences in details of the
DTFs produced markedly different results in the acoustical
model and in the physiology.
We regard our measurements of inter-cat differences in
DTFs as conservative. All the measurements in the present
study were from domestic short hair cats supplied from one
of two breeding colonies. Similarly, previous studies appear
to have used purpose-bred domestic short hair cats. We have
by no means explored the great variability that can be found
among other breeds of cats. A visit to any cat show reveals a
wide variety of shapes and sizes of heads and ears. The potential for error derived from a mismatch between cats and
DTFs is large. Nevertheless, the present results indicate that
under certain conditions DTFs are generally similar among
cats. We urge caution in interpreting results obtained with
nonindividualized DTFs, but affirm that such procedures are
acceptable for studies of spatial hearing when suitable care is
taken to match animals by breed, size, and gender.
ACKNOWLEDGMENTS
We acknowledge the expert technical assistance by
Zekiye Onsan. Shigeto Furukawa helped in DTF measurements. Shigeto Furukawa, Ewan Macpherson, Brian Mickey,
and David Moody made valuable comments on an early draft
of the manuscript. This research was supported by NIH
Grant Nos. RO1 DC00420 and T32 DC00011.
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