Median-plane sound localization as a function of the number of spectral channels using a channel vocoder.
ABSTRACT Using a vocoder, median-plane sound localization performance was measured in eight normal-hearing listeners as a function of the number of spectral channels. The channels were contiguous and logarithmically spaced in the range from 0.3 to 16 kHz. Acutely testing vocoded stimuli showed significantly worse localization compared to noises and 100 pulses click trains, both of which were tested after feedback training. However, localization for the vocoded stimuli was better than chance. A second experiment was performed using two different 12-channel spacings for the vocoded stimuli, now including feedback training. One spacing was from experiment 1. The second spacing (called the speech-localization spacing) assigned more channels to the frequency range associated with speech. There was no significant difference in localization between the two spacings. However, even with training, localizing 12-channel vocoded stimuli remained worse than localizing virtual wideband noises by 4.8 degrees in local root-mean-square error and 5.2% in quadrant error rate. Speech understanding for the speech-localization spacing was not significantly different from that for a typical spacing used by cochlear-implant users. These experiments suggest that current cochlear implants have a sufficient number of spectral channels for some vertical-plane sound localization capabilities, albeit worse than normal-hearing listeners, without loss of speech understanding.
Median-plane sound localization as a function of the number of
spectral channels using a channel vocoder
Matthew J. Goupell,a?Piotr Majdak, and Bernhard Laback
Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, A-1040 Vienna, Austria
?Received 25 June 2009; revised 4 December 2009; accepted 9 December 2009?
Using a vocoder, median-plane sound localization performance was measured in eight
normal-hearing listeners as a function of the number of spectral channels. The channels were
contiguous and logarithmically spaced in the range from 0.3 to 16 kHz. Acutely testing vocoded
stimuli showed significantly worse localization compared to noises and 100 pulse/s click trains,
both of which were tested after feedback training. However, localization for the vocoded stimuli was
better than chance. A second experiment was performed using two different 12-channel spacings for
the vocoded stimuli, now including feedback training. One spacing was from experiment 1. The
second spacing ?called the speech-localization spacing? assigned more channels to the frequency
range associated with speech. There was no significant difference in localization between the two
spacings. However, even with training, localizing 12-channel vocoded stimuli remained worse than
localizing virtual wideband noises by 4.8° in local root-mean-square error and 5.2% in quadrant
error rate. Speech understanding for the speech-localization spacing was not significantly different
from that for a typical spacing used by cochlear-implant users. These experiments suggest that
current cochlear implants have a sufficient number of spectral channels for some vertical-plane
sound localization capabilities, albeit worse than normal-hearing listeners, without loss of speech
understanding. © 2010 Acoustical Society of America. ?DOI: 10.1121/1.3283014?
PACS number?s?: 43.66.Qp, 43.66.Ts, 43.66.Ba ?JCM?
Vertical-plane sound localization ?i.e., the perception of
elevation and the discrimination of front from back sound
sources? depends primarily on directionally-dependent filter-
ing introduced by reflections from the pinnae, head, and
torso ?e.g., Middlebrooks, 1999a; Algazi et al., 2001?. For
free-field sources, these vertical-plane cues, together with the
binaural cues ?interaural time and level differences? for
horizontal-plane localization, are typically represented by
acoustical transfer functions called head-related transfer
functions ?HRTFs? ?Shaw, 1974; Møller et al., 1995?. Due to
the size of the pinnae, the relevant peaks and notches result-
ing from diffraction effects used in vertical-plane localization
occur for frequencies between about 4 and 16 kHz ?Blauert,
1969; Hebrank and Wright, 1974; Morimoto and Aokata,
1984; Middlebrooks, 1992; Blauert, 1997; Langendijk and
Despite the substantial amount of previous work on un-
derstanding the role of HRTFs in vertical-plane sound local-
ization, it is still unclear as to the type, scale, size, and po-
sition of spectral features most important to this task. What is
clear is that HRTFs are subject dependent ?Wightman and
Kistler, 1989; Wenzel et al., 1993; Middlebrooks, 1999a?.
One method to investigate the role of spectral features has
been to test localization abilities with spectrally-distorted
HRTFs. These spectral distortions have been performed in a
fairly uncontrolled way by occluding pinnae with some sub-
stance ?Gardner and Gardner, 1973; Musicant and Butler,
1984; Oldfield and Parker, 1984; Hofman et al., 1998?. In
more controlled experiments, signal processing methods
have been used to distort spectral localization cues. For ex-
ample, HRTF spectral distortions have been done by truncat-
ing HRTF impulse responses ?Zahorik et al., 1995; Senova et
Several studies have shown that relatively broad high-
frequency spectral features ?on the order of octaves? are the
relevant vertical-plane sound localization cues ?Asano et al.,
1990; Kistler and Wightman, 1992; Kulkarni and Colburn,
1998; Langendijk and Bronkhorst, 2002; Macpherson and
Middlebrooks, 2003; Kulkarni and Colburn, 2004; Qian and
Eddins, 2008?. For example, Kulkarni and Colburn ?1998?
systematically removed fine-scale HRTF spectral compo-
nents and showed that substantial spectral smoothing of the
HRTF spectrum could be performed before listeners’ eleva-
tion errors and number of front-back confusions increased.
Langendijk and Bronkhorst ?2002? performed another type
of spectral distortion by flattening 1/2-, 1-, and 2-octave
bands in the sound spectrum. They found that there was no
effect on sound localization when one 1/2-octave band was
flattened in the sound spectrum. However, for the broader
bands, a large effect was found. For the flattening of a
2-octave band, sound localization was impossible.
The experiments reported in this paper evaluated the po-
tential of cochlear-implant ?CI? users to perform median-
plane sound localization via another method of spectral al-
teration. We tested median-plane sound localization in
normal-hearing ?NH? listeners using a CI simulation and in-
vestigated the number of channels necessary to present ad-
equate spectral localization information. The advantages of
using CI simulations with NH listeners were that the popu-
a?Author to whom correspondence should be addressed. Electronic mail:
990 J. Acoust. Soc. Am. 127 ?2?, February 2010 © 2010 Acoustical Society of America0001-4966/2010/127?2?/990/12/$25.00
lation of NH listeners was much more readily available for
the long testing times needed for sound localization experi-
ments, and the interindividual variability is typically much
less for NH listeners. The latter reason is due to many factors
that affect CI users’ performance, including the placement of
the electrode array and the number of surviving spiral gan-
glion cells. CI simulations with NH listeners often provide
an upper bound on CI user’s performance in psychophysical
tasks ?e.g., Dorman and Loizou, 1997; Fu et al., 1998; Frie-
sen et al., 2001; Carlyon and Deeks, 2002; van Wieringen
et al., 2003; Carlyon et al., 2008; Goupell et al., 2008b?.
Sound localization in the horizontal plane in CI users
has been the topic of many recent papers. In particular, with
the ever increasing number of bilaterally-implanted CI users,
there has been much work on interaural time and/or level
difference sensitivity ?Lawson et al., 1998; Long et al., 2003;
Laback et al., 2004; Majdak et al., 2006; Laback et al., 2007;
van Hoesel, 2007; Grantham et al., 2008; Laback and Ma-
jdak, 2008; van Hoesel, 2008? and sound localization in the
horizontal plane ?van Hoesel and Tyler, 2003; Nopp et al.,
2004; Seeber et al., 2004; van Hoesel, 2004; Schoen et al.,
2005; Seeber and Fastl, 2008; van Hoesel et al., 2008?. How-
ever, much less attention has been paid to localization in the
vertical planes in CI users. Results from a recent study by
Majdak et al. ?2008? showed that CI listeners using current
clinical speech processors with behind-the-ear microphones
had a substantial deterioration of vertical-plane localization
performance compared to NH listeners.
The speech processors of multi-channel CIs typically
separate acoustic signals into several spectral channels. This
information is used to stimulate different tonotopic places
with electrical pulse trains. The amount of transmitted spec-
tral information is determined by the number of spectral
channels used to analyze the signal, the amount of tonotopic
overlap that occurs when the electrical pulse trains excite the
auditory nerve, and the sensitivity in the excited region.
Present day CIs typically have 12–24 electrodes. The band-
pass signals typically subdivide the spectrum logarithmically
between frequencies on the order of 0.1 and 10 kHz. For
example, a MED-EL Combi 40+ implant has 12 electrodes
that typically subdivide an incoming acoustic sound spec-
trum between 0.3 and 8.5 kHz. This means that there are
nine electrodes presenting acoustic information below 4 kHz
and three electrodes above 4 kHz. Since median-plane sound
localization relies on frequencies above 4 kHz, using only
three electrodes for this frequency region places CI listeners
at a noticeable disadvantage for this task compared to NH
listeners. Additionally, a large portion of the relevant sound
spectrum ?between 8.5 and 16 kHz? is omitted in this ex-
ample, which may further hinder median-plane localization
for CI listeners. Lastly, the typical placement of the micro-
phone behind the ear and above the pinna causes a lack of
directional filtering from the pinna, arguably the most impor-
tant anatomical vertical-plane directional filter. It is obvious
that substantial changes to CI speech processing strategies
and systems are needed if they are to incorporate vertical-
plane localization cues. However, these changes must respect
the primary use of a CI, which is to provide speech under-
standing to profoundly hearing-impaired and deaf individu-
als. Therefore, new processing strategies should carefully
balance the competing needs for speech understanding and
Although spectral distortions can cause decreased local-
ization performance, it has been shown that NH listeners can
adapt to some localization-cue modifications after long-term,
real-world experience ?Hofman and Van Opstal, 1998?. This
is promising for CI users who, if post-lingually deafened,
will have to relearn their auditory spatial map. Additionally,
as mentioned above, studies show that vertical-plane local-
ization relies upon fairly broadly tuned features in the HRTF
spectrum. This is a necessity for CI users who, for this gen-
eration of CIs, can be presented only a few channels of spec-
tral localization information.
The goal of this study was to determine the number of
spectral channels necessary to perform median-plane sound
localization. If this number is sufficiently low, then it may be
possible for CI users to perform the task. The experiments
tested median-plane localization in NH listeners using a CI
simulation. The first experiment consisted of extensive pro-
cedural training and localization training to wideband ?WB?
virtual stimuli. This was followed by the localization of vo-
coded stimuli, where the number of logarithmically-spaced
frequency channels was varied from 3 to 24, which were
acutely tested. The second experiment consisted of long-term
localization training and testing for the vocoded stimuli,
which focused on two 12-channel spacings, one from experi-
ment 1 and one with a custom configuration of channels
designed to balance speech and vertical-plane localization
cues. An additional experiment investigated a potential dete-
rioration in speech understanding using a clinical spacing
and the spacing introduced in experiment 2.
II. EXPERIMENT 1: ACUTE VOCODER
A. Listeners and equipment
Eight listeners participated in the experiment. All eight
listeners had audiometrically normal hearing and were be-
tween 21 and 46 years old.
The virtual acoustic stimuli were presented via head-
phones ?Sennheiser HD580? in a semi-anechoic room. A
digital audio interface ?RME ADI-8? was used to present
stimuli with a 48-kHz sampling rate and 24-bit resolution.
A visual environment was presented via head-mounted
display ?HMD; Trivisio 3-Scope?. It provided two screens
with a field of view of 32°?24° ?horizontal?vertical di-
mensions?. The HMD did not enclose the entire field of view.
The visual environment was presented binocularly, the same
picture used for both eyes. Listeners could adjust the inter-
pupillary distance and the eye relief so that they viewed a
single focused image. The position and orientation of the
listener’s head were measured by an electromagnetic tracker
?Ascension Flock of Birds? in real-time. One tracking sensor
was mounted on the top of the listener’s head. The second
tracking sensor was mounted on the end of a pointer, which
was held by the listener. The tracking device was capable of
measuring six degrees of freedom ?three translations, three
J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization991
rotations? at a rate of 100 measurements per second for each
sensor. The tracker accuracy was 1.7 mm for translations and
0.5° for rotations.
B. HRTF measurements
The HRTFs were measured for each listener individu-
ally. Twenty-two loudspeakers ?custom-made boxes with
VIFA 10 BGS as drivers? were mounted on a metal arc
?1.2-m radius? at fixed elevations from −30° to +80° relative
to the listener’s eye level. The loudspeakers were driven by
amplifiers adapted from Edirol MA-5D active loudspeaker
systems. The loudspeakers and the arc were covered with
acoustic damping material to reduce the reflections from the
construction. The listeners were seated in the center of the
arc and had microphones ?Sennheiser KE-4-211-2? placed in
his/her ear canals, which were connected via pre-amplifiers
?RDL FP-MP1? to the digital audio interface. Each HRTF
was measured with a 1728.8-ms exponential frequency
sweep from 0.05 to 20 kHz. The multiple exponential sweep
method ?MESM? was used to measure HRTFs in an inter-
leaved and overlapped fashion for one azimuth and all eleva-
tions ?Majdak et al., 2007?. After measuring HRTFs for 0°
azimuth, the listener was rotated by 2.5° and the measure-
ment of HRTFs for the next azimuth began. In total, 1550
HRTFs were measured for one listener, where the positions
were distributed with a constant spherical angle on the
sphere. During the procedure, the head position and orienta-
tion were monitored with the head tracker. The entire HRTF
measurement procedure lasted approximately 20 min. The
HRTFs were calculated from the recordings according to the
MESM system identification procedure ?Majdak et al.,
The equipment transfer functions were derived from a
reference measurement performed by placing the in-ear mi-
crophones in the center of the arc and using the system iden-
tification procedure as before. The transfer function of the
equipment was individually measured for each loudspeaker
and removed from the HRTF measurements by filtering each
HRTF with the appropriate inverse equipment transfer func-
Directional transfer functions ?DTFs? were calculated
according to the procedure of Middlebrooks ?1999b?. The
magnitude of the common transfer function ?CTF? was cal-
culated by averaging the log-amplitude spectra of all the
HRTFs. The phase of the CTF was the minimum phase of the
CTF amplitude spectrum. The DTFs were the result of filter-
ing the HRTFs with the inverse complex CTF. Since the
headphone transfer function is the same for all positions,
removing the CTF removes the headphone transfer function,
which is known to be important for proper virtual stimulus
externalization ?Pralong and Carlile, 1996?. No further head-
phone transfer function compensation was used. Finally, all
the DTFs were temporally windowed with a Tukey window
to a 5.33-ms duration. A typical set of DTFs for the median
plane is shown in Fig. 1?a?. More details about the HRTF
measurement procedure can be found in Majdak et al.
Three types of free-field stimuli were used as acoustic
targets: WB Gaussian noises, WB click trains, and vocoded
pulse trains. They were uniformly distributed along the me-
dian plane of a virtual sphere with the listener in the center of
this sphere. Positions from −30° to +210° in elevation, rela-
tive to the eye level of the listener, were tested. These posi-
tions varied within the lateral range of ?10° of the median
plane. Therefore, 290 of the 1550 measured DTFs were used.
The level of the stimuli was 50 dB with respect to the
hearing threshold. The hearing threshold was estimated in an
experimenter-controlled manual up-down procedure using a
Relative level (dB)
Azimuth: 0°; Elevation: 0°
FIG. 1. ?Color online? A set of DTFs in the median plane for a typical
listener. Panel ?a? shows the measured DTF. Panel ?b? shows the amplitude
spectra of the same DTF for 0° azimuth and 0° elevation ?solid thin line? and
processed by the GET vocoder ?vertical lines? for different numbers of chan-
nels ?N?. Channel corner frequencies are marked by the triangles.
992J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization
target positioned at an azimuth and elevation of 0°. In the
experiment, the level for each presentation was randomly
roved within the range of ?5 dB to reduce the possibility of
localizing targets based on level.
1. Wideband signals
The WB Gaussian white noises ?to be called WB noises?
and 100 pulse/s WB click trains ?to be called WB clicks?
had 500-ms duration, which included temporal shaping by a
Tukey window with a 10-ms rise-fall time. The stimuli were
filtered with the listener-specific DTFs.
2. Vocoded signals
A Gaussian-enveloped tone ?GET? vocoder ?Lu et al.,
2007? was used to simulate CI sound processing. A more
conventional vocoder was not used for the following reasons.
A sine vocoder has a sparse spectral representation, meaning
that there is a single sine tone at the center frequency of the
channel and possible sidebands, which may hinder the peak
and notch detection necessary for vertical-plane sound local-
ization. A GET vocoder has spectrally full channels with
harmonics spaced at the pulse rate of the stimuli. We think
that spectrally full channels better reproduce the electrical
stimulation of a CI. A noise vocoder generates a non-
deterministic signal, where random fluctuations make the
characteristic spectral peaks and notches between 4 and
16 kHz difficult to visually identify. On the other hand, a
GET vocoder generates a deterministic signal. Thus we
needed only one token, and there was no problem in visually
identifying the spectral peaks and notches. Lastly, we think
that presenting pulsatile stimulation, albeit relatively low-
rate acoustic pulses, better represents the electrical pulse
trains delivered by a CI.
Detection of GETs has been previously studied in NH
listeners ?Gabor, 1947; van den Brink and Houtgast, 1990;
van Schijndel et al., 1999?. Our targets were multi-channel
GET trains with incorporated spatial information. The total
processing scheme can be seen in Fig. 2. A single WB click
was filtered with a DTF corresponding to the particular po-
sition of the target. The resulting directional impulse re-
sponse was filtered into N=3, 6, 9, 12, 18, or 24 contiguous
channels by a filter bank. The filters were eighth-order But-
terworth bandpass filters. The lowest corner frequency was
0.3 kHz. The highest corner frequency was 16 kHz. The
other corner frequencies were logarithmically spaced accord-
ing to the value of N. Each channel, n, had a center fre-
quency, fn, defined as the geometric mean of the channel’s
corner frequencies. After filtering the DTF, each channel had
For a single channel, n, a Gaussian pulse, An?t?, is given
An?t? =??nfn· e−???nfnt?2,
where ?nis the shape factor. The value of ?nwas chosen so
that the equivalent rectangular bandwidth, Bn=?nfn, equaled
the bandwidth of the corresponding bandpass filter for that
channel. A GET, Pn?t?, is created by modulating a sinusoidal
carrier with frequency fnby the Gaussian pulse:
Pn?t? = An?t? · sin?2?fnt +?
where the phase shift of ?/4 was used to keep Pn?t?’s energy
independent of fn?van Schijndel et al., 1999?. The single-
channel GET train, Gn?t?, is the sum of 50 delayed GETs:
Pn?t − mT −T
where T is the delay between each GET. The delay was
10 ms, which corresponds to a rate of 100 pulses/s. The T/2
phase shift was used to have Gn?t? not begin at a maximum.
Note that for low fn, especially when N is relatively
large, Gn?t? would have overlapping GETs. Hence, the
modulation depth is not 100%. In such cases, if the Gaussian
pulses modulate the carrier before being summed into a GET
train, a spurious higher-order modulation of the signal would
be introduced from the interfering phases of adjacent pulses.
We determined that a modulation depth of 99% occurred if
the equivalent rectangular duration of An?t? was longer than
3.75 ms. To avoid overlapping pulses and unwanted modu-
lations, if An?t? is longer than 3.75 ms, then Gn?t? is the sum
of 50 Gaussian pulses, which then modulate the carrier:
An?t − mT −T
Gn?t? = sin?2?fnt? ·?
Note that by using this method, in the worst case of 0%
modulation depth, the GET vocoder reduces to a sine
The amount of energy in Gn?t? depends on fn. Therefore,
Gn?t? was normalized with respect to its total energy, called
Gn??t?. Finally, the multi-channel GET train x?t? is the sum
over the normalized GET trains Gn??t? weighted by the en-
ergy Enfrom the spatial information ?i.e., the energy from
each channel of the DTF?:
GET vocoded signal, x(t)
FIG. 2. Processing scheme for the GET vocoder. DTF information is band-
pass filtered ?BP filter? into N channels, where the energy ?En? is measured.
Gaussian envelopes modulate a sine tone, are replicated, and delayed ?Rep?
to make a GET train. The GET trains are energy normalized, weighted by
the energy Enfrom a channel of the DTF, and summed. After temporal
windowing, the result is the GET-vocoded signal.
J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization993
x?t? = w?t? ·?
Gn??t? · En,
where w?t? is a Tukey window with a 10-ms rise-fall time.
Figure 1?b? shows amplitude spectra of the same DTF as in
Fig. 1?a? for 0° azimuth and 0° elevation ?horizontal line?
and processed by the GET vocoder ?vertical lines? for differ-
ent N values.2
The listeners were immersed in a virtual sphere with a
5-m diameter. To facilitate the listeners’ orientation, horizon-
tal grid lines were placed every 5° and vertical grid lines
every 11.25°. The reference position ?azimuth and elevation
of 0°?, horizontal plane, and medial plane were marked with
small spheres. Rotational movements were rendered in the
virtual environment but not translational movements. The lis-
teners could see the visualization of the hand pointer and its
projection upon the sphere whenever they were in the listen-
ers’ field of vision. The projection of the pointer direction on
the sphere’s surface, calculated from the position and orien-
tation of listeners’ head and the pointer, was recorded as the
indicated target position.
Prior to the acoustical tests, listeners performed a proce-
dural training. In order to familiarize the listeners with the
equipment and virtual environment, the listeners were
trained to quickly and accurately respond to visual targets
presented on the sphere. After the training, the listeners were
able to respond to visual targets with an error smaller than
Acoustical sound localization training was provided,
which was similar to that provided to listeners in Zahorik
et al. ?2006?. In the acoustic training, at the beginning of
each trial, the listeners aligned their head to the reference
position. By pressing a button, the acoustic target was pre-
sented. During the presentation, the listeners were instructed
not to move. After the acoustic presentation, the listeners
were asked to point to the perceived position with the pointer
and respond by pressing a button. This response was col-
lected for further analysis. Next, a visualization of the acous-
tic target appeared on the surface of the sphere. The listeners
were instructed to find the visualization, to point and respond
to the visualization, and return to the reference position. Af-
ter pressing the button, the same acoustic target with visual-
ization was presented to the listeners and they had to point
and respond to the acoustic target again. In total, for each
acoustic target, listeners heard the stimulus twice, responded
once to the initial perceived position, and responded twice to
the actual position. The training was performed in blocks of
50 targets. Each block lasted for approximately 20–30 min.
More details on the procedure and training are given in Ma-
jdak et al. ?2010?.
Listeners were first trained to WB noises within ?10°
around the median plane ?290 possible positions?. For six
listeners, the training consisted of 500–600 trials. For the
other two listeners, the training consisted of 300 trials be-
cause they had extensive localization training over the entire
sphere from previous studies. After training to WB noises,
listeners were trained to WB clicks for 100 trials.
Seven conditions were tested in this experiment, the vo-
coded stimuli with N=3, 6, 9, 12, 18, and 24 channels and
the WB clicks. As in the training, stimuli were randomly
chosen from ?10° around the median plane. Due to the large
number of positions, the same number of responses was not
required from each position. Each condition consisted of
three blocks of 100 trials and no feedback on the target po-
sition was given. The blocks were presented in random order
for each listener.
The metrics used to evaluate localization ability were
the local polar error and the percentage of trials with quad-
rant errors. Localization errors were calculated by subtract-
ing the target polar angles from the response polar angles.
The polar error was the root-mean-square of the localization
error. A quadrant error was defined as having an absolute
polar error of greater than 90°. In tests with a large number
of quadrant errors, the polar error is highly correlated to the
quadrant error rate, showing the dominant role of the quad-
rant error rate in the metric. Therefore, the local polar error
was used, which was the polar error after removing all the
quadrant errors.3Assuming uniformly distributed random re-
sponses ?i.e., guessing? within the range from −45° to 225°,
the local polar error converges at 52° and the percentage of
quadrant errors converges at 39%.4
Figure 3 shows the individual ?top panels? and average
?bottom panels? localization results. Data from the WB noise
localization training were included with the experimental
conditions. The local polar error and quadrant error rate for
the WB clicks were similar to those for the WB noises. In
general, the local polar error and quadrant error rate in-
creased from the WB conditions to the vocoded conditions.
For the local polar error, performance becomes worse for a
decreasing number of channels, which appears to plateau
around 18 channels. For the quadrant error rate, there seems
to be a relatively flat plateau between 9 and 24 channels and
increases for fewer channels. All of the conditions showed
average local polar errors and average quadrant error rates
much better than chance. Only one listener ?NH41? showed
chance performance for any vocoded condition.
For the WB noises, individual listener quadrant error
rates were mostly within the measured range reported by
Middlebrooks ?1999b? for virtual WB noise stimuli. The lo-
cal polar error shows some listeners near the lower limit of
the Middlebrooks range. However, the average local polar
error is near the upper limit of the Middlebrooks range. This
discrepancy may be due to the fact that Middlebrooks tested
targets distributed in the whole lateral range, not just near the
median plane. The average quadrant error rate and standard
deviation correspond well to the Middlebrooks range.
A repeated-measures analysis of variance ?RM ANOVA?
was performed on the factor N, including the WB noises and
WB clicks as additional factor levels for the local polar error
and quadrant error rate. There was a significant effect of N
for both metrics ?p?0.0001 for both?.
994J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization
Tukey HSD post-hoc tests were performed for the local
polar error and quadrant error rate. For the local polar error,
there was no significant difference between the WB noises
and WB clicks ?p=0.75?. There were significant differences
between the WB conditions and the vocoded conditions
?p?0.007 for all?, with the exception of the difference be-
tween N=24 and the WB clicks ?p=0.33?. The differences
between N=24 and N=18, 9, and 6 were not significant
?p?0.1 for all?, but the differences between N=24 and
N=12, 6, and 3 were significant ?p?0.05 for all?. There
were no significant differences between any pair of N=18,
12, 9, 6, and 3 at the 0.05 level.
For the quadrant error rate, there was no difference
between the WB noises and WB clicks ?p=0.99?. There were
significant differences between the WB conditions and the
vocoded conditions ?p?0.011 for all?. The difference be-
tween N=24 and N=18 was not significant ?p=0.090?, but
the differences between N=24 and N=12, 9, 6, and 3
were significant ?p?0.003 for all?. The differences between
N=18 and N=12, 9, 6, and 3 were not significant
?p?0.098 for all?. The difference between N=12 and N=9
was not significant ?p=1?, but the differences between
N=12 and N=6 and 3 were significant ?p?0.038 for both?.
The difference between N=9 and N=6 was not significant
?p=0.14?, but the difference between N=9 and N=3 was
significant ?p=0.011?. The difference between N=6 and
N=3 was not significant ?p=0.97?.
The localization of WB noises corresponded well to that
measured by Middlebrooks ?1999b?, who tested well-
practiced listeners with virtual acoustic WB noises in both
the horizontal and vertical dimensions. As expected, the lo-
calization of our virtual sources is worse than that of the real
sources measured in Middlebrooks ?1999b?. In our experi-
ment, there was no significant difference between the WB
noises and clicks, even though there was markedly less train-
ing for the clicks. Several studies have found that there are
level, duration, and rate effects in vertical-plane localization
?e.g., Vliegen and Van Opstal, 2004?. However, few studies
on vertical-plane localization have directly compared long-
duration WB noises and click trains. Hartmann and Rakerd
?1993? tested 880-ms WB noises and 10.4 pulses/s click
trains in a speaker identification task. For levels comparable
to the levels used in our experiment, localization perfor-
mance of click trains appeared slightly worse than that of
WB noises. Macpherson and Middlebrooks ?2000? showed
that the localization of click stimuli was qualitatively similar
to 3-ms noise bursts. Hofman and Van Opstal ?1998? tested
500-ms WB noises and 500-ms burst trains ?3-ms noise
bursts? at various rates, including 100 pulses/s. They found
that the localization performance in the vertical direction for
burst trains at 100 pulses/s was comparable to that for WB
noises. Lower rates caused worse performance for burst
trains compared to the WB noises. However, all three of
these studies did not include a statistical comparison of the
FIG. 3. Results of experiment 1. The upper panels show the individual data. The lower panels show the listener average and ?1 standard deviation. The left
column shows the local polar error in degrees as a function of the number of channels. The right column shows the percentage of quadrant errors. Results for
the WB clicks ?CL? and WB noises ?NS? are also included. The dashed lines show chance performance. The shaded area shows the average ?solid line? and
?1 standard deviation ?dotted lines? of the results from Middlebrooks ?1999b? for virtual WB noise stimuli.
J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization995
localization of clicks and noises. Also, the localization train-
ing for these three studies was not extensive; some testing
could be considered acute for some listeners. Hence, our re-
sult that there is no significant difference in the localization
of WB noise and clicks is not inconsistent with these studies.
There was a marked increase in the local polar error and
quadrant error rate when the GET vocoder was used, even
for 24 channels. On one hand, performance was expected to
be worse because the spectral cues were intentionally de-
graded and listeners received no training for the vocoded
conditions, unlike the WB conditions. On the other hand, this
is slightly surprising because it has been shown that the
broadband spectral cues are sufficient for vertical-plane lo-
calization. For example, Kulkarni and Colburn ?1998?
showed that HRTF amplitude spectra smoothed to as few as
32 Fourier coefficients could be used before sound localiza-
tion significantly deteriorated.5This corresponds to approxi-
mately five peaks and five notches in the sound spectrum in
the frequency range from 4 and 16 kHz. Our 24-channel vo-
coded signal has approximately nine channels in the same
frequency range, thus having nine potential critical points in
the sound spectrum. However, it may be that the spectral
contrast between channels in the vocoder is less than that of
a HRTF with a smoothed sound spectrum. The GET vocoder
had channels that were contiguous with respect to their cor-
ner frequencies, and the slopes of the channels were approxi-
mately 12 dB/oct; thus the channels have spectral profile in-
formation that overlaps. An extrapolation of this result to CI
users, who typically have extensive channel interactions,
which are analogous to overlapping channels, is that vertical-
plane sound localization may be limited by the spectral res-
olution and contrast, even for 24 electrodes.
A recent study by Qian and Eddins ?2008? explored the
effect of varying the spectral modulation content of WB
noises on virtual localization performance. In that study it
0.1 to 0.4 cycles/octave or from 0.35 to 0.65 cycles/octave
resulted in significantly poorer localization ?unsigned eleva-
tion difference between target and response angle? for low
elevations ?−30° to −20°? for three of six listeners. The vo-
coder used in the present experiment removed spectral
modulation content, especially for a small number of chan-
nels. For example, for a stimulus at −30° elevation, the
modulation spectrum was at least 10 dB down between 0.3
and 0.4 cycles/octave for N=3 compared to a WB noise. We
analyzed a portion of our data as a function of angle by
splitting the data into low elevation target ?−30° to 0°? and
high elevation target ?0° to 30°? groups. Using a RM
ANOVA ?factors N and elevation?, for the local polar error,
there was a significant effect of N ?p?0.0001?, no signifi-
cant effect of elevation ?p=0.26?, and no significant interac-
tion between N and elevation ?p=0.083?. For the quadrant
error, there was a significant main effect of N ?p?0.0001?,
no significant effect of elevation ?p=0.97?, and no significant
interaction between N and elevation ?p=0.84?. The RM
ANOVA was repeated with just WB noises and N=3, the
comparison that should show the largest contrast in spectral
modulation content. The results did not change for the quad-
rant error rate, but did change for the local polar error be-
cause the interaction between N and elevation became sig-
nificant ?p=0.028?. Therefore, this significant interaction
may show modest support that removing spectral modulation
information around 0.3–0.4 cycles/octave affects localiza-
tion performance at low elevations. Note that there are sev-
eral differences between this study and Qian and Eddins
?2008?, the most important being that we used individualized
HRTFs while they used non-individualized HRTFs ?although
they did customize the HRTFs to each listener?. As expected
when using individualized vs non-individualized HRTFs, the
overall performance of their listeners was much poorer than
ours. For example, their average front-back confusion rate
was 31?8% compared to our 9.4?7.2% average quadrant
error rate for WB noises. Hence, it appears that the quality of
the HRTFs used may affect the interpretation of the impor-
tance of spectral modulation cues in vertical plane sound
Although localization performance was worse for the
vocoder conditions, it was always better than chance. Said
another way, CI listeners with their poorer frequency selec-
tivity will be hindered in localizing sounds compared to NH
listeners, but it seems possible to present salient vertical-
plane localization cues to CI users. In the experiment, per-
formance was roughly constant from 3 to 18 channels in
local polar error and from 9 to 18 channels in quadrant error
rate. Listeners also retained some sense of front-back direc-
tionality even for three channels. Median-plane sound local-
ization with three channels may seem surprising at first.
However, examining a typical set of DTFs ?see Fig. 1?a??, the
back positions can be approximated as a low-pass filtering of
the front positions. Hence, one might predict some median-
plane localization abilities with as few as two channels, a
low-frequency channel to be used as a reference and a high-
frequency channel for the front-back information. A similar
view to median-plane localization was taken by Iida et al.
III. EXPERIMENT 2: VOCODER TRAINING
The results of experiment 1 showed that there is little
difference in localization ability for NH listeners acutely
tested using a CI simulation from 9 to 18 channels. This
experiment will address two issues from experiment 1: long-
term training with GET-vocoded stimuli and maintaining ad-
equate resolution for the low-frequency channels associated
with speech understanding. Majdak et al. ?2010? showed that
training on the order of several hundred trials is essential for
saturation in the localization performance of virtual sound
sources. It was hypothesized that listeners would need train-
ing for saturation in localization performance for GET-
vocoded virtual sound sources, and that the results of experi-
ment 1 underestimate the localization performance. It was
also hypothesized that given the results of speech under-
standing tests from Goupell et al. ?2008b?, it would be pos-
sible to balance the competing demands of speech under-
standing and vertical-plane sound localization without
significant loss of performance in either.
996J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010 Goupell et al.: Number of channels for median-plane localization
Stimuli were GET vocoded like those in experiment 1.
The number of channels was fixed at N=12, which corre-
sponds to the number of electrodes in the MED-EL Combi
40+, Pulsar, and Sonata implants. This condition showed lo-
calization performance better than chance in experiment 1,
and little decrease in localization performance compared to
N=24, the maximum number of electrodes available for any
Two spacings were used in this experiment. The first,
called the “Log” spacing, corresponded to the spacing used
for N=12 of experiment 1. The second, called the “speech-
localization ?SL?” spacing, represented an attempt to pre-
serve speech information with a minimal sacrifice of spatial
information. It is justified as follows.
Goupell et al. ?2008b? low-pass filtered speech signals at
cutoff frequencies of 8500, 4868, 2788, 1597, or 915 Hz for
CI and NH listeners using a CI simulation while keeping the
lower-frequency boundary fixed at 300 Hz. They found that
there is almost no improvement in speech understanding per-
formance beyond eight spectral channels ?cutoff frequency
of 2788 Hz?. Keeping this in mind, the corner frequencies
for the SL spacing were chosen such that the first eight low-
frequency channels were logarithmically spaced from
0.3 to 2.8 kHz. This allowed for adequate resolution of the
speech signal over the first two formants of speech. We refer
to these eight channels as “speech” channels. The four
spaced from 2.8 to 16 kHz.6This was to include more of the
high-frequency vertical-plane localization information that is
typically omitted in CI processing of acoustic waveforms.
We refer to these four channels as “spatial” channels. Visual
inspection of the individualized HRTFs showed that this
choice of corner frequencies yields reasonable contrast for
the spatial channels so that vertical-plane sound localization
might still be possible. Therefore, we chose the SL spacing
in an attempt to allow for both good speech understanding
and vertical-plane localization ability. As in experiment 1,
the center frequency of each channel of the GET vocoder
corresponded to the geometric mean of the corner frequen-
cies. The information for each channel is given in Table I.
The eight listeners of experiment 1 were split into two
groups of four listeners each. The groups were chosen with
respect to the rank-ordered quadrant error rate from experi-
ment 1 for the condition N=12, which attempted to balance
the average quadrant error rate for the groups. One group had
listeners ranked 1, 4, 5, and 8 ?average quadrant error rate
was 22.0%?. The other group had listeners ranked 2, 3, 6, and
7 ?average quadrant error rate was 20.8%?.
Both groups were provided acoustic training to Log-
spaced or SL-spaced vocoded signals before testing. The
training was similar to that in experiment 1. As before, lis-
teners were trained until performance saturated. This was
between 300 and 700 items depending on the listener. After
the training, listeners were tested without feedback for 300
items. After data were taken for one type of spacing, the
listeners were trained and tested on the other type of spacing
in a similar fashion. Therefore, the results of experiment 2
show data from all eight listeners for each condition.
The results of the experiment are shown in Fig. 4. Note
that the WB noise and WB click data were taken from ex-
periment 1. Qualitatively, the results show that the local po-
lar error and quadrant error rate were smallest for the WB
noise, followed by the WB clicks, followed by the Log spac-
ing, followed by the SL spacing. The errors for the SL spac-
ing were slightly larger than the errors for the Log spacing.
Results for all conditions were much better than chance per-
formance. Comparing the results of the training on the Log
spacing to the same condition with acute testing ?experiment
TABLE I. Stimulus information for the spacings used in experiment 2.
FIG. 4. Results of experiment 2 averaged over listeners. Error bars show
one standard deviation of the mean. The dashed lines show chance perfor-
mance. Listeners were trained to all conditions before testing. Data from the
WB noise and WB click conditions are repeated from experiment 1.
J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization 997
1, condition N=12?, on average, the local polar error de-
creased by 4.6° and the quadrant error rate decreased by
A RM ANOVA was performed over the factor condition
for the local polar error and the quadrant error rate. There
was a significant effect of condition for the local polar error
and quadrant error rate ?p?0.0001 and p=0.006, respec-
tively?. Table II shows p-values for post-hoc tests for both
metrics. The WB conditions were significantly different from
the vocoded conditions for the local polar error. The WB
conditions were significantly different from the SL spacing
for the quadrant error rate. The differences were not signifi-
cant between WB conditions for both metrics. The differ-
ences were not significant between the Log and SL spacings
for both metrics.
This experiment aimed to test two hypotheses. The first
hypothesis was that listeners could improve their localization
performance of GET-vocoded stimuli with training when
compared to experiment 1. Listeners’ performance did im-
prove significantly, but performance for the GET-vocoded
stimuli remained slightly worse than that for the WB noise.
Although there is a small but significant difference in local-
ization performance between the Log spacing and the WB
noise, listeners still performed much better than chance.
The second hypothesis was that listeners could localize
using the SL spacing, which attempts to compromise be-
tween adequate spectral resolution of low frequencies ?re-
quired for speech understanding? and the necessity of spec-
tral information from 4 to 16 kHz ?required for vertical-
plane localization?, without a marked decrease in localization
performance. Listeners localized well below chance perfor-
mance with the SL-spacing stimuli. This performance was
significantly worse than that for the WB noise, but there was
no significant difference from the Log-spacing stimuli.
IV. EXPERIMENT 3: SPEECH TEST
The previous experiment showed that NH listeners using
a CI simulation could localize in the median plane relatively
well using only 12 channels, 8 channels assigned to speech
frequencies and 4 channels assigned to spectral localization
frequencies. To ensure that the SL spacing does not degrade
speech understanding, we performed a speech test using this
spacing and a spacing similar to the clinical mapping used in
current CI processing strategies.
Three sessions of feedback training and subsequent test-
ing of speech understanding were performed using the Old-
enburg Sentence Test. The procedure was similar to that in
experiment 2 of Goupell et al. ?2008b?. The feedback train-
ing session consisted of listening to sentences with visual
feedback on the computer screen. Eighty sentences were pre-
sented at four different signal-to-noise ratios ?SNRs?: +10, 5,
and 0 dB, or in quiet. The testing session consisted of 40
sentences presented in a random order either at a 0-dB SNR
or in quiet, 20 sentences for each SNR. Because of ceiling
effects, it was not necessary to include the 10- and 5-dB
conditions. At beginning of each session, ten sentences were
presented in quiet to eliminate any short-term adaptation ef-
fects. The percentage of correct words was calculated from
the third of the three sessions.
The training and testing were performed for two spac-
ings, the SL spacing and a spacing similar to the processing
of the Combi40/40+ and Pulsar CIs, called the “clinical
map.” The clinical map was the baseline condition in
Goupell et al. ?2008b?. It had a lower-frequency boundary of
300 Hz, an upper-frequency boundary of 8500 Hz, and had
12 contiguous logarithmically-spaced frequency channels. A
noise vocoder was used to simulate CI processing and the
corner frequencies of the synthesis channels corresponded to
that of the analysis channels. More details of the vocoder and
procedure can be found in Goupell et al. ?2008b?.
The listeners were the same as the previous experiments,
except that NH42 did not participate because of her limited
availability. NH42 was replaced by NH10, the first author of
the paper, who had audiometrically normal hearing and was
29 years old.
B. Results and discussion
Figure 5 shows the results of the experiment. There was
very little difference between the two spacings, as expected.
TABLE II. Experiment 2: p-values for differences between conditions. Sig-
nificant p-values ?at the 0.05 level? are in bold.
Local polar errorWB clicksLogSL
Quadrant errorWB clicksLogSL
FIG. 5. Results of experiment 3 averaged over listeners, the percentage of
correct words ?Pc? for two spacings, and two SNRs in a speech understand-
ing test. Error bars show one standard deviation of the mean.
998 J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization
In a RM ANOVA ?factors: SNR and spacing?, the difference
was significant between SNRs ?p?0.0001?, but not between
spacings ?p=0.58?. The interaction was also not significant
?p=0.58?. Therefore, the small change to the SL spacing did
not decrease speech scores from the reference map for NH
listeners. This was expected given the results of Goupell et
al. ?2008b?, who tested speech understanding with a similar
condition ?called the extended-frequency range mapping or
“M14N12”? that had an upper-frequency boundary of 16 kHz.
The difference between the SL spacing and the extended-
frequency range mapping is that the SL spacing mapped fre-
quencies to the appropriate tonotopic places, while the ex-
tended range mapping compressed the frequency information
from 0.3 to 16 kHz to tonotopic places from 0.3 to 8.5 kHz.
NH listeners did not show a decrease for the extended-
frequency range mapping compared to the clinical map. CI
listeners did show a significant decrease between these con-
ditions. Thus, if CI listeners were tested with the SL spacing,
it remains possible that they will have decreased speech un-
derstanding. Therefore, it is imperative that CI speech under-
standing is tested in future experiments for any novel spacing
that includes a larger than typical frequency range.
V. GENERAL DISCUSSION
Experiments 1 and 2 tested NH listeners’ ability to lo-
calize WB and GET-vocoded sound sources in the median
plane. The experiments showed that while localization per-
formance was worse for the spectrally degraded vocoded
stimuli, localization performance was better than chance.
This result validates results from previous studies, which
maintain that the gross spectral structure is needed for
vertical-plane sound localization ?e.g., Kulkarni and Col-
burn, 1998; Langendijk and Bronkhorst, 2002; Qian and Ed-
dins, 2008?. In fact, our reasonably good localization perfor-
mance was maintained for 9 or 12 channels logarithmically
spaced from 0.3 to 16 kHz. Such a result is promising for the
incorporation of spectral localization information in CI pro-
Experiment 2 included a special 12-channel spacing,
called the SL spacing, in the localization tests. The idea be-
hind this spacing was a compromise between the competing
demands of including adequate speech and median-plane lo-
calization information. Assuming that frequencies up to
2.4 kHz are essential for adequate vocoded-speech under-
standing ?Goupell et al., 2008b?, the Log spacing provided
seven speech channels and the SL spacing provided eight
speech channels, thus a difference of approximately one
channel assigned to spatial information. Experiment 2
showed that localization with the SL spacing was not differ-
ent from localization with the Log spacing, which means that
it is a viable option for future vertical-plane localization test-
ing in CI listeners. Experiment 3 confirmed that speech un-
derstanding was not hindered by using the SL spacing.
Of course, localization of real sounds is better than vir-
tual sounds. The local polar error is 22.7?5.1° for real
sounds compared to 28.7?4.7° for virtual sounds, and the
quadrant error rate is 4.6?5.9% for real sounds compared to
7.7?8.0% for virtual sounds ?Middlebrooks, 1999b?. For the
12-channel vocoder with the SL spacing of channels, there
was an average degradation of 6.3° in local polar error and
8.8% in quadrant error rate for the virtual vocoded stimuli
compared to the virtual WB noises. There was an average
degradation of 17.4° in local polar error and 13.6% in quad-
rant error rate compared to the real WB sounds of Middle-
brooks ?1999b?. Assuming no other deficits from using a CI
than channelization, CI users will have less ability to distin-
guish elevation ?increase in local polar error in the range
from 6.3° to 17.4°? and will confuse front and back more
often ?increase in quadrant error rate in the range from 8.8%
to 13.6%? than NH listeners.
All of the tests were performed with NH listeners using
a CI simulation. Testing with CI listeners will also need to be
done to determine the usefulness of the SL spacing for
vertical-plane localization and speech understanding. Cur-
rently, CI listeners using behind-the-ear microphones and a
clinical processing scheme ?the highest frequency used was
8.5 kHz? cannot localize in the vertical planes ?Majdak et al.,
2008?. This study shows that the incorporation of high fre-
quencies and spectral HRTF information, possibly by an in-
the-ear microphone or other types of directional microphone,
may provide salient cues for CI listeners, but perception of
these cues is understandably worse than for NH listeners.
Vertical-plane localization in CI users is expected to be even
worse than that measured here for the NH listeners using a
CI simulation for a myriad of reasons. One reason is that
electrode arrays do not necessarily stimulate tonotopic places
with matching frequency information. Ketten et al. ?1998?
reported the most apical electrode of some CIs, which often
receive frequency information around 300 Hz, at a cochlear
place tuned to greater than 1.4 kHz. Such a frequency-to-
place mismatch is detrimental to speech understanding ?e.g.,
Fu and Shannon, 1999?. It could also be detrimental for
vertical-plane sound localization, assuming that the CI user
previously had hearing and developed an auditory map of
space. The problem of tonotopic mismatch could be com-
pounded by dead regions in the cochlea ?Shannon et al.,
2001?; important spectral features may be lost for some el-
evations, which would probably greatly hinder vertical-plane
localization. Another reason is that the fidelity of current CI
processing schemes cannot completely reconstruct a CI lis-
tener’s individualized HRTF. It is well known that vertical-
plane localization is worse with non-individualized than in-
dividualized HRTFs ?e.g., Wenzel et al., 1993?. Despite all of
these hurdles to overcome, it is possible that the plasticity of
the auditory system would be able to cope with these poten-
tial problems. CI users may be able to learn a new auditory
map of space, which was shown to be possible in NH listen-
ers by Hofman et al. ?1998?.
Vertical-plane sound localization will also be affected by
the poor spectral resolution in CI listeners. CIs typically pro-
duce relatively large excitation patterns in the cochlea ?Nel-
son et al., 2008?. This large spread of excitation translates to
a much poorer spectral resolution for CI listeners compared
to NH listeners, which has been measured with a ripple-noise
reversal test ?Henry and Turner, 2003; Henry et al., 2005?.
Related to this is the small number of perceptual channels
available in CI users. Although we have assumed that 12
J. Acoust. Soc. Am., Vol. 127, No. 2, February 2010Goupell et al.: Number of channels for median-plane localization 999
electrodes will translate to 12 perceptual channels for sound
localization, many speech studies have shown that there are
only about eight distinct perceptual channels in CI users
?Dorman and Loizou, 1997; Fu and Shannon, 1999; Friesen
et al., 2001; Başkent and Shannon, 2005?. Nevertheless, we
have shown that median-plane sound localization remains
quite good for as little as nine channels, nearly the same
performance as 18 channels. Additionally, vertical-plane
sound localization remains possible even with as few as three
or six channels, although approaching chance performance.
Even if the inclusion of spectral localization cues to CI pro-
cessing simply gives the ability to distinguish front from
back sources, this may well be worth it.
Lastly, Goupell et al. ?2008a? showed that CI listeners
depended mostly on intensity cues rather than spectral shape
cues in several types of profile analysis tasks, tasks that are
necessary to detect spectral vertical-plane sound localization
cues. Detecting spectral shape cues may be the major chal-
lenge to cope with in addressing vertical-plane sound local-
ization in CI users.
We would like to thank our listeners for participating in
this study and Michael Mihocic for running the experiments.
We would also like to thank the Associate Editor John
Middlebrooks, Fred Wightman, and an anonymous reviewer
for comments about a previous version of this work. Portions
of this study were presented at the Conference on Implant-
able Auditory Prostheses in Lake Tahoe in 2009. This study
was funded by the Austrian Science Fund ?FWF Project No.
1The advantage of the first method of generating GET trains ?generating a
single Gaussian envelope, modulating the carrier with a fixed phase, and
summing several GETs into a GET train? over the second method ?gener-
ating the envelope for the entire train and modulating the carrier to obtain
a GET train? is that the peak amplitude in all single GETs is constant for
the first method but not necessarily constant for the second. Although the
second method removes some higher-order modulations due to overlap-
ping GETs, it cannot control the peak amplitude in each GET.
2The first channel for N=24, the smallest analysis bandwidth used in this
experiment, had an unstable filter configuration. This perceptually trans-
lated into a strong pitch around 300 Hz. The entire stimulus was not per-
ceptually distinct from the N=18 condition. Because of low frequency of
this anomaly, we assumed that it would not affect median-plane sound
3Middlebrooks ?1999b? removed all targets that were outside a ?30° lat-
eral region. We removed all responses that were outside a ?30° lateral
region. For experiment 1, 8.2% of the data were removed because of this.
4Although the range of the experimental stimuli was from −30° to 210°,
listeners were not restricted to this range in their responses. Hence, we
used a slightly larger range in the calculation of chance performance to
5Note that the smoothing performed in Kulkarni and Colburn ?1998? was
linear-frequency based, not log-frequency based. Although the high-
frequency spectral localization features appear to have approximately
linear-frequency scaling, since the auditory system has approximately log-
frequency scaling, there was effectively less smoothing at higher frequen-
cies than low frequencies.
6Impulse responses between n=9 and 10 canceled with logarithmic spac-
ing, so we chose slightly different corner frequencies to avoid this.
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