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First published online August 30, 2006
Journal of Experimental Biology 209, 3599-3609 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02398
Size discrimination of hollow hemispheres by echolocation in a nectar feeding bat
University of Erlangen, Institute of Zoology II, Staudtstrasse 5, 91058 Erlangen, Germany
* Author for correspondence (e-mail: helver{at}biologie.uni-erlangen.de)
Accepted 20 May 2006
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We chose a simple geometric form, the hollow hemisphere, as the training object because of its resemblance to the bell-shaped concave form of many bat flowers, as well as its special acoustic qualities. The hemispheres showed a characteristic echo pattern, which was constant over a wide range of angles of sound incidence. We found systematic size-dependent changes in the echo's temporal and spectral pattern as well as in amplitude.
Bats were simultaneously confronted with seven different sizes of hollow hemispheres presented from their concave sides. Visits to one particular size were rewarded with sugar water, while we recorded the frequency of visits to the unrewarded hemispheres. We found that: (1) bats learned to discriminate between hemispheres of different size with ease; (2) the minimum size difference for discrimination was a constant percentage of the hemisphere's size (Weber fraction: approximately 16% of the radius); (3) the comparison of behavioural data and impulse response measurements of the objects' echoes yielded discrimination thresholds for mean intensity differences (1.3 dB), the temporal pattern (3-22 µs) and the change of spectral notch frequency (approximately 16%). We discuss the advantages of discrimination in the frequency and/or time domain.
Key words: flower-visiting bat, echoes of hollow hemispheres, object discrimination by echolocation, Weber-Fechner law
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). To
acquire new sources, the bats use olfactory
(von Helversen et al., 2000),
visual (Suthers et al., 1969;
von Helversen and Winter,
2003; Winter et al.,
2003) and echoacoustic features
(von Helversen et al., 2003;
von Helversen and von Helversen,
1999) offered by the flowers to attract bats and use them as
pollen vectors. Close to the flower, echoacoustic features seem to play the
major role in guiding the bats to the nectar chamber
(von Helversen and von Helversen,
2003).
A serious problem for the echoacoustic perception of single flowers in a
rainforest is that flower echoes are acoustically buried in echo clutter
produced by the surrounding vegetation. In contrast, aerial hawking
insectivorous bats have fewer problems with disturbing background echoes and
any echo indicating an object of adequate size will most likely be a flying
prey insect (Schnitzler and Henson,
1980).
Insectivorous bats hunting close to vegetation are affected by echo clutter
in the same way as nectarivorous bats. They employ extremely short
(Schnitzler and Henson, 1980)
and broadband (Siemers and Schnitzler,
2004) signals, because such signals facilitate separation of
objects from background. To circumvent problems caused by echo clutter, some
bats rely on additional prey-specific information. Many gleaning bats, for
example, listen passively for sounds generated by their prey
(Kalko and Schnitzler, 1998).
Rhinolophid bats use the Doppler shift in echoes caused by wing motions of
flying prey (Neuweiler, 1990;
Schnitzler et al., 2003).
Chiropterophilous flowers do not stand out by motion or by sounds they
produce themselves, but have evolved floral shapes generating conspicuous and
characteristic echoacoustic features that help bats to discriminate between
nectar-bearing flowers and the surrounding vegetation. In the
chiropterophilous vine Mucuna holtonii the vexillum of the flower is
echoacoustically conspicuous for the bat
(von Helversen and von Helversen,
1999), because it broadcasts its echo back to the bat over a wide
range of sound incidence angles. Therefore its echo is audible over many calls
for a bat passing by; in contrast a flat leaf will only `twinkle' when
ensonified perpendicularly, i.e. is audible only for a single call. Many
chiropterophilous plants have concave bell-shaped flowers. Such concave
flowers show temporal and spectral echo characteristics, which could be
acoustically conspicuous for bats (von
Helversen et al., 2003). Nectar feeding bats can easily be trained
in the laboratory to discriminate between different artificial concave forms
of the same frontal diameter based on echolocation alone, and they are also
able to correctly classify such forms independent of their size
(von Helversen, 2004).
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;
Schmidt, 1988;
Schmidt, 1992;
Schnitzler and Henson, 1980;
Simmons et al., 1974).
Hitherto the objects used for object recognition tasks were such that their
echo heavily changed with the angle of sound incidence
(Bradbury, 1970;
Simmons et al., 1974;
Simmons and Vernon, 1971),
which renders it difficult to determine the decisive echo feature. We used the
simplest possible concave form, the hollow hemisphere, because of its
extraordinary acoustic properties. Its echoes are nearly constant over a wide
range of angles of sound incidence (von
Helversen et al., 2003), and echo intensity as well as spectral
and temporal echo characteristics scale with hemisphere radius in a
predictable but differing manner (von
Helversen, 2004). In the present study we determine the ability of a glossophagine bat to distinguish between different sized hollow hemispheres by echolocation. We used nine individuals of the flower-visiting bat Glossophaga soricina (Phyllostomidae), a species well suited for training and object recognition tasks. We also measured the `echoes' (i.e. impulse responses) of the hollow hemispheres, extracted the three relevant acoustic features (amplitude, temporal and spectral features), and compared them with the bats' performance. From this comparison we aimed to identify the acoustic feature used by the bats for size discrimination.
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Experimental set-up
The experiments were conducted in a circular flight cage of 3.5 m diameter
and a height of 2.5 m. A training apparatus was positioned in the centre of
the cage. This apparatus consisted of a central column holding electronics,
nectar reservoirs and valves. From this column 16 spokes protruded in two
horizontal planes. A feeder was mounted at the end of each spoke (see
Fig. 1). To avoid position
learning, the central column with the spokes was slowly turned clockwise or
counterclockwise with angular velocities of up to 360° min-1
during all experiments. Turning direction changed in a pseudorandom sequence
of rotation angles with smooth deceleration and acceleration. The feeders were
short PVC tubes of diameter 25 mm. They contained an infrared light barrier
and were connected to a sugar water reservoir via silicone tubing.
Training objects were fixed directly above each feeder. Each interruption of a
light barrier was recorded by the computer, and in the case of a correct
visit, the computer triggered the valve to release a small reward of sugar
water (17-20 µl). In order to prevent repetitive visits a second visit to
the same feeder within 20 s was recorded but not rewarded. The reward was 17%
sugar solution of a mixture of sucrose, glucose and fructose (1:1.5:1.5)
(w/w). Sugar water is scentless.
Stimulus objects
Training objects were different sized hollow hemispheres of acrylic glass.
They were displayed directly above the feeder with their concave surface
pointing outwards. We used 14 different sizes of hollow hemispheres of radii
between 6 mm and 58.5 mm (see Fig.
2). From this pool we chose five different sets of hemispheres,
each with seven different hemisphere sizes, for experiments.
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Training and testing
Bats were allowed to fly freely in the flight cage and could access each
feeder with equal ease. As soon as a bat was accustomed to the training
apparatus and accepted the feeders as food source, one hollow hemisphere was
mounted on top of each of the 16 feeders. During the first, and sometimes also
the second, night of training, a reward was accessible at each of the four
feeders that displayed the hollow hemisphere with the positive radius. The
following night we started the tests with only two rewarded feeders as
described above. During all training and test periods the room was in total
darkness such that the bats had to rely on echolocation alone to orient and
find the feeders.
Data analysis
We analysed our data in two steps. First, all successive visits to the same
feeder within a 20 s period were regarded as one single visit. In a second
step the whole series of consecutive visits was split into blocks of 100
unrewarded visits. We excluded 100-visit-blocks when the number of visits to
the rewarded positive hemisphere exceeded the visits to the unrewarded
positive hemisphere by more than a factor of 1.5, as this indicated that bats
temporally adopted an unknown deviant strategy to find the rewarded feeder.
For each block the numbers of unrewarded visits to each size of hollow
hemispheres were counted. Then we calculated the relative frequency of visits
with respect to the number of visits to the unrewarded positive stimulus,
which was set to 100% (see Fig.
3). Statistical analysis was performed using SPSS 11.0 (SPSS,
Chicago, IL, USA).
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The downward frequency modulated (FM) echolocation calls of G. soricina show two harmonics covering frequencies of approximately 50 kHz to 140 kHz (first harmonic 56-96 kHz, second harmonic 87-137 kHz). Call durations are between 1 and 2 ms. The auditory threshold curve of this species reaches from 15 to 130 kHz (maximum sensitivity between 60 kHz to 110 kHz, best frequency around 80 kHz) (J. Lopez, Y. Winter and O. von Helversen, manuscript in preparation).
Impulse response measurements
The impulse response function (IR) fully characterizes the transmission
properties of any linear system. In an echoacoustic context, one might think
of the IR as the echo of an indefinitely short click. Actual echoes of natural
calls can be derived from the impulse response by convolution with the calls.
We used the impulse responses for our analysis.
The acoustic measurements were conducted in an anechoic chamber. To irradiate the objects we used a custom-built condenser speaker with a membrane diameter of 15 mm, and a 1/4'' condenser microphone without protecting grid (G.R.A.S. 40BF with preamplifier 26AB and power module 12AA; Holte, Denmark). The speaker and the microphone were fixed in parallel at the end of a holder. To mimic the dimension of a bat's head, the distance between the centre of the microphone and the loudspeaker membrane was set to 18 mm. This `artificial bat head' was mounted 20 cm or 40 cm above a bench and pointed in the direction of the object to be irradiated. Objects were fixed at the same height on a turntable by means of a piece of wire. By moving their position on the bench the distance between the object and `artificial bat head' could be changed. The measurements were taken from distances of 20 cm or 40 cm, respectively. First, the opening of the hollow hemisphere was directed exactly towards the artificial bat head. We defined this orientation of the hollow hemisphere as 0°. Then the turntable bearing the hollow hemisphere was turned around the vertical axis in steps of 2° or 10° from -90° to +90°. The frequency response of the loudspeaker and the microphone allowed measurements from 20 kHz to 140 kHz.
The objects were irradiated with a continuously replayed MLS (maximum length sequence) signal, which was generated by a custom-built sound generator. Replaying and recording were sample-synchronous at a sampling rate of 500 kHz. The microphone signal was digitized with 12-bit resolution and recorded by a custom made hard disc recorder (Institut für Technische Elektronik, Universität Erlangen, Germany).
As the impulse response is not directly accessible from the recordings, we
had to process our recording with the original MLS in a `Fast Hadamard
Transformation' (FHT). From the impulse response the frequency response
(spectrum) was calculated, using a Fast Fourier Transformation (FFT; window
size 1024 samples; rectangular window). The actual spectra of the object's
impulse responses, without influence of the loudspeaker frequency
characteristic, were calculated as the (complex) difference spectrum between
the spectra of the loudspeaker and the impulse response. To acquire the
frequency response of the loudspeaker, we replaced the object with an acrylic
glass plate directed perpendicularly to the angle of sound incidence. Thus, we
obtained the same impulse response as if we had placed the microphone on the
acoustic axis facing the loudspeaker at twice the distance from the object
(i.e. 40 cm) (for details, see von
Helversen et al., 2003).
We analysed the impulse responses with regard to three features: the relative amplitude, the temporal structure and the spectral pattern. To derive relative amplitude (Fig. 4A, Fig. 5C) of each individual impulse response we first integrated its spectrum (Pa/Hz) over a frequency range of 20 kHz to 140 kHz and then normalized this to the maximum such value. As a measure of temporal structure we used the duration of the pause between first and second reflection (gap1-2) of the impulse response. It was defined as the duration between the maximum of the first peak and the maximum of the second peak (Fig. 5A). To describe the spectral pattern of the impulse response we determined the frequency of the notches, which were defined as the local minima in the corresponding frequency area (Fig. 6).
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 | (1) |
where n=number of reflections. Assuming a velocity of sound in air
of 340 m s-1 (or 0.34 mm µs-1) and d in mm,
the time t necessary to pass the hemisphere will be
t=dx1/0.34 (µs). For n=1 the travelling
path length within the hemisphere will be d=2r and for
n=>
it will be d=
r; the maximum
duration of the impulse response will thus be
tmax=(-2)rx1/0.34 (µs). The time gap
(µs) between reflection number n1 and
n2 will be:
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We pooled the numbers of visits of all individuals that were tested with the same set and normalized the frequency of visits to the unrewarded positive hemisphere to 100%. Comparing the five curves in Fig. 3, it is noticeable that all sets elicited the same general preference pattern: the closer a hollow hemisphere's radius was to the radius of the positive hemisphere, the more frequently it was visited (see Fig. 3A).
To get a measure for the breadth of the curves, the intercept points of the
individual curves with the 75% level were determined. This resulted in two
r measurements, one to the smaller radius and one to the
larger. r plotted over the smaller radius increased with the
radius of the hollow hemisphere. We found a mean Weber fraction of
r/r=0.16±0.06, the linear regression was
r=0.13r+0.48 (F1,16=19.65,
R2=0.55, P=0.0004), when forced through the
origin the regression equation was r=0.15r
(F1,17=181.62, R2=0.91,
P<0.0001; please note that these values cannot be compared to
values for models that include an intercept).
Echoes of hollow hemispheres
Fig. 4 shows relative
amplitude, impulse response and frequency spectrum of the impulse response for
a hemisphere of 25 mm radius as a function of angle of sound incidence. Within
a wide range of angles of sound incidence (approximately -70° to +70°)
the impulse response of each hemisphere was nearly constant with respect to
its spectral and temporal pattern (Fig.
4B,C). The relative amplitude was steadily high for incidence
angles between -45° and +45° (Fig.
4A).
We measured the impulse response functions of 16 different sized hollow hemispheres, the 14 sizes used in the training experiments and two additional ones. It is noticeable that all three echo parameters depend on the radius r of the hemisphere (see Figs 5, 6): the relative amplitude of the object's impulse response is linearly dependent on r, because the reflected power linearly scales with target surface and both scale with r2 (Fig. 5C).
Fig. 5A depicts one hemisphere's impulse response taken from an angle of 10°. The first two small peaks in the impulse response originate from the edges of the hemisphere. Their position changes with the angle of incidence (labelled as `edge' in Fig. 4B and Fig. 5A; 1000-1300 µs). The next large solitary peak corresponds to the first reflection in Fig. 5D. The subsequent gap is followed by many peaks with gradually decreasing amplitude corresponding to the second to nth reflection (see Fig. 5D).
The most striking feature of the impulse response functions is the time gap between the first and the second reflection. The duration of this gap complies with the time the sound needs to cover the path length difference between first and second reflection (gap1-2; see Fig. 5B,D). Its duration increased linearly with the radius (Fig. 5B), and is in agreement with the expectation from Fig. 5D and Eqn 2.
Every feature in the time domain (temporal pattern) has its mathematical equivalent in the frequency domain (spectral pattern) and vice versa. Through interference, multiple reflections with different path length and thus different time delays cause reinforcement and cancellation, resulting in a complex spectral composition. Fig. 4C depicts the spectral directional pattern, i.e. the spectrum of the impulse response as a function of angle of sound incidence. It shows distinct horizontal ridges and valleys corresponding to notches, which are at the same frequencies for all angles of sound incidence. The hemisphere with a radius of 25 mm had its lowest notch at about 45 kHz (Fig. 4C). This was also the most prominent notch in the spectrum. Proceeding to higher frequencies, more or less regularly spaced further notches arose that were separated by flat peaks, giving the plots their characteristic banded pattern.
The larger the radius of a hollow hemisphere, the more notches were present
in the spectral pattern (Fig.
6). We determined the frequency of the most prominent notches in
the spectrum and found that single notches could be traced throughout the
range of different sized hollow hemispheres. The frequency of individual
notches was inversely proportional to the hemisphere radius, yet with
different proportionality factors (Fig.
6G). For every notch:
 | (3) |
where anotch is a constant coefficient, characteristic
for every particular notch (see Fig.
6G legend). In other words, notch wavelength was linearly
proportional to hemisphere radius - a result that can be derived from
geometry, compare Fig. 5D. This
is true not only for single notches but for the whole spectrum. Thus, the
spectral distribution s(
) of a larger hemisphere is a compressed
version of a smaller hemisphere's one. In a first approximation, the function
s() is constant for all hemispheres and changes only by an
expansion factor inversely proportional to the factor by which the radius of
the hemisphere is altered:
 | (4) |
(see Fig. 6). On a
logarithmic scale, according to Eqn 3, this becomes:
 | (5) |
This means that on a logarithmic frequency scale, a change in radius will
shift each notch by a constant factor of -logr. In other words,
spectra plotted over log are identical, but shifted by -logr (see
Fig. 6A-F).
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), we used the 75%
discrimination level as an indicator of the just-discernible radius difference
and then derived the respective difference threshold by interpolation
(Fig. 7).
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Intensity of the impulse response
The difference in sound pressure level between the just-discriminable
hemispheres in our experiment was at a mean of 1.3 dB (see
Fig. 7A). Just-detectable level
differences between two pure tones are at 4-6 dB in the mouse, 1-2 dB in
macaques and 0.5-1 dB in humans (for a review, see
Fay, 1992). The level
discrimination threshold for noise in humans seems to be slightly higher,
ranging around 1-4 dB (Zwicker and
Feldtkeller, 1967). Several authors have published values for
intensity discrimination by echolocation in bats. A 17% surface area
difference threshold was found for triangles, giving a corresponding intensity
difference of 1.5-3 dB (Simmons and
Vernon, 1971); however, temporal and/or spectral cues may also
have been used by the bats in these experiments, but these were not discussed.
The same is true for experiments with Noctilio leporinus (1-2 dB)
(Suthers, 1965) or for
experiments with Rhinolophus ferrumequinum, which were trained to
discriminate spheres of different sizes. In such experiments, thresholds of
2.4-4.4 dB (Airapetianz and Konstantinov,
1974) and 2.8-3.2 dB
(Fleissner, 1974), were
measured. These values are in a similar range but slightly higher than the 1.3
dB (Fig. 7A) needed by the bats
in the present study, given they had based their decision solely on intensity
differences.
It thus seems possible that the bats used intensity differences for size discrimination of hollow hemispheres, but one needs to consider that a level difference of 1.3 dB is comparatively small, taking into account that echo intensity is strongly dependent on the bat's distance to the target. Intensity-based discrimination would thus require highly accurate distance-intensity-compensation. This might not pose a major problem for a bat, however.
Temporal pattern
The just-noticeable difference of the most obvious time domain pattern, the
gap1-2, ranged between 3-22 µs; the gap1-2 itself
ranged from 12 to 148 µs. The time resolution, measured as the threshold of
recognizing two `pips' as two separated `pips', was about 100-200 µs in
Megaderma lyra (Weissenbacher et
al., 2002). Neurophysiological studies revealed a cochlear
integration time of about 
300-400 µs for Eptesicus fuscus
(Simmons et al., 1989). It is
thus highly unlikely that time gaps in the low µs range are resolved
exclusively in the time domain.
Temporal pattern and spectral domain
The limited temporal resolution led to the conclusion that bats generally
evaluate echoes in the frequency domain when time differences of less than 100
µs in overlapping echoes are offered
(Beuter, 1980;
Simmons et al., 1974).
Nevertheless, behavioural experiments showed that Eptesicus fuscus
perceives electronically generated echoes of two front targets in terms of two
distinct reflections, and this with a resolution of up to 2 µs
(Simmons, 1989;
Simmons et al., 1998). The
discrepancy between the limited temporal resolution found in other studies and
these results are explained by a mechanism that combines perception in the
time and spectral domain.
Through interference, a two-front echo with a given gap in the time domain
corresponds to notches at particular frequencies in the spectral domain.
Spectral notches are particularly expedient for resolving small changes in
time gaps, because changes in two-front spacing that are too small to be
resolved in the time domain correspond to drastic and more easily accessible
changes in notch frequency. It was therefore suggested that bats perceive two
front echoes in the spectral domain and then translate the spectral notch
pattern into a full time domain representation of the actual range profile
(Simmons et al., 1990). The
spectrogram correlation and transformation (SCAT) model
(Saillant et al., 1993)
explains the transformation of spectral information into time information.
Assuming this mechanism, gap1-2 duration may well have played a
decisive role for the discrimination of different sized hollow
hemispheres.
Spectral pattern
Hollow hemispheres reflect echoes with a characteristic spectral
composition that is clearly size-dependent. From Eqn 4 it becomes clear that
the just-noticeable change of the spectrum can be measured by the relative
change, expressed as /, of any particular peak or notch of the
spectrum. We chose the lowest notch (see 1. notch in
Fig. 6G), as this notch is
least blurred by noise and easiest to measure. Each higher notch would have
the same result, however. The importance of the fact that / is
constant for all notches, irrespective of the absolute notch frequency,
becomes apparent when one considers that the bandwidth of the echolocation
call is limited (50-140 kHz). A bat can only evaluate spectral changes when
they are within the frequency range of the bats' echolocation call
(Mogdans and Schnitzler,
1990). Yet, a certain notch being within the spectral range of the
call at one hemisphere size might at another size be out of it and thus
unavailable. Minimal noticeable change expressed as / is a
reliable and comparable measure as long as at least one notch occurs within
the echo's frequency range.
From Eqn 5 it can be deduced that:
 | (6) |
The average / detected by the bats was thus 16% (7-21%, one
outlier at 40%; see Fig. 7C).
This is not much larger than the values (6-13%) obtained for Megaderma
lyra (Schmidt, 1992) in
experiments with `two-front phantom targets' with delays of 7.8 and 20.7
µs.
How does the observed discrimination ability relate to cochlear morphology?
Cochlear frequency maps of humans, many mammals and unspecialised FM bats
(Greenwood, 1990;
Vater and Siefer, 1995) show
an exponential frequency distribution along the cochlea. We have shown above
that the spectra of different hemispheres, when plotted on a logarithmic
frequency scale, are at a first approximation identical and only shifted
by-logr (see Eqn 5). This means that the spectral echo pattern (peaks
and notches) projected onto the cochlea is about the same for all hemisphere
sizes, but its position shifts along the cochlea for a constant distance
depending on hemisphere size change (Eqn 5;
Fig. 6A-F). Thus every notch or
peak will be shifted by the same number of hair cells on the basilar membrane.
This also might be a mechanism facilitating generalization of form independent
of size (von Helversen, 2004).
As discrimination ability is believed to depend on cochlear distance, our
finding of a constant / supports the spectral basis of size
discrimination.
An adequate measure for frequency discrimination in broadband signals is
the critical bandwidth, as it takes masking and integration in the cochlea
into account (e.g. Greenwood,
1961). The critical bandwidth is a function of the centre
frequency and is presumed to represent equal distances on the basilar
membrane. Typical values for the critical bandwidth (CB, expressed as percent
of the mean frequency) and the corresponding critical distance (CD) on the
basilar membrane are: CB 17% (CD 1.2 mm) for humans, 21% (1.1 mm) for the
macaque, about 23% (1.1 mm) for the cat and 40% (1.5 mm) for the chinchilla
(for a review, see Fay, 1992).
This is in the same order of magnitude as our mean of 16%. For G.
soricina, equation 6 in Fay (Fay,
1992) would yield a CD estimate of 0.46 mm [assumed CB: 16%,
cochlear length: 14 mm, derived from Pye
(Pye, 1980) and highest
audible frequency Fmax: 130 kHz (J. Lopez, Y. Winter and
O. von Helversen, manuscript in preparation)]. This is between the values
mentioned above for non-echolocating mammals and the only available CD value
for a bat [Rhinolophus: 6%; 0.2 mm; outside of the acoustic fovea
(Long, 1977)]. Thus the
observed discrimination ability might well be a consequence of the mechanical
filtering properties of the inner ear.
The magnitudes of differences in intensity, in gap1-2 duration
and spectral pattern all agree reasonably well with known mammalian
performance. With our experimental approach we are not able to decide whether
discrimination was achieved in the time or in the spectral domain. Of course
echolocating bats will profit from evaluating all acoustic information
available to them, including temporal/spectral and intensity differences. In
support of a spectral basis for the observed discrimination ability it is
nevertheless important to note that frequency mapping and filtering properties
of the mammalian cochlea can explain the finding of a constant
/ in general and a value of about 16% in this species in
particular.
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Acknowledgments |
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References |
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