Echolocation signal structure in the Megachiropteran bat Rousettus aegyptiacus Geoffroy 1810
School of Biology, University of Leeds, Leeds, LS2 9JT, UK
* Author for correspondence (e-mail: bgyraho{at}leeds.ac.uk)
Accepted 20 September 2004
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Summary |
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Key words: echolocation, click, Megachiroptera, bat, Rousettus aegyptiacus, intensity
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Introduction |
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Among the Megachiropteran bats, only the genus Rousettus has
developed vocal echolocation, producing signals by clicks of the tongue
(Möhres and Kulzer,
1956). The clicks of Rousettus aegyptiacus Geoffroy 1810
are emitted in pairs and have been reported to be in the region of 0.61
ms duration, with a frequency range of 1270 kHz and peak frequency at
2040 kHz (von Herbert,
1985
). Despite the apparently rudimentary nature of its
echolocation system, R. aegyptiacus appears to have spatial
resolution comparable to Microchiropterans in some tasks, such as wire
avoidance (Griffin et al.,
1958
; Waters and Vollrath,
2003
). This leads to a conundrum if, as discussed earlier, the
echoes of impulse clicks are difficult to detect in the terrestrial
environment. However, to date, no measurement of amplitude or energy content
of impulse clicks produced by terrestrial echolocating animals has been
made.
A recent study (Waters and Vollrath,
2003) recorded click durations in R. aegyptiacus that
were shorter than in previous studies
(Möhres and Kulzer, 1956
;
Novick, 1958
;
von Herbert, 1985
), and are
closer in duration to those of dolphins than other terrestrial animals using
similar signals, such as oil birds and cave swiftlets
(Griffin, 1953
; Suthers and
Hector, 1982).
When analysed by conventional sonagraphic methods based on Fourier
decomposition, short-duration impulsive clicks appear to contain a wide range
of frequencies, some of which may lie outside the animal's range of
sensitivity. Since the total energy content of the click is limited, this
spreading of energy into inaudible frequencies would further degrade the
detectability of the echo. However, Fourier methods are not well suited to the
analysis of brief time-limited signals, because the technique confounds
frequency components of the emitted carrier frequency with frequency
decomposition of an amplitude envelope, and the apparent wide bandwidth may be
artefactual. Fourier methods can be extended to be applied to time-limited
signals by employing a range of windowing functions (e.g. short-term Fourier
transform; Vetterli and Kovacevic,
1995); one of the more appropriate windows is the Gaussian, but
others are available. However, as with all Fourier methods, the resolution of
the carrier frequencies is constrained by the sampling frequency;
short-duration signals may not contain sufficient samples to allow the
spectral information of carrier frequencies to be determined reliably, and
amplitude transients can dominate the frequency spectrum of short-duration
signals. An alternative to Fourier methods is wavelet decomposition, in which
case the Gaussian-envelope MorletGabor wavelet
(Vetterli and Kovacevic, 1995
)
could be used. The initial choice of basis function in wavelet analysis is
usually arbitrary unless there are a priori reasons to select a
specific basis function type. Different basis functions may be tried until the
required level of resolution and/or signal characteristics are revealed. As an
alternative approach to both fast Fourier transform (FFT) analysis and wavelet
decomposition, we adopt here a related technique that has previously been
applied to the very short duration clicks of dolphins: this is to fit a Gabor
function of arbitrary frequency and other parameters to the sampled signals
(Lanen and Kamminga, 1988
;
Kamminga and Beitsima, 1990
).
In this analysis, we fit a specific function to the captured signals, as there
are good a priori reasons for so doing related to the inverse
relationship between the duration of a signal and its bandwidth. A Gabor
function consists of a constant-frequency carrier enveloped by a Gaussian
amplitude term. An appropriate choice of carrier frequency and Gaussian width
can represent a signal containing few pressure amplitude peaks, as is the case
in dolphins and in R. aegyptiacus. Uniquely this signal has a power
spectrum that is also modulated by a Gaussian envelope, centred on the carrier
frequency, and has a minimum time-bandwidth product that conveys advantages
for sonar detection (Wiersma,
1988
). If R. aegyptiacus signals can realistically be
approximated in this way, then the technique should give more meaningful
estimates of signal properties in the frequency domain than can Fourier
methods.
The expectation that a Gabor function might approximate the signals is not
based solely on a perceived similarity in waveform. Signals with a Gaussian
envelope are potentially of great importance to animals using short-duration
impulsive clicks since they have the minimum bandwidth for any given duration,
they minimize frequencies transmitted in unfavourable bands away from the
carrier frequency, and they also minimize detection ambiguity of signals in
space and time (Vetterli and Kovacevic,
1995). By reducing the energy in signals and echoes outside the
animal's best frequency of hearing, and concentrating energy into the most
sensitive range, a bat using a signal of this type should improve the chances
of detection. It is also more likely to be able to measure the start time of
the returning echo, and thus should have a more accurate ranging ability.
Additionally, focussing the energy into a limited bandwidth will increase the
energy per unit frequency, with a subsequent increase in the signal-to-noise
ratio within each critical band, further enhancing detection
(Zwicker et al., 1957
).
Experiments that have measured the total energy content of Microchiropteran
signals have shown that the energy is distributed across the duration of the
signal (Waters and Jones,
1995). It should be predicted, therefore, that for click sonar to
be effective with comparable distances and targets, each click should be
comparable in energy content with that of a Microchiropteran, but the short
duration of a click signal would necessitate much higher peak amplitude to
maintain energy content. Given the previous lack of accurate data on the
waveform structure of R. aegyptiacus clicks it is crucial that
measurements of amplitude, energy, duration and peak frequency are made, to
determine whether R. aegyptiacus signals are like those of other
terrestrial animals using broadband clicks or are more similar to those of
dolphins. Accurate measurements will also allow the modelling of signals by
Gabor functions, to determine whether, like dolphins, R. aegyptiacus
clicks minimise bandwidth for any given duration.
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Materials and methods |
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Waveform structure and signal intensity
Measurements were made using '' microphones (Larson Davis
2520; Provo, UT, USA) with the protective grid removed (±4 dB
20100 kHz). The signals were recorded in a flight corridor (length 25
m, height 2.59 m, width 1.45 m) that was unfamiliar to the bats upon their
first release. Signals were recorded using a symmetrical star array of four
microphones oriented perpendicular to the flight path. The array resembled a
letter Y with each arm 42.5 cm long and separated by an angle of 120° with
one microphone in the centre. The bats were released facing directly towards
the array at a distance 7 m from it, and recording was triggered
simultaneously. The signals were recorded with all lights in the corridor off
and light levels were measured at 0.0002 mW m2 using a
Tektronix J16 Digital Photometer (Beaverton, OR, USA) (effectively complete
darkness). Data were captured at 12 bits at a rate of 300 kHz on a Keithley
Metrabyte kPCI 3110 A/D board (Cleveland, OH, USA) mounted in a PC. The
microphone was calibrated using a 1411E calibrator (Dawe Instruments, London,
UK). At least five signal trains from separate runs were recorded for each
bat. Data files collected were converted to WAV format and analysed using Cool
Edit Pro© software (Syntrillium Software; San Jose, CA, USA). For signal
duration, ten signals were analysed for each bat. Mean click duration was
measured as the point at which amplitude had reduced to less than 10% of its
maximum intensity, as this provided the most consistent estimate of signal
duration before the amplitude of the signal became indistinguishable from
fluctuations in the noise floor. Inter-click pair interval was measured, and
frequency at the peak amplitude was estimated by a 512 point FFT with Hanning
window.
The range of the bat was determined using the methodology of Aubauer
(1995) as modified by Au and
Herzing (2003
), by measuring
the time of arrival difference between the centre and the other three
microphones. If the difference in arrival time is denoted as
0i, where the three microphones are represented as i=1, 2 and
3, then the range R can be expressed as:
![]() | (1) |
All sound pressure levels are expressed as peak-equivalent (dB peSPL)
values after Stapells et al.
(1982).
To calculate intensity at 1 m (source level) a regression of distance on
intensity was performed from the data. As many signals as were available for
each of the five bats and conformed to the criterion defined above were
included in the intensity regression. Intensity I at range R
is given by the power P per unit area. The area over which the power
is distributed is expected to conform to the spherical spreading law for
transmission loss so that
![]() | (2) |
![]() | (3) |
Sound level S is expressed on a decibel scale as 10 times the
logarithm of sound intensity at distance R (m) compared to intensity
at distance 1 m, and following Equation
3 can be evaluated as:
![]() | (4) |
The measured relationship between sound level and intensity was tested against the predicted values derived from this equation (though there would be additional extra losses through excess atmospheric attenuation that may be frequency-dependent).
Energy flux density
The energy flux density E is a measure of the energy content of a
sound pulse at 1 m from the source, assuming the source is isotropic. Au
(1993) defined E in a
form compensated for the density of the medium as:
![]() | (5) |
Modelling a Gabor function
Preliminary analysis suggests that the echolocation signals of R.
aegyptiacus are brief and intensely amplitude-modulated, with either a
uniform frequency or a slow frequency sweep. Such signals are not amenable to
conventional Fourier or sonagraphic analysis because of the relatively poor
frequency information available owing to the brevity of the signals (and
correspondingly low number of samples), and potential cross talk between
frequency information in the signal envelope and the signal frequency itself.
Typically, sonographic analysis resolves the signals simply as broadband
clicks with poorly determined frequency structure. To better understand the
frequency content and duration of such signals, they are compared to an
idealised Gabor function where frequency and temporal parameters can be
extracted directly.
For any given signal duration, the minimum bandwidth is achieved using a
Gabor function, in which the carrier frequency is modulated by a Gaussian
envelope. The real zero-centred Gabor function G(t) is
written:
![]() | (6) |
![]() | (7) |
![]() | (8) |
Suppose that an experimental signal has been digitized at sampling
frequency fs as:
![]() | (9) |
![]() | (10) |
![]() | (11) |
Gabor functions modelling the real data were generated by determining the
values of a, f, and
that minimize
s2e with the solver function in Microsoft
Excel, using the Generalized Reduced Gradient (GRG2) method. Starting
estimates of the parameters a, f,
and
were extracted
from real signals using custom functions written within Testpoint.
Ten signals from each bat were analysed and the fit between the sampled
signal and the estimated Gabor function was then tested by cross-correlation.
The frequency f of the carrier wave extracted by the Gabor model
should be equivalent to the frequency at peak amplitude of the click; the
duration tc of the Gabor modelled click, determined by the
times at which the envelope amplitude exceeds 10% of its maximum, satisfies
etc2/42=0.1 and can be
calculated as:
![]() | (12) |
The Fourier transform
![]() | (13) |
![]() | (14) |
![]() | (15) |
By substituting G(t) from
Equation 7 into
Equation 5 the signal energy flux
density E for a Gabor model can be evaluated as:
![]() | (16) |
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Results |
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Signal intensity and energy
Fig. 2 shows a logarithmic
regression of signal sound level S=10logI against distance
from the target. The regression line
S=24.27logR+89.92 (r2=0.717) is
not significantly different (t200=0.12,
P>0.05) from the predicted line
S=20logR+88.05 (in which 20 is the theoretical slope
for spherical spreading from Equation
4) and 88.05 dB peSPL is the intensity at 1 m generated from the
idealised fit of the data equivalent to 108.05 dB peSPL at 10 cm).
Fig. 3 shows a scatter plot of
source level 1 m from the bat plotted as a function of the range from the
microphone array. If the bats are signalling at a source level that is
constant regardless of the distance from the target, a level response would be
expected, i.e. S=0.logR+C for constant intensity
C=88.05. The fitted regression
S=4.27logR+89.92 (r2=0.073) shows
no significant difference from this prediction (t200=0.12,
P>0.05). Table 2
shows measured amplitude and estimated energy for each bat.
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Gabor function
Representative Gabor function models compared with the sampled waveform,
together with the error between the two, are shown in
Fig. 4. A good fit to the
earlier portion of the bat signal is obtained in each case, although there may
be as few as three pressure peaks present, and cross correlations between the
sample waveform and the Gabor function is greatest at time offset=0 in all
signals analyzed. The Gabor function does not capture the quasi-regular low
amplitude oscillations that follow the main portion of the signal, however.
Comparison of the error between signal and Gabor function suggests that
including the first harmonic gives a better fit using the mean square error
estimate, and the FFT of the Gabor signal more closely matches the FFT of the
actual signal when the first harmonic is included with amplitude of 12% of the
carrier amplitude (Fig. 4C).
Fig. 5 shows representative
signals from bat 1 and their associated Gabor functions including the first
harmonic. Comparison of the duration and peak frequency estimated by
Fourier-based sonagraph methods with duration and carried frequency estimated
by the Gabor model shows that there is a significant difference in both cases
(REML Variance Components Analysis; duration: response = duration; treatment =
FFT vs Gabor; random term = individual; Wald statistic
2=574.31, d.f.=1, P<0.001; Frequency: response =
frequency; treatment= FFT vs Gabor; random term = individual; Wald
statistic
2=12.13, d.f.=1, P<0.001). The energy of
the Gabor function was estimated from
Equation 16 and is reported in
Table 2. Comparison of the
energy derived from the integral of the waveform and that derived from the
Gabor fit showed no significant difference (REML Variance Component Analysis:
response = log energy; treatment = FFT vs Gabor; random term =
individual; Wald statistic
2=1.46, d.f.=1,
P>0.05).
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Discussion |
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Dolphin signals have been modelled successfully using a Gabor function
(Kamminga, 1988;
Wiersma, 1988
). This
theoretical model for signal structure is expected to be realistic for
short-duration signals since it provides the minimum spread of frequencies,
thus minimising energy outside the animals audiogram of best frequencies,
focuses energy into fewer critical bands
(Vetterli and Kovacevic,
1995
), and has the minimum time-bandwidth product, which has
implications for the sonar detection model used (Urkovitz, 1967). Here we make
the assumption that the signals we record are optimised for echolocation alone
and do not also serve a secondary function such as communication. The Gabor
model applied to R. aegyptiacus signals provides an excellent match
with the part of the signal that contains the majority of the energy, and most
of the error occurs in the smaller oscillations seen afterwards. It is unclear
whether these are a significant part of the signal that is in some way
employed in signal detection, or is a function of constraints on the signal
production method. The signal durations calculated from the Gabor models are
significantly shorter than those of the actual signal, due to the fact that
the Gabor model does not capture these oscillations. There is also a
significant difference in the peak frequency of the Gabor model when compared
to Fourier estimates. This is not unexpected, since Fourier techniques are not
good models of spectral information for short-duration signals (see
Introduction). Cross-correlation shows that there is good agreement between
signal and model, so it seems that the echolocation signals of R.
aegyptiacus conform well to a Gabor model and are thus well designed to
contain the minimum bandwidth for the given duration. Such a structure will
ensure that most energy within the returning echo is focussed within the
animal's region of highest hearing sensitivity, and additionally is focussed
into fewer critical bands, with a subsequent increase in signal-to-noise ratio
and an increased chance of signal detection. An audiogram by Koay et al.
(1998
) reported this region of
high sensitivity to be between 8 and 45 kHz. The peak frequencies reported
here fall within this region. Audiograms of bats may, however, show
sensitivity to other frequency ranges that are not used for echolocation, such
as social calls (Bohn et al.,
2004
) and passive prey localisation
(Heffner et al., 2003
).
However, in R. aegyptiacus maximising detection through a good match
between signal and hearing may be especially important due to the very brief
nature of the signals and their low energy content.
The peak amplitude of signals is comparable to measurements of
Microchiropteran bats recorded in the laboratory, but the energy flux density
of R. aegyptiacus clicks in the range
27x108 J m2 is an order of
magnitude smaller than that of laboratory-based microbat echolocation signals
in most cases (in the region of 107 J m2;
Waters and Jones, 1995).
Cetacean echolocation signals have amplitudes in the region of 200 dB SPL
(Au, 1993
). Energy flux density
is a more meaningful comparison, however, since this allows for the impedance
of the medium and the duration of the signal. Au
(1993
) reports that
Tursiops truncatus has an energy flux density in the region of 8
x103 J m2 but that all other
cetacean species studied have similar energy flux density to microbats, of the
order of 107 J m2. The low energy flux
density of R. aegyptiacus clicks is due to their much shorter
duration when compared to microbat signals. The recordings were made under
laboratory conditions and some studies have shown that Microchiropteran bats
use much higher intensity calls in the field
(Surlykke and Moss, 2000
;
Holderied and Helversen,
2003
). However, the energy flux density measurements comparing
R. aegyptiacus and microchiropterans are all laboratory based studies
so it seems likely that the signals of R. aegyptiacus do indeed
contain relatively little energy. The lower energy content should make echoes
of R. aegyptiacus clicks harder to detect than echoes of microbat
echolocation signals.
In addition to the relatively low energy content of the signals, the
detection of impulsive echoes may be compounded by the relatively long
duration of mammalian integrating time constants (ITC). The integration time
of an auditory system is the duration over which acoustic energy is summed
(Plomp and Bouman, 1959). The
ITC is the duration at which a pure tone pulse is detected or the duration at
which two click stimuli can be discriminated
(Zwislocki, 1960
). The length
of the time constant depends on the method used. If a pure tone is used then
the ITC is relatively long compared to a method in which the separation of two
click stimuli is detected. Using the tone pulse paradigm, Suthers and Summers
(1980
) demonstrated a time
constant of 15 ms in R. aegyptiacus. In microbats and dolphins, if
the double click paradigm is used, then a shorter constant is obtained (220
µs in Megaderma lyra, Wiegrebe
and Schmidt, 1996
; 264 µs in Tursiops truncates;
Au et al., 1988
). However, it
remains to be seen whether R. aegyptiacus has a shorter integrating
time constant with this method. Nevertheless, the short duration of click
stimuli produced by R. aegyptiacus is below the ITC values so far
recorded, and unless it is markedly shorter for a signal of the type now
measured the echo of such a stimulus is likely to be difficult to detect. Even
if the ITC values of bats and dolphins are comparable, dolphins still have an
advantage in echo detection over bats by virtue of their impedance matching to
their environment.
The source level of the signals remains constant with decreasing distance.
Although we cannot be entirely certain that the bats were ensonifying the
microphone array, it presented a large target that the bats had to avoid, and
on some occasions would collide with. There was no modulation of source level
with distance when the array was placed at the end of the corridor right
against the entrance doors (R. A. Holland, D. A. Waters and J. M. V. Rayner,
unpublished). Thus these bats are unlike dolphins and Microchiroptera, which
modulate signal amplitude, decreasing it with decreasing distance to the
target (Au and Benolt-Bird,
2003; Hartley,
1992
). This is thought to have the effect of achieving automatic
gain control to optimise signal-to-noise ratio over all target distances. The
Microchiropteran bat Eptesicus fuscus has also been shown to have an
additional automatic gain control mechanism: it increases the sensitivity of
its hearing as a function of time from emission of the echolocation signal,
rather than by modulating signal amplitude
(Simmons et al., 1992
). Given
that the signals are similar in amplitude to those of Microchiropterans,
R. aegyptiacus might be predicted to have some mechanism to achieve
automatic gain control, as this would allow them to signal at high amplitude
at further distances, while reducing the amplitude at nearer distances to
optimise signal to noise ratio. This effectively increases the dynamic range
of the sonar system. Although R. aegyptiacus does not have
specialised ear muscles to achieve self-deafening, they do have highly mobile
pinnae, and preliminary high-speed video analysis suggests that these move in
a highly regulated fashion that corresponds with click emission (R. A. Holland
and D. A. Waters, unpublished). Further analysis is required to discover
whether these ear movements function to self deafen and/or control gain. If
R. aegyptiacus do not use automatic gain control then they would be
forced to compromise. They could signal at the highest amplitude at which no
signal distortion or forward masking would occur at short distance to the
target, but this would reduce the range of the echolocation system.
Alternatively, they could signal at the maximum amplitude available, which
would reduce accuracy at short distance due to distortion and forward masking
of early returning echoes. Given the relatively low energy content of these
impulses, if they chose the former, this would add further constraints on the
effective range of the echolocation system of R. aegyptiacus.
The results of this study indicate that the impulse clicks of R. aegyptiacus are very short in duration and similar in length to the clicks of cetacean bio-sonar than to those of other terrestrial vertebrates using comparable mechanisms. As for cetaceans, a Gabor function, which contains the minimum bandwidth for the frequencies present and therefore avoids spreading energy into bands outside the frequencies of best hearing, is a good model for the signal. However, the relatively low energy content of the signals, coupled with the mismatch between the integrating time constant and the click stimulus of these animals, may make the echoes of these clicks hard to detect. Impulse bio-sonar remains a difficult system to use in air and the performance of this animal in obstacle avoidance experiments using echolocation continues to provide something of a conundrum.
List of symbols
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Acknowledgments |
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References |
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