2 Simmons 
Acoustic-Imaging Computations by Echolocating Bats: 
Unification of Diversely-Represented Stimulus 
Features into Whole Images. 
James A. Simmons 
Department of Psychology 
and Section of Neurobiology, 
Division of Biology and Medicine 
Brown University, Providence, RI 02912. 
ABSTRACT 
The echolocating bat, Eptesicus fuscus, perceives the distance to 
sonar targets from the delay of echoes and the shape of targets 
from the spectrum of echoes. However, shape is perceived in 
terms of the target's range profile. The time separation of echo 
components from parts of the target located at different distances 
is reconstructed from the echo spectrum and added to the 
estimate of absolute delay already derived from the arrival-time 
of echoes. The bat thus perceives the distance to targets and 
depth within targets along the same psychological range 
dixnension, which is computed. The image corresponds to the 
crosscorrelation function of echoes. Fusion of physiologically 
distinct time- and frequency-domain representations into a fmal, 
common time-domain image illustrates the binding of within- 
modality features into a unified, whole image. To support the 
structure of images along the dimension of range, bats can 
perceive echo delay with a hyperacuity of 10 nanoseconds. 
Acoustic-Imaging Computations by Echolocating Bats 3 
THE SONAR OF BATS 
Bats are flying mammals, whose lives are largely noctumal. They have evolved 
the capacity to orient in darkness using a biological sonar called echolocation, 
which they use to avoid obstacles to flight and to detect, identify, and track flying 
insects for interception (Griffin, 1958). Echolocating bats emit brief, mostly 
ultrasonic sonar sounds and perceive objects from echoes that return to their ears. 
The bat's auditory system acts as the sonar receiver, processing echoes to 
reconstruct images of the objects themselves. Many bats emit frequency- 
modulated (FM) signals; the big brown bat, Eptesicus fuscus, transmits sounds 
with durations of several milliseconds containing frequencies from about 20 to 
100 kltz arranged in two or three harmonic sweeps (Fig. 1). The images that 
Eptesicus ultimately perceives retain crucial features of the original sonar wave- 
100[ 
, 60 
' 40 
g . 
2 
I msec 
Figure 1: Spectrogram of a 
sonar sound emitted by the 
big brown bat, Eptesicus 
fuscus (Simmons, 1989). 
forms, thus revealing how echoes are processed to reconstruct a display of the 
object itself. Several important general aspects of perception are embodied in 
specific echo-processing operations in the bat's sonar. By recognizing constraints 
imposed when echoes are encoded in terms of neural activity in the bat's auditory 
system, recent experiments have identified a novel use of time- and frequency- 
domain techniques as the basis for acoustic imaging in FM echolocation. The 
intrinsically reciprocal properties of time- and frequency-domain representations 
are exploited in the neural algorithms wlfich the bat uses to unify disparate 
features into whole images. 
IMAGES OF SINGI,E-GLINT 'FARGETS 
A simple sonar target consists of a single reflecting point, or glint, located at a 
discrete range and reflecting a single replica of the incident sonar signal. A 
complex target consists of several glints at slightly different ranges. It thus reflects 
compound echoes composed of individual replicas of the incident sound arriving 
4 Simmons 
at slightly different delays. To determine the distance to a target, or target range, 
echolocating bats estimate the delay of echoes (Sinmons, 1989). The bat's image 
of a single-glint target is constructed around its estimate of echo delay, and the 
shape of the image can be measured behaviorally. The performance of bats 
trained to discriminate between echoes that jitter in delay and echoes that are 
stationary in delay yields a graph of the hnage itself (Altes, 1989), together with 
an indication of the accuracy of the delay estimate that underlies it (Simmons, 
1979; Simmons, Ferragamo, Moss, Stevenson, & Altos, in press). Fig. 2 shows 
Jitter Performance 
Crasscorrelatian Function 
-50 -40 -30 -20 -tO 0 tO 20 30 40 50 
Time (m,croseconds) 
e--e / j ' ' 'x./ \ 
-0-;'0-50-0-;0 6 1'0 2'0 3'0 i0 5'0 
Time (microseconds) 
Figure 2: Graphs showing the bat's image of a single-glint target 
from jitter discrimination experhnents (left) for comparison with 
the crosscorrelation function of echoes (riglt). The zero pabst 
on each tine axis corresponds to the objective arrival-time of the 
echoes (about 3 msec in this experiment; Sinmons, Ferragamo, 
et al., in press). 
the image of a single-glint target perceived by Eptesicus, expressed in terms of 
echo delay (58 gsec/cm of range). From the bat's jitter discrimination 
performance, the target is perceived at its true range. Also, the image has a fine 
structure consisting of a central peak corresponding to the location of the target 
and two prominent side-peaks as ghost images located about 35 [tsec or 0.6 cxn 
nearer and farther than the main peak. This image fme structure reflects the 
composition of the waveform of the echoes themselves; it approximates the 
crosscorrelation function of echoes (Fig. 2). 
The discovery that the bat perceives an image corresponding to the cross- 
correlation function of echoes provides a view of the hidden machinery of the 
bat's sonar receiver. The bat's estimate of echo delay evidently is based upon a 
capacity of the auditory system to represent virtually all of the information 
available in echo waveforms that is relevant to determining delay, including the 
phase of echoes relative to emissions (Simnons, Ferragamo, et al, in press). The 
bat's initial auditory representation of these FM signals resembles spectragrams 
Acoustic-Imaging Computations by Echolocating Bats 5 
that consist of neural impulses marking the time-of-occurrence of successive 
frequencies in the FM sweeps of the sounds (Fig. 3). Each nerve im- 
8O 
6O 
 50 
-- 40 
25 
2O 
15 
150 
120 
IO0 
'; 
,. 
o 
I I 
5 
time (msec) 
Figure 3: Neural spectrograms 
representing a sonar emission 
(left) and an echo from a target 
located about 1 m away (fight). 
The individual dots are neural 
impulses conveying the 
instantaneous frequency of the 
FM sweeps (see Fig. 1). The 6- 
msec time separation of the two 
spectrograms indicates target 
range in the bat's sonar receiver 
(Simmons & Kick, 1984). 
pulse travels in a "channel" that is tuned to a particular excitatory frequency 
(Bodenhamer & Pollak, 1981) as a consequence of the fi'equency analyzing 
properties of the cochlea.. The cochlear filters are followed by rectification and 
low-pass filtering, so in a conventional sense the phase of the filtered signals is 
destroyed in the course of forming the spectrograms. Itowever, Fig. 2 shows that 
the bat is able to reconstruct the crosscorrelation function of echoes from its 
spcctrogram-like auditory representation. The individual neural "oints"in the 
spectrogram signify instantaneous frequency, and the recovery of the fme 
structure in the image may exploit properties of instantaneous frequency when 
the images are assembled by integrating numerous separate delay measurements 
across different frequencies. The fact that the crosscorrelation function emerges 
from these neural computations is provocative from theoretical and technological 
viewpoints--the bat appears to employ novel real-time algorithms that can 
transform echoes into spectrograms and then into the sonar ambiguity function 
itself. 
The range-axis image of a single-glint target has a fine structure surrounding a 
central peak that constitutes the bat's estimate of echo tielay (Fig. 2). The width 
of this peak corresponds to the liniting accuracy of the bat's delay estimate, 
allowing for the ambiguity represented by the side-peaks located about 35 pscc 
away. In Fig. 2, tile data-points are spaced 5 psec apart along the time axis 
(approximately the Nyquist smnpling interval for the bat's signals), aid the true 
width of the central peak is poorly shown. Fig. 4 shows the performance of three 
Eptesicus in an experiment to measure Illis width with smaller delay steps. The 
6 Simmons 
loo 
9o 
õ 80 
- 70 
 60 
 o 
0 5 10 15 20 25 30 25 40 45 50 55 60 
Tme (nanoseconds) 
Figure 4: A graph of the 
performance of Eptesicus 
discriminating echo-delay 
jitters that change in small 
steps. The bats' limiting 
acuity is about 10 nsec for 
75 % correct responses 
(Simmons, Ferragamo, et al., 
in press). 
bats can detect a shift of as little as 10 nsec as a hyperacuity (Altes, 1989) for 
echo delay in the jitter task. In estimating echo delay, the bat must integrate 
spectrogram delay estimates across separate frequencies in the FM sweeps of 
emissions and echoes (see Fig. 3), and it arrives at a very accurate composite 
estimate indeed. Timing accuracy in the nanosecond range is a previously 
unsuspected capability of the nervous system, and it is likely that more complex 
algorithms than just integration of information across frequencies lie behind this 
fine acuity (see below on amplitude-latency trading and perceived delay). 
IMAGES OF TWO-GLINT TARGETS 
Complex targets such as airborne insects reflect echoes composed of several 
replicas of the incident sound separated by short intervals of time (Simmons & 
Chen, 1989). For insect-sized targets, with dimensions of a few centimeters, this 
time separation of echo conponents is unlikely to exceed 100 to 150 [zsec. 
Because the bat's signals are several milliseconds long, the echoes from complex 
targets thus will contain echo components that largely overlap. The auditory 
system of Eptesicu, has an integration-time of about 350 lzsec for reception of 
sonar echoes (Simmons, Freedman, et aL, 1989). Two echo components that 
arrive together within this integration-time will merge together into a single 
compound echo having an arrival-time as a whole that indicates the delay of the 
first echo component, and having a series of notches in its spectrum that indicates 
the time separation of the first and second components. In the bat's auditory 
representation, echo delay corresponds to the time separation of the enission and 
echo spectrograms (see Fig. 3), while the notches in the compound echo 
spectrum appear as "holes" in the spectrogram--that is, as frequencies that fail to 
appear in echoes. The location and spacing of these notches or holes in 
frequency is related to the separation of the two echo components in time. The 
crucial point is that the constraint inposed by the 350-[tsec integration-time for 
echo reception disperses the information required to reconstruct the detailed range 
Acoustic-Imaging Computations by Echolocating Bats 7 
structure of the complex target into both the time and the frequency dimensions 
of the neural spectrograms. 
Eptesicus extracts an estimate of the overall delay of the waveform of compound 
echoes from two-glint targets. This time estimate leads to a range-axis image of 
the closer of the two glints in the target (the target's leading edge). This part of 
the image exhibits the same properties as the image of a single-glint target--it is 
encoded by the time-of-occurrence of neural discharges in the spectrogrmns and it 
resembles the crosscorrelation function for the first echo component (Simmons, 
Moss, & Ferragamo, 1990; Simnons, Ferragamo, et al., in press; see Simmons, 
1989). The bat also perceives a range-axis image of the thrthcr of the two glints 
(the target's trailing edge). This inage is located at a perceived distance that 
corresponds to the baffs estimate of the time separation of the two echo 
components that make up the compound echo. Fig. 5 shows the performance of 
Eptesicus in a jitter discrimination experiment in wlfich one of the 
a + a 
a a' 
3ø r- )[ 
I I I i i I I 
0 20 40 
t,me (psec) 
Figure 5: A graph comparing 
the crosscorrelation function of 
echoes from a two-glint target 
with a delay separation of 10 
pscc (top) with the baVs jitter 
discrimination performance 
using ttfis compound echo as a 
stimulus (bottom). The two 
glints are indicated as a 1 and 
a 1' (Simmons, 1989). 
jittering stitnulus echoes contained two replicas of the bat's emitted sound 
separated by 10 psec. The bat perceives two distinct reflecting points along the 
range axis. Both glints appear as events along the range axis in a time-domain 
image even thougl the existence of the second glint could only be inferred from 
the frequency domain because the delay separation of 10 psec is much shorter 
than the receiveds integration thne. The image of the second glint resembles the 
crosscorrelation function of the later of the two echo components. The bat adds 
it to the crosscorrelation function for the earlier component when the whole 
image is formed. 
8 Simmons 
ACOUSTIC-IMAGE PROCESSING BY FM BATS 
Somehow Eptesicus recovers sufficient information from the timing of neural 
discharges across the frequencies in the FM sweeps of emissions and echoes to 
reconstruct the crosscoxelation function of echoes from the first glint in the 
complex target and to estimate delay with nanosecond accuracy. This 
fundamentally time-domain image is derived fr(nn the processing of information 
initially also represented in the time domain, as demonstrated by the occurrence 
of changes in apparent delay as echo amplitude increases or decreases: The 
location of the perceived crosscorrelation function for the first glint can be shifted 
by predictable amounts along the time axis according to the separately-measured 
amplitude-latency trading relation for Eptesicus (about -17 [tsec/dB; Simmons, 
Moss, & Ferragamo, 1990; Simmons, Ferragamo, et al., in press), indicating that 
neural response latency--that is, neural discharge timing--conveys the crucial 
information about delay in the bat's auditory system. 
The second glint in the complex target manifests itself as a crosscorrelation-like 
image component, too. Itowever, the bat must transform spectral information 
into the time domain to arrive at such a time- or range-axis representation for the 
second glint. This transformed time-domain image is added to the time-domain 
image for the first glint in such a way that the absolute range of the second glint 
is referred to that of the first glint. Shifts in the apparent range of the first glint 
caused by neural discharges undergoing amplitude-latency trading will carry the 
image of the second glint along with it to a new range value (Simmons, Moss, & 
Ferragamo, 1990). Evidently, the psychological dimension of absolute range 
supports the image of the target as a whole. This helps to explain the bat's 
extraordinary 10-nsec accuracy for perceiving delay. For the psychological range 
or delay axis to accept fine-grain range information about the separation of glints 
in complex targets, its intrinsic accuracy must be adequate to receive the 
information that is transformed from the frequency domain. The bat achieves 
fusion of image components by transforming one component into the nmnerical 
format for the other and then adding them together. The experimental 
dissociation of the inages of the first and second glints from different effects of 
latency shifts demonstrates the independence of their initial physiological 
representations. Furthermore, the expected latency shift does not occur for 
frequencies whose amplitudes are low because they coincide with spectral 
notches; the bat's fine nanosecond acuity thus seems to involve removal of 
discharges at "untrustworthy" frequencies prior to integration of discharge timing 
across frequencies. The delay-tuning of neurons is usually thought to represent 
the conversion of a temporal code (timing of neural discharges) into a "place" 
code (the location of activity on the neural map). The bat's unusual acuity of lO 
nsec suggests that this conversion of a temporal to a "place" code is only partial. 
Acoustic-Imaging Computations by Echolocating Bats 9 
Not. only does the site of activity on the neural map convey information about 
delay, but the timing of discharges in map neurons may also play a critical role in 
the map-reading operation. The bat's free acuity may emerge in the behavioral 
data because initial neural encoding of the stimulus conditions in the jitter task 
involves the same paraxneter of neural responses--timing--that later is intimately 
associated with map-reading in the brain. Echolocation may thus fortuitously be 
a good system h which to explore this basic perceptual process. 
Acknowledgments 
Research supported by grants frown ONR, NIIt, NIMH, DRF, and SDF. 
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