Echo delay versus spectral cues for temporal hyperacuity in the big

Echo delay versus spectral cues for temporal hyperacuity in the big
J Comp Physiol A (2003) 189: 693–702
DOI 10.1007/s00359-003-0444-9
O R I GI N A L P A P E R
J. A. Simmons Æ M. J. Ferragamo Æ M. I. Sanderson
Echo delay versus spectral cues for temporal hyperacuity
in the big brown bat, Eptesicus fuscus
Received: 3 June 2003 / Revised: 6 June 2003 / Accepted: 19 June 2003 / Published online: 23 July 2003
Springer-Verlag 2003
Abstract Big brown bats can discriminate between echoes
that alternate in delay (jitter) by as little as 10–15 ns and
echoes that are stationary in delay. This delay hyperacuity
seems so extreme that it has been rejected in favor of an
explanation in terms of artifacts in echoes, most likely
spectral in nature, that presumably are correlated with
delay. Using different combinations of digital, analog,
and cable delays, we dissociated the overall delay of jittering echoes from the size of the analog component of
delay, which alone is presumed to determine the strength
of the apparatus artifact. The bats’ performance remains
invariant with respect to the overall delay of the jittering
echoes, not with respect to the amount of analog delay.
This result is not consistent with the possible use of delayrelated artifacts produced by the analog delay devices.
Moreover, both electronic and acoustic measurements
disclose no spectral cues or impedance-mismatch reflections in delayed signals, just time-delays. The absence of
artifacts from the apparatus and the failure of overlap and
interference from reverberation to account for the 10-ns
result means that closing the gap between the level of
temporal accuracy plausibly explained from physiology
and the level observed in behavior may require a better
understanding of the physiology.
Keywords Bats Æ Delay hyperacuity Æ Echo delay Æ
Echolocation Æ Target ranging
Abbreviations FM frequency-modulated Æ XCR
cross-correlation function
J. A. Simmons (&) Æ M. I. Sanderson
Department of Neuroscience, Brown University,
Providence, RI 02912, USA
E-mail: [email protected]
Tel.: +1-401-8631542
Fax: +1-401-8631074
M. J. Ferragamo
Department of Biology, Gustavus Adolphus College,
St. Peter, MN 56082, USA
Introduction
Big brown bats (Eptesicus fuscus) broadcast ultrasonic
frequency-modulated (FM) biosonar sounds and perceive objects from echoes that return to their ears
(Griffin 1958; Grinnell 1995; Neuweiler 2000). They
determine target distance, or range, from echo delay
(5.8 ms m)1 of range). In discrimination experiments—using two-alternative forced choice (2AFC), go/
no-go, or yes/no paradigms—the bat’s thresholds for
perceiving differences in delay are mostly in the range of
40–80 ls (Simmons and Grinnell 1988; Moss and
Schnitzler 1995). However, these thresholds are similar
to the amount of uncertainty in delay introduced by the
bat’s head movements within or between trials, so they
cannot be taken as valid measurements of the bat’s
underlying delay accuracy (Simmons et al. 1995) even
though they are similar to the timing accuracy of responses in individual neurons (Pollak et al. 1977). To
minimize this uncertainty, a new method was developed
in which the arrival-time of echoes is varied (jittered)
from one broadcast to the next over the much shorter
interval between broadcasts rather than from one scan
or one trial to the next (Simmons 1979). Figure 1 illustrates the procedure for the 2AFC version of jitter
experiments (Simmons et al. 1990a). Echoes that alternate in delay are generated by picking up the bat’s sonar
sounds with microphones (m), passing the resulting
electrical signals through electronic delay lines, and then
reconstituting the delayed signals as acoustic echoes
delivered back to the bat from loudspeakers (s). Figure 2
shows the signal path used to create the stimuli. By
electronically switching delay lines from one broadcast
to the next, successive echoes can be made to arrive at
different delays. In experiments of this type, big brown
bats can detect changes in delay of 0.5 ls or less (Simmons 1979; Menne et al. 1989; Moss and Schnitzler
1989). At an echo signal-to-noise ratio of 36 dB, the
smallest detectable change in delay is about 0.04 ls, or
40 ns, and at 49 dB it is about 10 ns (Simmons et al.
694
Fig. 1 Diagram of two-choice paradigm for jittering-echo experiments, showing bat on Y-shaped platform with microphones (m)
and loudspeakers (s) (center), alternating delays of jittering echoes
a and b (left), and fixed delays of alternating stationary or
nonjittering echoes c and d (right). See Simmons et al. (1990a)
1990a). This exceptional sensitivity is termed hyperacuity
for delay by analogy with the concept of hyperacuity in
vision (Altes 1989; Simmons et al. 1990a). Here we
report experimental evidence that the so-called ‘‘10-ns
result’’ cannot be dismissed as due to artifacts, which
suggests that conventional thinking about how the
auditory system manages information about timing
needs to be revised.
Objections to jitter results
It has been asserted that the 10-ns result is impossible—both because bats would have no conceivable
biological purpose for registering submicrosecond
changes in delay and because the thresholds seem too
small for the auditory system to achieve (Pollak 1993;
Beedholm and Møhl 1998; Menne et al. 1989). The result also has been described as impossible for information-theoretical reasons (Beedholm and Møhl 1998), but
in fact the bat’s performance is within the bounds of
delay accuracy for matched-filter reception of sonar
echoes (Simmons et al. 1990a; Sanderson et al. 2003).
First, we take the biological purpose objection. It is
true that the jitter experiment has no acoustic counterpart in nature, but this is true for any scientific experiment because the need to make measurements
Fig. 2 Diagram of acoustic and digital electronic delays for echoes
delivered to the bat in jittering-echo experiments (see Fig. 1).
Microphones and loudspeakers are at distances of 20 cm for
acoustic path-length delay of 580 ls, augmented by digital delay
lines to achieve a total average delay, including air-path and
electronic delay, of 3.275 ms. Jittering echoes (a and b) alternate
between two delays determined by settings on digital delay lines,
which are variable in steps of 1.3 ls. The same system is used to
control delays for stationary echoes (c and d) except that both
electronic delays are fixed at 2,115 ls
necessarily imposes constraints on conditions. The jitter
procedure was never intended to estimate how accurately
the bat uses information about delay for guiding its
flight while chasing insects (for factors influencing delay
estimates in flight, see Boonman et al. 2003). For this
reason the stimuli do not mimic echoes received from
moving targets by flying bats any more than tone-bursts
in frequency discrimination experiments with humans
mimic natural sounds or speech. Instead, the jitter
experiment was designed to measure the intrinsic delay
sensitivity of the bat’s auditory system. The stimulus
configuration emphasizes changes in delay while holding
all other echo parameters constant or irrelevant to
accomplishing the task. Contrary to what is asserted by
critics (Pollak 1993; Beedholm and Møhl 1998), there
has been no claim that the 10-ns result represents the
bat’s ordinary acuity for delay, only its hyperacuity
(Simmons et al. 1990a). Ordinary acuity has been estimated to be of the order of 1 ls from echo-delay resolution results (Simmons et al. 1998), from analysis of
performance in obstacle avoidance and airborne-target
discrimination tests (Simmons et al. 1995, 1996), and
from jitter experiments with echoes shifting over large
intervals of absolute delay while they jitter (Masters et al.
1997). Thus, it is misleading to reject the 10-ns result as
impossible by asserting that it is biologically without
purpose, particularly without reference to the relevant
material.
Second, we take the auditory timing-accuracy
objection, which is twofold. Disbelief about the 10-ns
result is accompanied by disbelief about the other major finding from jitter experiments, which occurs on a
more plausible microsecond, not nanosecond, time
scale. As shown in Fig. 3, when the phase of echoes is
shifted by 0 or 180 while delay is being jittered, big
brown bats perceive the phase shift as equivalent to a
change in delay of about ±15 ls. Moreover, bats easily
discriminate between echoes that have phase shifts of 0
versus 180 (as in Fig. 3) or +90 versus )90 when
delay jitter itself is zero (Menne et al. 1989; Simmons
et al. 1990a; Moss and Simmons 1993). These demonstrations of ‘‘pure’’ phase sensitivity are important
because, at signal-to-noise ratios of 36 or 49 dB, the
bat’s respective jitter thresholds of 40 ns and 10 ns
cannot be achieved without coherent processing of
echoes (Simmons et al. 1990a; Sanderson et al. 2003).
The phase-shift and 10-ns results are collectively
dismissed as being physiologically impossible without
695
Fig. 3 Performance of bats in jitter experiments with changes in
delay derived entirely from digital delay lines making 5-ls delay
steps combined with 0 or 180 change in echo phase for echoes a
and b: Gray curves and circles show mean±standard error of mean
(SEM) for percentage errors by 4 bats (40–60 trials per bat per
point) detecting jitter values from 0 to 50 ls with 0 change in
phase. Black curves and circles show mean±SEM for percentage
errors by 4 bats detecting jitter values from 0 to 50 ls with 180
change in phase
citing any evidence besides a neuroscience textbook
chapter that makes no mention of these phenomena in
bats (Beedholm and Møhl 1998). Because the objections
to both results are linked, they have to be addressed
together to explain why we did the experiments reported here.
Phase sensitivity and the 10-ns result are thought to
be well beyond the capacity of the auditory system to
encode neurally (Menne et al. 1989; Pollak 1993; Beedholm and Møhl 1998). In mammals studied previously,
phase sensitivity for coding of sounds by the inner ear
extends no higher that 1–5 kHz (Weiss and Rose 1988;
Koppl 1997), whereas the big brown bat’s biosonar
sounds are wholly at ultrasonic frequencies. Furthermore, although delay accuracy as small as 0.5 ls is
marginally plausible from present physiological knowledge (Schnitzler et al. 1985), the finding that hyperacuity
may be in the range of tens of nanoseconds goes beyond
any previous conception of the timing accuracy of the
auditory system. Either the bat uses some acoustic cue
other than delay in the jitter experiments, or essential
capabilities of the bat’s auditory nervous system are not
yet appreciated. The former is possible, but the latter is
virtually certain (for relevant aspects of what is unknown in auditory function, see Casseday and Covey
1995; Shamma and Klein 2000). Critical commentary
about the jitter results has focused entirely on the likelihood of artifacts (e.g., Menne et al. 1989; Pollak 1993;
Beedholm and Møhl 1998) without mentioning the need
to examine the bat’s auditory system more carefully,
even though the most important physiological parameter (low-pass smoothing of receptor excitation) for
auditory coding of the time of occurrence of FM sounds
has not even been measured in bats (Simmons 1980).
Applicability of artifact hypothesis to phase result
Evidence for perception of echo phase shifts (0–180 or
±90) and for perception of delay changes from 50 ls
down to about 1 ls comes from jitter experiments that
employ all-digital delay lines (Menne et al. 1989;
Simmons et al. 1990a). These devices introduce no delayrelated changes in echo spectra and thus are not susceptible to possible artifacts of the type potentially
created by analog delay devices (see below). For example, jitter performance curves for 0 and 180 phaseshifted echoes (Fig. 3) are based on data collected for
delay steps of 5–50 ls, and there is scant basis for
claiming that bats cannot perceive 5-, 10-, or 15-ls
changes in delay. The locations of the error peaks in the
curves in Fig. 3 move left or right by ±15 ls, which is a
difference in delay that bats manifestly can detect. The
other source of spectral artifacts is overlap and interference between stimulus echoes and reverberation in the
room. Acoustic measurements show no extraneous
echoes from objects in the room that overlap with the
jittering stimuli inside a critical time window of about
2.5 ms. Bats that use sounds shorter than 2.5 ms
and bats that use sounds longer than 2.5 ms perform
identically, which rules out spectral artifacts derived
from reverberation in the room as a viable explanation
for the results in Fig. 3 (for this and other reasons see
Simmons 1993). The most important fact is that the
locations of the error peaks in Fig. 3—in fact, the entire
shape of the curve for either 0 or 180 phase shift—can
be moved left or right along the delay axis according to
predicted amplitude-latency trading ( )15 ls dB)1;
Simmons et al. 1990a). Big brown bats encode the phaserelated difference in their jitter-detection performance
from corresponding phase-related changes in the latencies of neural responses that jointly register echo arrival
time and phase. The hypothesis that some artifact supplants delay and phase as joint cues for detecting jitter in
steps of 5 ls or changes in phase thus has been rejected
(Simmons 1993). Instead of dwelling on this disproved
hypothesis, physiological parameters already identified
as determining the high-frequency limit for auditory
coding of FM echo phase in relation to delay (Simmons
1980) need to be measured in bats. Computational
modeling of auditory transduction reveals that, contrary
to speculation (Beedholm and Møhl 1998), the most
important factor—the low-pass cutoff frequency for
smoothing the envelopes of excitation delivered to
auditory neurons by hair cells—only has to be in the
range of 8–10 kHz to achieve fully coherent processing
of FM echoes in the 20–100 kHz band (Sanderson et al.
2003).
Applicability of artifact hypothesis to 10-ns result
Delay changes smaller than 0.5–1 ls are produced with
analog delay lines because digital sampling rates of less
than 1 MHz preclude making finer digital adjustments
of delay. Here there is scope for introduction of artifactual changes in echo spectra correlated with delay,
and the artifact hypothesis may be relevant as an alternative explanation for very small jitter thresholds.
696
However, at present, only electronically produced artifacts remain viable as an alternative explanation of the
10-ns result because spectral artifacts caused by acoustic
reverberation have been shown not to explain the results
(Simmons 1993). Differences between channels in passive components, analog electronic switches, or analog
operational-amplifier chips could have produced frequency-dependent changes in gain between jittering
echoes if these variable components were switched along
with delay. However, during system calibration, overall
analog gain differences between channels were nulled
out at 40 kHz using a precision analog voltmeter to reduce those differences to 0.3% (0.03 dB) or less. Following this adjustment, acoustic measurements of the
output of the target simulator showed no frequency
dependence of gain in the apparatus larger than 0.05–
0.1 dB for different amounts of analog delay in the
critical 0- to 50-ns range. Even these spectral differences
are too small to detect in the presence of random spectral
variations caused by the flat-spectrum ultrasonic noise
deliberately added to the echoes to control the signal-tonoise ratio of echoes, which was approximately 49 dB in
the conditions for the 10-ns result (Simmons 1993).
Neither Beedholm and Møhl (1998) nor Pollak (1993)
account for how the 10-ns result could be caused by
these minuscule artifacts in the presence of random noise.
The only remaining source of delay-related artifacts is
the analog delay lines or cables. These devices retard
signals directly by having a propagation-time proportional to electronic length, and they conduct signals
bidirectionally, which makes them susceptible to generation of spurious signals if their input or output
impedances are not matched by the source or load. For
example, if the output impedance of the analog delay
line is not matched by the outgoing load, a reflection of
the original signal is created proportional in strength to
the impedance mismatch, and this reflection travels back
and forth through the delay line to reappear at the
output with an additional delay that is twice the intended delay of the original signal (Beedholm and Møhl
1998). The point of their objection is that the presence of
the thrice-delayed reflection following the once-delayed
signal converts the jitter task into detection of closely
spaced overlapping reflections at different separations.
With regard to this putative artifact, however, Beedholm
and Møhl (1998) give no information about how a 10ns+30-ns pattern of echo delays is any easier for the bat
to perceive than a 10-ns delay change. The bat’s measured two-point resolution is about 1 ls (Simmons et al.
1998), not the 20 ns required to make use of the putative
reflection, which, as it happens, is impossible for information-theoretical reasons at a signal-to-noise ratio of
49 dB (Neretti et al. 2003). Moreover, it is a fact that the
analog delay lines or cables were specifically terminated
by their characteristic impedances (see Materials and
methods). Nevertheless, to test for the presence
of impedance-mismatch reflections using the same display format as Beedholm and Møhl (1998), we made
measurements of delay line impulse responses at a
sampling rate of 0.5 ns using microwave equipment (see
Fig. 5). The waveforms of short (80 ns) pulses delayed
by the analog delay lines or the cables show no evidence
whatsoever for any effect other than delay, so artifacts
derived from impedance mismatches are not present.
As further evidence for their reflection artifacts,
Beedholm and Møhl (1998) cite the presence of small
distortions in the waveshape of a difference signal
(Simmons 1993) computed to calibrate the delay lines.
The method of calibration that yields this difference
signal involved computing cross-correlation functions
(XCRs) between FM test broadcasts and corresponding
FM echoes for the jittering echoes a and b in Fig. 1. The
difference between these XCRs was then determined for
different small changes in delay (e.g., 0–25 ns; see
Fig. 6A), and the resulting waveshape was used to
estimate the difference in delay itself. This roundabout
method was employed because the delay steps in the
jitter experiment (0–50 ns) are very small compared to
the sampling interval (2,000 ns for a 500-kHz sampling
rate) for digitizing the signals prior to computing the
XCRs. The waveshape for the difference function should
approximate a 90 phase-shifted version of the XCR
itself (Simmons 1993; Beedholm and Møhl 1998). As
explained in Materials and methods, Fig. 6A illustrates
the graded emergence of this phase-shifted difference
function from the subtracted XCRs for jitter values of 0,
5, 10, 15, 20, and 25 ns. This plot also shows the level of
noise in the method, which can be used to detect delay
changes less than 10 ns, but not less than 5 ns. Small
variations in a representative XCR difference function
calculated for an 11-ns delay difference (Simmons 1993),
were singled out by Beedholm and Møhl (1998) as evidence for impedance-mismatch reflections. However,
Beedholm and Møhl (1998) did not attempt to use this
method themselves; instead, they simulated it with noisefree XCRs, which unfairly creates a cartoon of the
process, not the process itself. As Fig. 6A shows, variations in the XCR difference functions are caused by the
noise intrinsic to making such small measurements of
delay. To establish whether spectral artifacts are present,
Fig. 6B shows a series of corresponding difference
functions computed for the spectra of echoes a and b at
delay changes of 0–25 ns in 5-ns steps. Examination of
these spectral difference functions reveals the absence of
any delay-related features that emerge as the amount of
jitter increases from 0 to 25 ns. The plots in Fig. 6
demonstrate unambiguously that the jittering echoes
differed only in delay due to the action of the analog
delay lines, with no added reflections and no differences
in their spectra, so the apparatus artifact hypothesis is
rejected.
Alternative method for detecting whether apparatus
artifacts are present
At the time the jitter experiments were carried out, the
microwave equipment was unavailable for direct mea-
697
surements of nanosecond delays, so we designed and
carried out ‘‘dissociation’’ experiments specifically to
deal with the possibility of spectral artifacts in the delay
lines that were not detected by our calibration procedures but might nevertheless be present in the sounds
reaching the bat’s ears. These were not done specifically
to control for the Beedholm and Møhl (1998) artifact,
but nevertheless that is one of several delay-related
artifacts covered by the outcome of the dissociation
experiments. The overall arrival time of echoes at the
bat’s ears is due to all the factors shown in Fig. 2. We
produced jittering stimuli with different combinations of
digital and analog delays, and then we observed whether
the bats responded according to the overall delay of
echoes or just to the analog delays which would produce
the putative artifacts.
Materials and methods
Jitter procedure
The animals in our experiments were big brown bats, E. fuscus
(Chiroptera: Vespertilionidae; see Kurta and Baker 1990), obtained
as adults from the attics of houses in Rhode Island. Figure 1 shows
the experimental paradigm we used for studying the accuracy of
echo-delay perception. The procedure (center of Fig. 1) is to
present the bat with echoes of its sonar broadcasts that either jitter
in delay from one broadcast to the next (left side of Fig. 1) or are
stationary in delay (right side of Fig. 1) and to determine the
smallest amount of jitter (Dt) which the bat can detect. (See Simmons et al. 1990a and Simmons 1993 for details about apparatus
and methods.) Each bat was trained to sit on an elevated Y-shaped
platform (shaded in Fig. 1) and broadcast sonar sounds into two
Bruel and Kjaer Model 4138 condenser microphones (m) located
approximately 10 cm (Fig. 4C, D) or 20 cm (Fig. 4A, B) from the
bat’s position, one on the bat’s left and one on the right. The
signals produced by the microphones were led to delay lines, and
the delayed signals were returned to the bat as artificially generated
echoes delivered from corresponding RCA type 112343 electrostatic loudspeakers (s) located next to the microphones and also
10 cm or 20 cm away from the bat. (Calculations of delay below
are based on a nominal 10-cm or 20-cm distance from the bat to the
microphones and from the loudspeakers back to the bat; actual
distances varied according to the bat’s position; see Fig. 4.) The
electronic apparatus which picked up the bat’s broadcasts, delayed
them, and determined whether the left or the right loudspeaker was
to be activated, constitutes a dual-channel target simulator. The
angle separating the microphone/loudspeaker assemblies (m, s) on
the left and right was 40. The effective bandwidth of the system
was about 20 to 80 kHz, with reduced output especially at
frequencies from 80 to 100 kHz. Variations between channels depended on the loudspeakers and ranged from zero to as much as
±1 to ±4 dB depending on frequency (Simmons et al. 1990a).
Psychophysical data on detection of jittering echoes were collected with a 2AFC procedure. The bat’s task was to determine
whether electronically delayed echoes of successive biosonar
broadcasts changed in delay from one sonar broadcast to the next
(‘‘jittering stimuli’’ a and b at left in Fig. 1) or were constant in
delay (‘‘stationary stimuli’’ c and d at right), and to chose which of
the two loudspeakers (left or right) delivered the echoes that
changed in delay on that particular trial. The bat indicated its
choice by moving forward towards the correct loudspeaker (producing jittering echoes) and onto the left or right arm of the
Y-shaped platform (arrow in Fig. 1), where it received a piece of
mealworm (Tenebrio larva) offered with forceps. If the bat moved
towards the wrong loudspeaker (producing stationary, nonjittering
echoes), it received no reward and was kept on the platform while
Fig. 4A–D Alternative methods for producing changes in electronic
echo delay smaller than 1.3 ls (see Fig. 1): total delays for jittering
echoes a and b at zero jitter (Dt=0) and for stationary echoes c and
d are 3.275 ms. Microphones and loudspeakers are at distances of
20 cm for acoustic delay of 580 ls in A, B and 10 cm for delay of
290 ls in C, D. A Combination of delay lines with a and b digital
delays of fixed same size (2,113.7 ls) and analog delays of equal
size (1.3 ls) at zero jitter. B Combination of digital delay lines of
fixed same size (2,115.0 ls) and variable cable delays (fine delay
increments depend on cable length; see Table 1). C Combination of
delay lines with a and b digital delays of fixed same size (2,693.7 ls)
and analog delays of equal size (1.3 ls) at zero jitter. D
Combination of delay lines with a and b digital delays of different
size (2,693.7 ls and 2,695.0 ls) and analog delays of different size
(1.3 ls and 0.0 ls) at zero jitter. Analog delays are 0–50 ns in
increments of 5 ns. In D, equal analog delays occur at nonzero
jitter, whereas in C equal analog delays occur at zero jitter. C and D
dissociate the null point of any potential analog-delay artifact
(Beedholm and Møhl 1998) away from zero jitter and should
displace performance curves away from zero if bats use this artifact
to detect jitter rather than perceive the delay change itself
the experiment halted for a brief time-out period. In these experiments, the amount of jitter (Dt in Fig. 1) ranged from ±50 ns down
to zero around a mean delay of 3.275 ms, which also was the delay
of the stationary echoes (Simmons et al. 1990a). The apparatus for
generating stationary echoes was the same as that for generating
jittering echoes except that the delay difference (Dt) between c and d
was set to zero. It is important that the jittering and stationary
echoes be presented at the same mean delay ([a+b]/2=c=d) because the bat’s performance is degraded by masking that occurs
when the value of c or d is equal to either a or b (see Fig. 23 in
Simmons et al. 1990a). The mean delay of both the jittering and the
stationary echoes is equivalent to a simulated target range of about
56 cm.
The correct (jittering) stimulus appeared on the left or right
from one trial to the next according to a pseudorandom schedule
(Simmons et al. 1990a). At each stimulus condition described below, 40–60 trials were conducted. Perfect performance was 100%
correct choices (0% errors), chance performance was 50% correct
choices (50% errors), and threshold performance was arbitrarily set
at 75% correct choices (25% errors). The psychophysical method
of limits was used, i.e., the size of the jitter interval (Dt) was
698
decreased in small steps from a value the bat easily could detect to
values too small for the bat to detect. In the course of reducing the
amount of jitter, the delays of a and b always were adjusted to keep
the mean delay at 3.275 ms. The data are presented as plots
showing percentage of correct responses achieved by each bat at
different values of the jitter interval (Dt).
Sequential activation of channels
Even though the procedure nominally was a two-choice simultaneous discrimination task, the appearance of jittering or stationary
echoes on the left and right channels actually was sequential (as
described in Simmons et al. 1990b) because the simulator apparatus
prevented the bat from actually receiving echoes through both the
left and the right channels at the same time (see Fig. 2 in Simmons
et al. 1990a). During trials, the bat on the platform scanned its head
to the left and right, activating one channel at a time and each
channel in succession. The bat’s echolocation signals are moderately directional (Hartley and Suthers 1989), and the broadcast
beam is steered by these head-scanning movements. Consequently,
the sound impinging on the microphone the bat aims its head towards will be stronger than the sound impinging on the microphone off to the side. Head scanning causes amplitude differences
between the microphones of up to 10–15 dB (see Fig. 6 in Simmons
and Vernon 1971). Activation of one channel over the other was
determined by electronic comparison of the envelopes of the signals
from the microphones to select whichever microphone’s signal was
stronger (in operational terms, whether the left or right envelope
crossed a preset amplitude threshold first; see Simmons et al.
1990a). We dealt with the special case of the bat aiming its
broadcasts exactly half-way between the two microphones, so that
the sounds impinging on them would cross both comparator’s
thresholds at the same instant, by incorporating a narrow ‘‘deadzone’’ in the microphone-selecting circuit that shut both loudspeakers off for that case (see Fig. 2 in Simmons 1993).
Signals received by the left and right microphones and the
signals delivered to the left and right loudspeakers (in Fig. 1) were
recorded on a Racal Store-4 instrumentation tape recorder (tape
speed 76 cm s)1) to serve as an acoustic log of representative
experimental trials. After the experiments, we examined recordings
in which the bat responded correctly to very small jitters (jitter Dts
of 5–20 ns, which are too small for the bat to detect according to
conventional wisdom—see Schnitzler et al. 1985; Pollak 1993;
Beedholm and Møhl 1998). A summary of the content of these
plots has been published (Simmons 1993; Simmons et al. 1990a),
together with a representative plot (Fig. 16 in Simmons et al.
1990a), and their content was described at the 1994 Sandbjerg
workshop on echolocation. For further analysis, we played the
recordings at 8:1 reduced tape speed (from 76 to 9.5 cm s)1) into a
stereo sound board (SoundBlaster 16) in a PC-type 486 computer,
digitized each channel at a 44-kHz sampling rate (equivalent to
352-kHz effective sampling rate at the original tape speed). We then
clipped out most of the silent interval between successive broadcast
sounds to reduce the computer files to manageable size, converted
the two channels of signals into two-channel spectrograms (using
GoldStar v1.52), and displayed the spectrograms side by side. We
found no occasion where the target simulator delivered an echo to
the bat from both the left and the right loudspeakers on the same
broadcast.
Generation of echo delays
The echo delays shown in Fig. 1 (a, b, c, d; mean value of 3.275)
were compounded in Fig. 2 from the air-path travel time of the
bat’s sound to the microphone (290 ls or 580 ls over a nominal
path length of 10 cm or 20 cm), a variable electronic delay generated by the apparatus (approximately 2,115 ls or 2,695 ls), and
the travel-time of the bat’s sound back from the loudspeaker
(290 ls or 580 ls over a nominal path length of 10 cm or 20 cm).
Figure 4 shows different combinations of hardware devices used to
Table 1 Lengths and delays of RG58U coaxial cable used for small
delay steps (see Fig. 4B)
Cable
length
Calculated
delay
(1 ns/20 cm)
Measured delay
(counter method;
±3 ns)
Measured delay
(oscilloscope;
±2 ns)
152
244
336
427
7.6 ns
12.2 ns
16.8 ns
21.3 ns
5 ns
11 ns
16 ns
23 ns
7 ns
12 ns
18 ns
21 ns
cm
cm
cm
cm
produce the electronic delays in the jitter experiments described
here and elsewhere. The configurations shown in Fig. 4A, B are
from experiments reported previously (Simmons et al. 1990a), and
the configurations shown in Fig. 4C, D are from the experiments
reported in this paper. In Fig. 4, the particular devices used to
adjust the delay of jittering echo a relative to echo b are marked
‘‘Dt.’’ Identical delay devices were used to produce the stationary
delays of echoes c and d, only the value of Dt was zero.
The signal picked up by each microphone (m in Fig. 1) was
amplified, filtered to a passband of 20 and 100 kHz (Wavetek/
Rockland Model 442 variable Butterworth band-pass filter; 24 dB/
octave) and then fed simultaneously into two specially built digital
delay lines corresponding to delays a and b for one microphone and
into delay lines corresponding to delays c and d for the other
microphone. Each digital delay line used an A-to-D sampling rate
of 750 kHz (12-bit accuracy) to supply delay values in nominal
steps of 1.3 ls from 0 to 42 ms using a solid-state memory that was
read out by a D-to-A converter through a 50-W buffer amplifier to
reconstitute the delayed, digitized echo as an analog signal. To
manipulate the delay of electronic echoes in steps smaller than the
minimum digital step-size of 1.3 ls, each digital delay line was
supplemented by either a switch-variable analog ‘‘lumped-constant’’ delay line or by different lengths of coaxial cable. In Fig. 4A
(Simmons et al. 1990a), the analog delay lines were Ad-Yu Electronics Model 801b1 (500 W impedance, input and output matched
with 500-W resistors and then buffered by operational amplifiers to
have a 10-kW input impedance and a 50-W output impedance). In
Fig. 4B (Simmons et al. 1990a), the analog delay devices were
different lengths of coaxial cable (see Table 1; RG58U, 50 W
impedance, driven by the 50-W buffered output of the digital delay
line and terminated by 50 W into a 10-kW operational amplifier
prior to being switched electronically). In Fig. 4C, D for the
experiments reported here, the analog delay devices were Ad-Yu
delay lines for 0 or 1.3 ls, in series with switch-selectable Allen
Avionics delay lines supplying 1-ns steps (75 W impedance, input
and output matched with resistors and then buffered with operational amplifiers).
Dissociation of analog delays
In the first dissociation experiment, shown in Fig. 4C, the digital
delay lines were both set to 2,113.7 ls, and the analog delay lines
were both set to 1.3 ls, plus fine delay changes of 0–50 ns. The
second dissociation experiment, shown in Fig. 4D, carried
the procedure in Fig. 4C a step further by deliberately offsetting the
size of the digital contributions to delays a and b. This offset was
matched by a countervailing offset in the analog contributions to
these same delays. In Fig. 4D, the digital delays are not identical, in
this case one (a) being 1.3 ls longer than the other (b). Differences
between the jittering echoes were adjusted by first increasing the
amount of delay on the analog delay line in series with the shorter
digital delay by 1.3 ls to make the total electronic delay the same
for both echoes a and b. Then, the analog delay line was used to
make fine delay changes of 0–50 ns. Through use of different
amounts of analog delay offset by different amounts of digital delay
for a and b, any putative artifactual effects of the analog delay lines
could be dissociated from the actual delay values for the echoes
delivered to the bat. In particular, when the total difference in the
699
delay of echoes a and b (Dt) is reduced to zero, the difference in the
amount of analog contribution to those delays would still be 1.3 ls.
Any delay-correlated artifact caused by the different sizes of the
analog delays (e.g., reflections due to delay line impedance mismatch) should still be available to the bats. If the bats perceived the
arrival times of the echoes to detect the jitter, their performance
should be the same in the experiments shown in Fig. 4C and D.
That is, the bats’ percentage of correct responses should decline to
chance levels at jitter interval Dt=0 for both experiments, regardless of whether one of the echoes still had a substantial amount of
analog delay. However, if the bats used the effects of analog delay
artifacts rather than delay itself, their performance curves should
remain uniformly high at all delay values in the range of 0–50 ns
for the configuration Fig. 4D because the 1.3-ls analog delay
difference always is present and its collateral artifact always
is available.
Calibration of delayed signals
For the analog delay lines, nominal delay values were set each day
using the switches, but values of delay actually used to specify the
stimuli were measured directly instead of relying on reading the
switch dials. The most recent method for determining the amount
of delay produced by the delay lines used short 80-ns input pulses,
with display of delayed signals on a microwave-frequency digital
oscilloscope at a 0.5-ns sampling interval. This method yields
results that confirm the calibrations reported previously (Simmons
et al. 1990a; Simmons 1993). Figure 5 (left) shows the delayed
signals for these short pulses traveling through the analog delay
lines in the configuration of Fig. 4C, D. The illustrated output
pulses are delayed by steps of 5 ns and separated by steps of 5 ns,
which was the nominal size of the increment in delay used for the
experiments. The series of output pulses in Fig. 5 contain no distortion or stretching of shape caused by changes in the frequencyresponse of the delay lines or the presence of reflections in
proportion to delay. That is, no delay-correlated changes in the
phase or spectrum of the signals are present, just changes in delay
itself. For the cables, their lengths were cut by crudely calculating
the propagation delay using an approximation of 1 ns/foot (1 ns/
30.5 cm) as a ‘‘rule-of-thumb.’’ As described at the Sandbjerg
meeting in 1994, these values were not used to specify the stimuli,
however, just to make the cables. Measured values for cable delays
are closer to 1 ns/20 cm, but even these depend on proper impedance matching (see Beedholm and Møhl 1998), so we also relied on
direct measurements for cable delays. Table 1 gives the increments
in length for the four RG58U cables used here, together with their
theoretical differences in delay and actual differences measured
Fig. 5 Electronic calibration of
fine delays: waveforms of input
impulse and output impulses
from analog delay lines in
Fig. 4C, D for delay steps of 0
to 30 ns in 5-ns steps (left) and
from coaxial cables in Fig. 4B
for delays of 0 to 21.3 ns (right).
There are no discernable
distortions of waveform shape
or rightward shift in delay
values which would indicate the
presence either of spectral
artifacts or of reflections due to
impedance mismatch
(Beedholm and Møhl 1998)
electronically with a digital counter at the time the experiments
were conducted or more recently with a microwave-frequency
oscilloscope. Figure 5 (right) shows the delayed signals for the
short (80 ns) pulses traveling through the cables in the configuration of Fig. 4B. There is no indication of spectral artifacts or
stretching of the output waveform due to reflections at multiple
delays. Differences between calculated and measured delays in
Table 1 are within the ±3-ns range we found to be our measurement accuracy from repeated measurements of the same delay.
These same calibration measurements examined whether spectral artifacts accompany the delays. Detailed information about
calibration of delays is given elsewhere (Simmons et al. 1990a,
Simmons 1993). Here, we give a summary of yet other new measurements to establish further that the delay system produced no
delay-related spectral artifacts. The total electronic delays which
have to be measured are 2,115 ls (Fig. 4A, B) or 2,695 ls (Fig. 4C,
D), while the accuracy needed to describe the stimuli is about
±0.003 ls (±3 ns), so even for purely electronic measurements
(not including the acoustic delays) the desired accuracy is about
10)6 or 1 ppm. This poses special problems because not only the
digital delay lines, which supply a large part of the delay to be
measured, but also the available measuring devices (oscilloscopes,
analog-to-digital converters, digital counters) rely upon internal
time-base oscillators to serve as a time standard. Over time, the
frequency of the reference oscillator in any of these measuring
devices drifts with temperature by several parts per million relative
to the corresponding oscillator in the delay lines, and it is difficult
to ensure that measurements of nanosecond-sized time steps made
more than a few minutes apart are not confounded by this time
drift. Our original delay estimates drifted progressively larger by
the order of 10 ns over a period of 30 min, which we found when
we carried out faster measurements of electronic delays over only a
few minutes to minimize this drift to less than 3 ns. (This time-base
drift was misinterpreted by Beedholm and Møhl 1998 as evidence
for an impedance mismatch in the delay lines or cables. Inspection
of the spectra of signals confirms that no such cues are present.)
Such slow drift does not materially affect stimulus jitter because the
bat’s broadcast sounds are emitted at intervals of only 20–50 ms.
For this paper, a new calibration of delays was done using an
R.C. Electronics ISC-16 data-acquisition board with a 1-MHz
sampling-rate limit to achieve simultaneous recording of input and
output, each at a 500-kHz sampling rate. We generated 1-ms FM
signals sweeping from 115 kHz down to 15 kHz (linear FM), digitally synthesized with 16-bit accuracy at a 500-kHz sampling rate
with a Tucker-Davis Model QC2 waveform-generator board.
These FM signals were supplied as input to the delay lines by the
electronic filter used in the target simulator (Wavetek/Rockland
Model 442 bandpass filter), and both the input and the output of
700
Fig. 6A, B Electronic calibration of analog delay lines. A Crosscorrelation (XCR) difference functions between echoes a and b for
jitter Dt values of 0–25 ns (see Fig. 4C, D). Three different
difference functions are shown for zero jitter to illustrate variability
of functions in the absence of any actual time difference (first 0
jitter slice is for identical XCRs so is flat in magnitude). Vertical
scale is numerical value of difference between the two XCRs. B
Corresponding spectral difference functions between amplitude
spectra of echoes a and b for jitter Dt values of 0–25 ns. In this case,
two different difference functions are shown for zero jitter. While
the spectral differences in B show no delay-dependent changes in
spectra that increase as jitter increases, the XCR differences in A
show the progressive emergence from the noise of a waveform that
is a 90 phase-shifted version of the XCR as jitter increases. Together,
these plots show that the only difference between echoes a and b
within the limits imposed by the noise is a difference in delay
the delay system was recorded on the data-acquisition board
without averaging to insure that time-base drift did not affect the
measurements. The resulting digitized input and output signals
were processed in MatLab to obtain the XCR in the time domain
and the transfer function in the frequency domain for each delay
setting used in the jitter experiments. Figure 6A plots values of
differences between the XCR of echo b and the XCR of echo a
relative to the FM test ‘‘broadcast’’ for jitter Dt values of 0–25 ns.
Figure 6B plots corresponding differences between the transfer
function of echo b and the transfer function of echo a relative to the
FM test ‘‘broadcast.’’ As the amount of jitter increases, the subtracted XCRs in Fig. 6A show the gradual rise of a difference
function that is a 90 phase-shifted version of the XCR. This difference function is obvious at 10 and 15 ns jitter, and it can be
discerned for jitter values down to 5–10 ns. Whereas the XCR
differences show a progressive increase in height as the size of the
jitter interval (Dt) increases, the spectral differences in Fig. 6B show
no such progressive change in frequency response related to delay.
This graded emergence of a well-defined series of peaks in the XCR
differences in Fig. 6A, coupled with the absence of any comparable
emergence of peaks in the spectral differences in Fig. 6B, shows, as
far as is methodologically possible, that the electronic equipment
did not create delay-related spectral artifacts or changes in waveform shape which could be used by the bats as a substitute for
perception of echo delay. Instead, the delay lines just delayed the
signals (as in Fig. 5).
Results
Jitter performance for different delay configurations
Two big brown bats (bat no. 3 and bat no. 5 from
Simmons et al. 1990a) completed all four experimental
protocols shown in Fig. 4A–D, yielding comparable sets
of data for each condition. Figure 7A–D plots the percentage of correct responses achieved by each bat in the
four different experiments. The first experiment (from
Fig. 4A) used equal-length digital delay lines supplemented by analog delay lines to generate the delays of
the stimuli. The bats’ performance shown in Fig. 7A
remained high (above 75% correct responses) for jitter
intervals from 60 ns down to 20 ns. Then, as the size of
the jitter interval declined to 15, 10, and 5 ns, the bats’
performance also declined, reaching near-chance levels
at 0 ls. In alternative versions of this basic jitter detection task (Fig. 4B–D), the bats’ performance was substantially the same as in the initial version. In Fig. 7B,
for the experiment using coaxial cable delay as a supplement to the digital delay line (Fig. 4B), the percentage
of correct responses achieved by both bats declined
smoothly as the size of the jitter interval declined from
21 ns, passing through the 75%-correct threshold at
about 10–12 ns and reaching chance at 0 ns. The
experiments shown in Fig. 4C–D used a different distance from the bat to the microphones and loudspeakers
(10 cm instead of 20 cm). In Fig. 7C, for the first of two
experiments which modified the amount of digital and
analog contributions to total delay (Fig. 4C), the performance of the bats remained above 75% correct responses for jitter intervals from 20 ns down to 10 ns,
and then it declined for smaller intervals, passing
through the 75%-correct threshold at 8–10 ns and
reaching chance at 0 ns. In Fig. 7D, for the experiment
that deliberately offset the amount of digital delay by
1.3 ls so that the analog delay was also offset but in the
opposing direction (Fig. 4D), the bats’ performance remained high for jitter intervals from 40–50 ns down to
20 ns, declining through the 75% threshold at 8–12 ns.
The results from the basic jitter experiment (Fig. 7A)
thus were replicated with three alternative methods for
generating electronic delay differences (Fig. 7B–D).
Most important is the fact that performance is the same
as seen in Fig. 7C, D, with either zero difference in
analog delay or 1.3 ls difference in analog delay between
echoes a and b at the condition where the jitter interval
itself is zero. This dissociation of analog delay from
701
Fig. 7A–D Performance of bat no. 3 and no. 5 in four experiments
using different configurations of delay lines from Fig. 4A–D. Each
data-point is from 40–60 trials. Different replications of the
jittering echo experiment all yield threshold levels for 75% correct
responses at about 7–15 ns. Comparison of plots C and D show no
effect related to changes in numerical values of analog delay for
echoes a and b, whether they are equal at zero jitter or are different
by 1.3 ls at zero jitter, only the effect of changes in overall delay
performance demonstrates that no delay-related analogdelay artifact is involved in determining the bats’ performance.
Discussion
Jittering-echo experiments employing four different
electronic ways to regulate the delay of simulated echoes
(Fig. 4A–D) have produced substantially the same
results: Eptesicus can detect changes in the arrival-time
of jittering echoes as small as 10–15 ns with high performance of 80–85% correct responses or better
(Fig. 7A–D). The performance of the bats declines for
smaller amounts of jitter, reaching threshold at 75%
correct responses for jitter intervals of about 10 ns, and
reaching chance performance at zero jitter. Given the
extreme temporal sensitivity implied by the results
shown in Fig. 7, there is concern that the bat’s performance might be due to some artifact that manifests itself
in easier-to-detect changes in the spectrum or stretched
waveform of jittering echoes instead of perception of
jitter in delay itself (Simmons 1979, 1993; Schnitzler et al.
1985; Menne et al. 1989; Simmons et al. 1990a; Pollak
1993; Beedholm and Møhl 1998). However, the signals
delayed by the apparatus do not contain delay-related
changes in their waveforms or spectra, only changes in
delay (Figs. 5 and 6). Moreover, bats that use sonar
sounds of different durations nevertheless perform the
same in the jitter task, indicating that overlap of stimulus echoes with background reverberation is neither
required nor quantitatively decisive for achieving submicrosecond jitter acuity (Simmons et al. 1990a; Simmons 1993). As presently formulated, none of the
artifact hypotheses (Pollak 1993; Beedholm and Møhl
1998) can accommodate the full of results shown in
Fig. 7A–D, and thus they can be rejected. Eptesicus indeed seems capable of perceiving changes as small as
10 ns in the arrival time of successive sonar echoes
regardless of the exact size or type of analog contribution to the total delay of echoes.
The bat’s sensitivity to small changes in echo delay is
extraordinary; the closest performance observed in other
animals is of the order of 1 ls for the electroreception
system of the weakly electric fish, Eigenmannia (Heiligenberg 1991), and for binaural time-difference orientation in barn owls (Moiseff and Konishi 1981). For
both electric fish and owls, however, the behavioral
procedures are different from that used for presentation
of jittering stimuli to bats, so it is not clear to what
extent the data are comparable—perhaps these other
animals could also perform in the submicrosecond range
if presented with jittering stimuli (Altes 1989). Another
factor to consider is the unusually broad bandwidth of
the biosonar sounds emitted by Eptesicus (about
80 kHz) and the correspondingly broad bandwidth of
the echoes the bats process in order to achieve their
submicrosecond delay acuity. The sounds used as stimuli
in experiments on passive sound localization by barn
owls have 3-dB bandwidths of only a few kiloHertz at
most, while Eptesicus is stimulated by sounds with
bandwidths 10–40 times greater. We conclude that the
bat’s submicrosecond performance may be compatible
with the poorer auditory temporal acuity of other animals when the bat’s very large bandwidth is taken into
account. The inability of other animals to perform better
than about 1 ls is not good evidence that the bat’s 10-ns
hyperacuity is biologically ‘‘impossible’’ and must
therefore be due to artifacts.
Acknowledgements This research was supported by ONR Grant
Nos. N00014-89-J-3055, N00014-95-L-1123, and N00014-99-l0350, by NSF Grant Nos. BCS-9216718 and BES-9622297, by
NIMH Grant No. MH00521 (RSDA) and NIMH Training Grant
No. MH19118, by McDonnell-Pew Grant No. T89-01245-023, and
by Deafness Research Foundation funds. A workshop was held at
Sandbjerg, Denmark, in August 1994, to examine current problems
702
in echolocation. Much of the discussion focused on issues surrounding observations of jitter hyperacuity by bats, and results
from additional jitter experiments and control procedures were
presented at that meeting. Pursuant to requests from several
workshop participants, this paper gathers together findings relevant to whether echo delay or spectral differences can explain the
bats’ performance. We thank colleagues at the Sandbjerg workshop
for their constructive suggestions about these experiments. Care
and use of the animals was supervised by Brown University veterinarians and the Institutional Animal Care and Use Committee in
accordance with Principles of Animal Care no. 86-23 (revised 1985)
of the US National Institutes of Health Publication.
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