The apparent immunity of high-frequency ‘‘transposed’’ stimuli
to low-frequency binaural interference
Leslie R. Bernstein and Constantine Trahiotis
Department of Neuroscience and Department of Surgery (Otolaryngology), University of Connecticut Health
Center, Farmington, Connecticut 06030
共Received 10 March 2004; revised 20 July 2004; accepted 21 July 2004兲
Discrimination of interaural temporal disparities 共ITDs兲 was measured with either conventional or
transposed ‘‘targets’’ centered at 4 kHz. The targets were presented either in the presence or absence
of a simultaneously gated diotic noise centered at 500 Hz, the interferer. As expected, the presence
of the low-frequency interferer resulted in substantially elevated threshold-ITDs for the
conventional high-frequency stimuli. In contrast, these interference effects were absent for ITDs
conveyed by the high-frequency transposed targets. The binaural interference effects observed with
the conventional high-frequency stimuli were well accounted for, quantitatively, by the model
described by Heller and Trahiotis 关L. M. Heller and C. Trahiotis, J. Acoust. Soc. Am. 99, 3632–3637
共1996兲兴. The lack of binaural interference effects observed with the high-frequency transposed
stimuli was not predicted by that model. It is suggested that transposed stimuli may be one of a class
of stimuli that do not foster an obligatory combination of binaural information between low- and
high-frequency regions. Under those conditions that do foster such an obligatory combination, one
could still consider models of binaural interference, such as the one described in Heller and
Trahiotis, to be valid descriptors of binaural processing. © 2004 Acoustical Society of America.
关DOI: 10.1121/1.1791892兴
PACS numbers: 43.66.Pn, 43.66.Ba 关AK兴
I. INTRODUCTION
It has recently been shown that the processing of ongoing interaural temporal disparities 共ITDs兲 at high frequencies
can be enhanced by using ‘‘transposed stimuli’’ similar to
those first employed by van de Par and Kohlrausch 共1997兲.
The purpose of using transposed stimuli is to provide highfrequency auditory channels with envelope-based information that mimics waveform-based information normally
available in only low-frequency channels. Specifically, the
use of high-frequency transposed stimuli yielded both
smaller threshold-ITDs 共Bernstein and Trahiotis, 2002兲 and
larger extents of laterality 共Bernstein and Trahiotis, 2003兲
than did the use of ‘‘conventional’’ high-frequency stimuli
such as narrow bands of Gaussian noise and sinusoidally
amplitude-modulated 共SAM兲 tones. Furthermore, with several of the high-frequency transposed stimuli, threshold-ITDs
were as small, and extents of laterality were as large, as those
measured with low-frequency pure tones and bands of noise
having low center-frequencies.
Such findings may be interpreted to mean that the highfrequency channels of the auditory system are not, in and of
themselves, less sensitive to ITDs than are the low-frequency
channels. It occurred to us that transposed stimuli could be
useful in evaluating current accounts and/or explanations of
what has been termed ‘‘binaural interference.’’ In order to
understand why this is so, it is necessary to consider what is
generally known empirically about binaural interference and
the nature of the theoretical explanations that have been offered to account for it.
Examples of binaural interference can be found in several experiments demonstrating that sensitivity to ITDs conveyed by a ‘‘target’’ presented within one spectral region can
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J. Acoust. Soc. Am. 116 (5), November 2004
Pages: 3062–3069
be degraded by the presence of a second, simultaneously
gated stimulus, the ‘‘interferer.’’ An important characteristic
of binaural interference is that the interferer occupies a spectral region remote from that of the target 共e.g., McFadden
and Pasanen, 1976; Davis, 1985; Zurek, 1985; Dye, 1990;
Trahiotis and Bernstein, 1990; Bernstein, 1991; Buell and
Hafter; 1991; Woods and Colburn, 1992; Buell and Trahiotis,
1993; Stellmack and Dye, 1993; Bernstein and Trahiotis,
1992a; 1995; Heller and Trahiotis, 1995兲. Another important
characteristic of binaural interference is that it is asymmetric
in that low-frequency stimulation adversely affects the processing of ITDs conveyed by high-frequency targets but
high-frequency stimulation does not adversely affect the processing of ITDs conveyed by low-frequency targets.
The general theoretical framework used to account for
binaural interference was first described by Buell and Hafter
共1991兲 and incorporates a form of ‘‘non-optimal’’ processing
wherein binaural interference arises from an obligatory combination of ITD-information conveyed by the target and the
interferer, respectively. According to this model, the ITDinformation conveyed within the target frequency channel
and within the interferer frequency channel receive differential weights. The weights for the target and interferer, respectively, are inversely proportional to the magnitude of the
threshold-ITD measured when each is presented in isolation.
As a result, the stimulus having the lowest threshold-ITD, be
it target or interferer, contributes most to the decision.
Recently, Heller and Trahiotis 共1996兲 showed that predictions of binaural interference measured in an ITDdetection task could be markedly improved if the Buell and
Hafter 共1991兲 weights were augmented to include a factor
representing the relative slopes of functions relating extent of
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© 2004 Acoustical Society of America
laterality to ITD for targets and interferers presented in isolation. Based on Heller and Trahiotis’ model, one would predict that less binaural interference would be observed for
high-frequency transposed targets than for conventional
high-frequency stimuli. This is so because high-frequency
transposed stimuli, unlike their conventional high-frequency
counterparts, yield threshold-ITDs and extents of laterality
that are similar to those obtained with low-frequency stimuli.
Therefore, within the model, high-frequency transposed
stimuli would receive greater weighting vis-a-vis the weighting applied to low-frequency interferers than would their
conventional high-frequency counterparts. The Buell and
Hafter 共1991兲 model would also predict less interference for
transposed targets but would do so based only on their relatively smaller threshold-ITDs.
In light of these issues, the purposes of this investigation
were 共1兲 to measure and to compare binaural interference
effects obtained with either transposed or conventional highfrequency targets in an ITD-discrimination task and 共2兲 to
determine whether either of the quantitative models of binaural interference discussed above could account for the
data. It will be seen that high-frequency transposed targets
appear to be ‘‘immune’’ to binaural interference from lowfrequency stimulation. In addition, it appears that neither of
the models can account for the lack of interference obtained
with transposed stimuli. The empirical and theoretical results, taken together, suggest that high-frequency transposed
stimuli are, in some sense, ‘‘special’’ in that they appear to
allow listeners effectively to disregard the presence of concurrent low-frequency stimulation and behave in a more
‘‘optimal’’ fashion.
II. EXPERIMENT 1
A. Stimuli
Five high-frequency stimuli served as targets: 共1兲 a
4-kHz tone sinusoidally amplitude-modulated 共SAM兲 at 128
Hz; 共2兲 a 200-Hz-wide band of Gaussian noise centered at 4
kHz; 共3兲 a 128-Hz tone transposed to 4 kHz; 共4兲 a 50-Hzwide band of Gaussian noise centered at 128 Hz that was
transposed to 4 kHz; 共5兲 a 100-Hz-wide band of Gaussian
noise centered at 128 Hz that was transposed to 4 kHz. The
transposed stimuli were generated in the manner described in
detail by Bernstein and Trahiotis 共2002; 2003兲. Briefly, the
time-domain representation of a low-frequency tone or a narrow band of low-frequency Gaussian noise was 共linearly兲
half-wave rectified by setting all negative values to zero.
Rectified waveforms were then transformed to the frequency
domain and the spectral components above 2 kHz were filtered out by setting their magnitudes to zero 共see pp. 1027–
1028 of Bernstein and Trahiotis, 2002 for a justification of
the choice of this type of rectification and filtering兲. Rectified
and filtered waveforms were then transformed back to the
time domain and multiplied by a 4-kHz sinusoidal ‘‘carrier.’’
The product was a transposed stimulus having an envelope
whose time signature mimicked that of the rectified and filtered low-frequency tone or low-frequency narrow band of
noise.
Examples of each type of high-frequency target are deJ. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
picted in Fig. 1. The left-hand panels show randomly chosen
50-ms epochs of each type of target; the right-hand panels
show the 共long-term兲 power spectrum of each target calculated over several tens of seconds. Beginning with the lefthand panels, note that there are six or seven envelope
maxima for each type of target during the 50-ms epochs
depicted. This reflects the fact that, by construction, the expected number of envelope maxima per second for each type
of target is 128. For the SAM and transposed targets, this is
more or less intuitively appreciated given that the basic
waveforms that served as the ‘‘modulators’’ of the 4-kHz
carriers were, as indicated in the figure, all centered on 128
Hz. For the 200-Hz-wide Gaussian noise target, some explanation seems in order. As shown by Rice 共1954兲, the expected number of envelope maxima per second for a Gaussian noise is equal to 0.6411 times its bandwidth in Hz.
Therefore, the bandwidth of the Gaussian noise target was
chosen to be 200 Hz so that its rate of envelope fluctuation
would be approximately 128 Hz, thereby matching the rate
of envelope fluctuation of the other four types of targets.
There were three primary reasons for choosing a rate of
envelope fluctuation of 128 Hz. First, transposed stimuli having a rate of envelope fluctuation of 128 Hz or so have been
shown to produce the greatest enhancements of ITDprocessing at high frequencies 共e.g., van de Par and Kohlrausch, 1997; Bernstein and Trahiotis, 2002; 2003兲. Second,
128 Hz is well within the range of rates of envelope fluctuation that yield the smallest threshold-ITDs for conventional
high-frequency stimuli such as SAM tones, two-tone complexes, and bands of Gaussian noise 共see Henning, 1974;
McFadden and Pasanen, 1976; Nuetzel and Hafter, 1981;
Bernstein and Trahiotis, 1994兲. Third, the choice of this rate
causes the vast majority of the energy to occur between 3750
Hz and 4250 Hz for all five types of targets 共see right-hand
panels of Fig. 1兲. This ensured that the energy within each
type of target would fall almost entirely within the approximately 500-Hz-wide auditory filter centered at 4 kHz 共see
Moore, 1997兲. This was deemed necessary to help maximize
the validity of comparisons of data obtained with the various
targets and, perhaps, to simplify interpretations of the results.
Also note that one of the two types of conventional targets
共the SAM tone兲 was deterministic and had a discrete spectrum while the other one 共the band of Gaussian noise兲 was
stochastic and had a continuous spectrum. In somewhat parallel fashion, one of the transposed targets 共the 128-Hz tone
transposed to 4 kHz兲 was deterministic and had a discrete
spectrum, while the other two transposed targets 共the 50-Hzwide and 100-Hz-wide bands of noise centered at 128 Hz
which were each transposed to 4 kHz兲 were stochastic and
had continuous spectra. These differences notwithstanding,
the relative amounts of power within corresponding ‘‘sidebands’’ composing each of the three types of transposed
stimuli was equal. For example, consider the sidebands centered on 3872 Hz. The level of that sideband within the spectrum of the target generated by transposing a 50-Hz-wide
noise 共fourth row兲 is 17 dB below the level of the corresponding sideband in the spectrum of the target generated by
transposing a tone 共third row兲. That difference results from
the fact that the power of that sideband for the transposed
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
3063
FIG. 1. Left-hand panels: Randomly chosen 50-ms epochs of the five types of targets employed in the main experiment. Right-hand panels: The long-term
power spectra of each of the five types of targets.
noise is spread across a 50-Hz-wide band of frequencies,
rather than being concentrated at a single spectral frequency.
Consistent with this, the level of the 3872-Hz sideband
within the spectrum of the target generated by transposing a
100-Hz-wide noise 共fifth row兲 is another 3 dB below the
level of the corresponding sideband in the spectrum of the
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J. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
target generated by transposing a 50-Hz-wide band of noise.
These comparisons ignore the negligible additional power
contributed to the 3872-Hz sidebands that results from
‘‘overlap’’ with neighboring sidebands.
The stimulus that served as the interferer was a 400-Hzwide band of Gaussian noise centered at 500 Hz. Such a
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
FIG. 2. Mean threshold-ITDs obtained
in the main experiment. The types of
target stimuli are indicated along the
abscissa. Unfilled bars indicate
threshold-ITDs for targets presented in
the absence of the interferer; filled
bars indicate threshold-ITDs obtained
in the presence of the interferer. The
cross-hatched bar at the left of the figure indicates the mean threshold-ITD
obtained when the 400-Hz-wide band
of noise centered at 500 Hz that served
as the interferer was presented in isolation.
stimulus was found by Bernstein and Trahiotis 共1995兲 to produce substantial amounts of binaural interference for the
resolution of ITDs conveyed by target bands of noise centered at 4 kHz. Thus, overall, the types of targets used in the
experiment were chosen to optimize sensitivity to ITD in
high-frequency channels while the interferer was chosen to
maximize the possibility of observing binaural interference
effects, should they occur.
All targets and interferers were generated digitally as
8192-point buffers using a sampling rate of 20 kHz 共TDT
AP2兲. Each stimulus used in the experiment was 300 ms long
including 20-ms cos2 rise-decay ramps and was extracted
from the appropriate longer buffer. The stimuli were lowpass filtered at 8.5 kHz 共TDT FLT2兲, and each was presented
via Etymotic ER-2 insert earphones at a level matching 70
dB SPL as produced by TDH-39 earphones in a 6-cc
coupler.1 Interfering stimuli were presented diotically and
were gated on and off synchronously and identically with the
target stimuli.
B. Procedures
Threshold-ITDs were determined using a four-interval,
two-cue, two-alternative, temporal forced choice, adaptive
task. Each trial consisted of a warning interval 共500 ms兲 and
four 300-ms observation intervals separated by 400 ms. Each
interval was marked visually by a computer monitor. Feedback was provided for approximately 400 ms after the listener responded. The stimuli in the first and fourth intervals
were diotic. The listener’s task was to detect the presence of
an ITD 共left-ear leading兲 that was presented with equal a
priori probability in either the second or the third interval.
The remaining interval, like the first and fourth intervals,
contained diotic stimuli.
J. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
The starting phases of the components that composed
each stimulus 共prior to the imposition of an ITD兲 were chosen randomly for each observation interval within and across
trials. All of the conventional waveforms required for a given
trial were computed immediately prior to that trial. Because
of the time required to generate the high-frequency transposed stimuli, it was necessary to calculate the transposed
waveforms prior to each adaptive run. Twenty independently
calculated tokens of the desired type of transposed stimulus
were stored and one of them was chosen randomly 共with
replacement兲 for each of the four observation intervals defining a trial. Twenty tokens were employed so that the behavioral data were not dependent upon the occurrence of any
particular stimulus. This set-size was considered to be sufficiently large based on Siegel and Colburn’s 共1989兲 findings
that only 10 independently generated tokens of noise yielded
essentially equivalent performance to that measured with
‘‘running’’ noise in a binaural discrimination task.
Ongoing ITDs were imposed by applying linear phaseshifts to the representation of the signals in the frequency
domain and then gating the signals destined for the left and
right ears coincidentally, after transformation to the time domain. The ITD for a particular trial was determined adaptively in order to estimate 70.7% correct 共Levitt, 1971兲. The
initial step-size for the adaptive track corresponded to a factor of 1.584 共equivalent to a 2-dB change of ITD, assuming
ITD to be a ‘‘10 log’’ quantity兲 and was reduced to a factor of
1.122 共equivalent to a 0.5-dB change of ITD, assuming ITD
to be a ‘‘10 log’’ quantity兲 after two reversals. A run was
terminated after 12 reversals and threshold was defined as
the geometric mean of the ITD across the last 10 reversals.
Four normal-hearing adults served as listeners and three
consecutive estimates of threshold-ITD were first obtained
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
3065
from each listener for each of the stimuli presented in isolation. Those stimuli were tested in random order. Then, three
more estimates were obtained after revisiting the same
stimulus conditions in reverse order. Estimates of threshold
for targets presented in the presence of the interferer were
obtained in the same manner after the estimates of threshold
were obtained with targets presented in isolation. The same
ordering of conditions was used for all listeners and all listeners received substantial practice before formal collection
of data began. For each listener and stimulus condition, final
estimates of thresholds were calculated by averaging the individual thresholds obtained from the six adaptive runs.
C. Results and discussion
Figure 2 contains the means of the threshold-ITDs
共taken across the four listeners兲 obtained in each of the experimental conditions. The types of target stimuli are indicated along the abscissa. Unfilled bars indicate thresholdITDs obtained without the interferer; filled bars indicate
threshold-ITDs in the presence of the interferer. The crosshatched bar at the far left of the figure indicates the mean
threshold-ITD obtained when the 400-Hz-wide band of noise
centered on 500 Hz that served as the interferer was presented in isolation. The error bars represent the standard errors of each mean threshold-ITD.
Visual comparisons among the data reveal two important
trends. First, threshold-ITDs obtained with the highfrequency transposed targets are, on the average, smaller
than those obtained with the conventional high-frequency
targets. This general outcome replicates our earlier findings
共Bernstein and Trahiotis, 2002兲. Second, sensitivity to ITD
was degraded in the presence of the interferer for conventional targets, but not for transposed targets. That is, it appears that high-frequency transposed targets are effectively
immune to binaural interference. This general outcome confirms the results of our preliminary or ‘‘pilot’’ studies 共Bernstein and Trahiotis, 2001兲.
The data in Fig. 2 were subjected to a three-factor 共关conventional vs transposed targets兴⫻关no interference vs
interference兴⫻关stochastic vs deterministic targets兴兲, withinsubjects analysis of variance. In order to perform a ‘‘balanced’’ analysis of variance, the data obtained when the targets were either 50-Hz-wide or 100-Hz-wide bands of noise
centered at 125 Hz and transposed to 4 kHz were averaged,
respectively, within interference and no-interference
conditions.2 The error terms for the main effects and for the
interactions were the interaction of the particular main effect
共or the particular interaction兲 with the subject ‘‘factor’’ 共Keppel, 1973兲. In addition to testing for significant effects, the
proportions of variance accounted for ( ␻ 2 ) were determined
for each significant main effect and interaction 共Hays, 1973兲.
Consistent with visual inspection of the data, the main
effect of conventional vs transposed targets was highly significant 共assuming a criterion of ␣⬍0.05兲 关 F(1,3)⫽137.80,
p⫽0.001] and accounted for 35% of the variability of the
data. This reflects the fact that, on average, listeners were
more sensitive to ITDs conveyed by transposed targets as
compared to their conventional counterparts. The main effect
of interference vs no interference was also significant
3066
J. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
关 F(1,3)⫽57.17, p⫽0.005] and accounted for 6% of the
variability in the data. This reflects the fact that, on average,
threshold-ITDs were elevated in the presence of the interferer. More importantly, for our purposes, the interaction of
关conventional vs transposed targets兴⫻关interference vs no interference兴 conditions was also significant 关 F(1,3)⫽33.31,
p⫽0.01] and accounted for 4% of the variability. This outcome reinforces the general conclusion stated above that
only the conventional targets, and not the transposed targets,
were subject to binaural interference.
The third main effect, deterministic vs stochastic targets,
was also significant 关 F(1,3)⫽17.33, p⫽0.025] and accounted for 7% of the variability in the data. This reflects the
fact that, on average, threshold-ITDs obtained with the deterministic targets were smaller than those obtained with the
stochastic targets. It is also the case that the interaction of
关conventional vs transposed targets兴⫻关deterministic vs stochastic targets兴 was also significant 关 F(1,3)⫽65.72, p
⫽0.004], accounting for 11% of the variability. This reflects
the observation that threshold-ITDs for the transposed targets
were essentially identical whether the stimuli were deterministic or stochastic while threshold-ITDs measured with the
conventional SAM stimuli were smaller than those measured
with the narrow-band Gaussian noise. The latter outcome
replicates findings previously reported in an earlier, independent investigation that also included those two particular
SAM and noise stimuli 共Bernstein and Trahiotis, 1994兲.
Finally, neither the interaction of 关interference vs no
interference兴⫻关deterministic vs stochastic targets兴, nor the
triple interaction among all three factors reached statistical
significance 共for both types of interactions, p⬎0.25). This
means that the double interactions found to be statistically
significant do not have to be qualified by reference to levels
of a third factor. In total, the within-subjects main effects and
interactions accounted for 62% of the total variance in the
data. Said differently, the properties of the stimuli accounted
for the majority of the total variability in the data. Considering that only four listeners participated in the study, the large
amount of variability accounted for attests to the robustness
of the changes in threshold-ITD brought about by the specific properties of the stimuli.
III. TESTING THE HELLERÕTRAHIOTIS QUANTITATIVE
MODEL OF BINAURAL INTERFERENCE
In 1996, Heller and Trahiotis described an extension of
the Buell and Hafter 共1991兲 ‘‘weighted combination’’ model
that was successful in accounting for binaural interference in
an experiment measuring threshold-ITDs. A fundamental underlying assumption of that model and of the Buell and
Hafter model is that interference arises from an obligatory,
across-frequency-channel, combination of binaural cues.
That is, the processing of the targets and interferers is assumed to be ‘‘non-optimal’’ in that low-frequency diotic interferers, which convey no information useful for detecting
ITDs within high-frequency targets, are not ignored. Said
differently, the ITD value of zero conveyed by the lowfrequency interferer is included in the decision variable and
serves to ‘‘dilute’’ the value of the ITD conveyed by the
high-frequency target. As a result, in the presence of the
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
low-frequency interferer, ITDs imposed on the highfrequency target must be increased in order to reach threshold.
The reader is referred to the appendix of Heller and
Trahiotis 共1996兲 for a detailed explication of their model and
its relation to the model of Buell and Hafter 共1991兲. In what
follows, a brief summary of the material in that appendix is
presented so that the manner in which the predictions for this
study were derived can be understood.
In mathematical terms, the Heller and Trahiotis 共1996兲
model can be represented by
⬘ ⫽
d t⫹i
a⌬x t ⫹b⌬x i
冑a 2 ␴ 2t ⫹b 2 ␴ 2i
共1兲
,
⬘ represents the listener’s sensitivity to changes in
where d t⫹i
target-ITD in the presence of the interferer. The term ⌬x t
represents the change in lateral position resulting from the
imposition of an ITD on the target when it is presented in
isolation. In parallel fashion, ⌬x i represents the change in
lateral position resulting from the imposition of an ITD on
the interferer, presented in isolation. Estimates of changes in
lateral position (⌬x t and ⌬x i ), as a function of ITD, are
obtained by using an acoustic pointing task to determine the
slope, s, of the linear portion 共between values of ITD of 0
and 600 ␮s兲 relating the IID of the pointer to the ITD of the
target or interferer when each is presented in isolation.
Within this rubric,
⌬x t ⫽s t ⌬ITDt ,
共2兲
⌬x i ⫽s i ⌬ITDi .
共3兲
Note that the changes in lateral position, (⌬x t and ⌬x i ) are
quantified by the IID of the pointer in dB.
Returning to Eq. 共1兲, the terms ␴ t and ␴ i represent the
square-roots of the variances associated with the auditory
processing that results in changes in the lateral position of
the target and interferer, respectively. The values ␴ t and ␴ i
are in units of dB. They are estimated by equating ⌬ITDt and
⌬ITDi in Eqs. 共2兲 and 共3兲, respectively, with the 共threshold兲
values of ITD required to yield d ⬘ ⫽1. When that is done
d ⬘t ⫽s t threshITDt / ␴ t ⫽1,
共4兲
d ⬘i ⫽s i threshITDi / ␴ i ⫽1.
共5兲
It follows that
␴ t ⫽s t threshITDt ,
共6兲
␴ i ⫽s i threshITDi .
共7兲
Within Eq. 共1兲, the weights a and b, applied to the target
and interferer ‘‘channels,’’ respectively, are taken to be inversely proportional to ␴ 2t and ␴ 2i , respectively.
When the interferer is diotic and, therefore, ⌬ITDi ⫽0,
making appropriate substitutions and rearrangements among
the relations given above 共see Heller and Trahiotis, 1996, p.
3637兲 yields an equation that can be used to make predictions of target-threshold-ITDs in the presence of an interferer:
threshITDt⫹i ⫽threshITDt
冑 冋
1⫹
册
s t threshITDt 2
.
s i threshITDi
J. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
共8兲
Note that, as emphasized by Heller and Trahiotis 共1996兲,
the predicted threshold-ITDs under conditions of interference are determined completely by quantities 共i.e., thresholdITDs and slopes of lateralization兲 obtained when targets and
interferers are each presented in isolation. It is also the case
that setting the slopes, s t and s i to 1 in Eq. 共8兲, yields the
formulation used by Buell and Hafter 共1991兲 to predict interference effects. The fundamental difference between the two
models is that the Heller and Trahiotis model derives predictions directly in terms of changes in laterality while the Buell
and Hafter model derives predictions directly in terms of
changes in stimulus-ITD.
In order to derive predictions of threshold-ITDs for targets presented simultaneously with the interferer in the current experiment, an acoustic pointing task was used to determine the slope of the linear function relating the IID of the
pointer to values of ITD from 0 to 600 ␮s for each of the five
types of target and for the interferer utilized in the main
experiment. The acoustic pointing task was the one employed successfully in several previous investigations.
Briefly, the listener was required to adjust the interaural intensitive disparity 共IID兲 of a 200-Hz-wide noise centered at
500 Hz until its intracranial position matched that of the
stimulus that conveyed the ITD 共see, Bernstein and Trahiotis,
1985, 2003; Heller and Trahiotis, 1996兲.
Three of the four listeners who participated in the main
experiment were available to participate in the acoustic
pointing task. For each listener and type of stimulus 共target
or interferer兲, the slope relating the IID of the pointer to ITD
was computed via linear regression. Because those slopes
were highly similar across listeners, we computed the average slope, taken across the three listeners, separately for each
of the six stimuli 共five types of target and the interferer兲.
Those mean slopes and the mean threshold-ITDs obtained in
the main experiment were entered into Eq. 共8兲 to derive predictions of ITD-thresholds for each type of target in the presence of the interferer. For archival purposes, those slopes and
threshold-ITDs are provided in Table I.
Figure 3 contains the data obtained in the main experiment replotted from Fig. 2 along with the predictions of
threshold-ITD in the presence of the interferer. The crosses
represent predictions obtained with the Buell and Hafter
共1991兲 model; the asterisks represent predictions obtained
with the Heller and Trahiotis 共1996兲 model. Beginning with
the conventional targets, note that the predictions derived
with the Heller and Trahiotis model are very accurate, being
well within the standard error of the measurement of the data
themselves 共see Fig. 2兲. The Buell and Hafter model, however, overestimates the effects of interference. These two
general outcomes replicate the findings of Heller and Trahiotis.
In contrast, and of great import for the purposes of this
study, note that both models, which assume an obligatory,
non-optimal combination of information in the low- and
high-frequency channels, fail to predict the absence of interference effects that was found with the transposed stimuli.
Given the success of the Heller and Trahiotis 共1996兲 model
in accounting for interference effects with conventional highfrequency targets, its inability to account for data obtained
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
3067
TABLE I. Mean threshold-ITDs and mean lateralization slopes for the five types of targets and the interferer
when each was presented in isolation. The values were entered into Eq. 共8兲 in order to derive predicted
threshold-ITDs for targets in the presence of the interferer.
Stimulus
Mean
Threshold-ITD
共␮s兲
Mean Lateralization
Slope 共dB/␮s兲
41.2
0.038
106.5
184.9
0.020
0.009
94.4
75.8
84.2
0.029
0.028
0.028
Interferer
Noise 共CF: 500 Hz; Bw: 400 Hz兲 关Interferer兴
Targets
Conventional
SAM 共CF: 4 kHz; MF: 128 Hz兲
Noise 共CF: 4 kHz; BW: 200 Hz兲
Transposed to 4 kHz
Tone 共128 Hz兲
Noise 共CF: 128 Hz; BW: 50 Hz兲
Noise 共CF: 128 Hz; BW: 100 Hz兲
with transposed stimuli does not appear to be attributable to
some kind of ‘‘experimental error’’ or shortcoming in the
experiment, per se. The model’s failure is consistent with the
notion that listeners were somehow able to ‘‘ignore’’ the noninformation-bearing diotic low-frequency interferer and base
their decisions solely on changes in ITDs conveyed by the
high-frequency transposed targets. At this time, it is unclear
to us what factor共s兲 render the transposed stimuli employed
in this experiment effectively immune to binaural interference. Perhaps future experiments using a wide variety of
transposed and conventional targets and interferers will provide information concerning which stimulus conditions are
necessary for binaural interference effects to occur and help
clarify why binaural interference effects appear to be asymmetric with respect to frequency. At this time it is not clear
whether such asymmetric binaural interference effects stem
from properties of the binaural system per se, or instead reflect ‘‘floor effects’’ resulting from the overall greater sensitivity to ITDs conveyed by low-frequency conventional
stimuli, as compared to their conventional high-frequency
counterparts.
IV. SUMMARY AND CONCLUSIONS
Threshold-ITDs were measured with a variety of conventional and transposed ‘‘targets’’ centered at 4 kHz. The
targets were presented either in the presence or absence of a
simultaneously gated diotic noise centered at 500 Hz, the
interferer. As expected, the presence of the low-frequency
interferer resulted in substantially elevated threshold-ITDs
FIG. 3. Data replotted from Fig. 2 accompanied
by
predictions
of
threshold-ITD for targets in the presence of the interferer. Crosses represent predictions obtained with the
Buell and Hafter 共1991兲 model; asterisks represent predictions obtained
with the Heller and Trahiotis 共1996兲
model.
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J. Acoust. Soc. Am., Vol. 116, No. 5, November 2004
L. R. Bernstein and C. Trahiotis: Transposed stimuli and binaural interference
for the conventional high-frequency stimuli. In contrast,
these interference effects were either greatly attenuated or
absent for ITDs conveyed by the high-frequency transposed
targets. The binaural interference effects observed with the
conventional high-frequency stimuli were well accounted
for, quantitatively, by the model described by Heller and Trahiotis 共1996兲. The lack of binaural interference effects observed with the high-frequency transposed stimuli was not
predicted by that model. It is suggested that transposed
stimuli may be one of a class of stimuli that do not foster an
obligatory combination of binaural information between
low- and high-frequency regions. If this were the case, then
one could still consider models of binaural interference, such
as the one described in Heller and Trahiotis to be valid descriptors of binaural processing under those conditions that
do foster such an obligatory combination.
ACKNOWLEDGMENTS
The authors thank Dr. Thomas N. Buell, Dr. Richard L.
Freyman, and Dr. Armin Kohlrausch. Their insightful comments served to strengthen the presentation. This research
was supported by research grants NIH DC-04147, DC04073, and DC-00234 from the National Institute on Deafness and Other Communication Disorders, National Institutes of Health.
1
Stimulus levels produced according to the calibration supplied with the
Etymotic ER-2 earphones sounded less loud than stimuli presented at nominally the same level via TDH-39 earphones, according to their calibration.
Dr. Mead Killion, of Etymotic Research, validated our listening experience
and agreed with us that the two respective methods of calibration would be
expected to produce levels of stimulation differing by about 10 dB. We
chose to ‘‘calibrate’’ the outputs of the Etymotic earphones to the nominal
levels produced by the TDH-39s so that listeners in this study would receive levels of stimulation directly comparable to those utilized by us and
others in prior psychophysical experiments employing TDH-39s. We verified that the levels from the Etymotic earphones were appropriate by presenting a high-frequency, stimulus to one ear via an Etymotic ER-2 earphone and simultaneously to the other ear via a TDH-39 earphone. We then
adjusted the relative levels between the two ears to produce a ‘‘centered’’
intracranial image, as is produced by diotic stimuli in normal-hearing listeners. In order to produce a centered image, it was necessary to impose a
10-dB larger voltage on the Etymotic ER-2 than would be expected on the
basis of its calibration. Incidentally, the same type of ear-to-ear comparison
allows one to compare and to cross-calibrate any earphone to any other one,
notwithstanding local variations in the frequency response of the earphones.
2
This was determined to be justified on two separate grounds. First, as the
data in Fig. 2 show, threshold-ITDs obtained with those two targets were
virtually identical within interference and no-interference conditions. Second, two additional, separate, analyses of variance were performed while
including only the data obtained with the 50-Hz-wide noise or only the
100-Hz-wide noise 共rather than their mean兲. All three sets of analyses of
variance resulted in the same factors and interactions either reaching or
failing to reach statistical significance. Therefore, our averaging of the data
across those two targets neither distorted nor compromised the meaning
共and meaningfulness兲 of the statistical analysis.
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