Enhancing sensitivity to interaural time differences at high modulation ...

Enhancing sensitivity to interaural time differences at high modulation rates by introducing temporal jitter Matthew J. Goupell,a兲 Bernhard Laback, and Piotr Majdak Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, A-1040 Vienna, Austria

共Received 26 June 2008; revised 18 June 2009; accepted 27 June 2009兲 Sensitivity to interaural time differences 共ITDs兲 in high-frequency bandpass-filtered periodic and aperiodic 共jittered兲 pulse trains was tested at a nominal pulse rate of 600 pulses per second 共pps兲. It was found that random binaurally-synchronized jitter of the pulse timing significantly increases ITD sensitivity. A second experiment studied the effects of rate and place. ITD sensitivity for jittered 1200-pps pulse trains was significantly higher than for periodic 600-pps pulse trains, and there was a relatively small effect of place. Furthermore, it could be concluded from this experiment that listeners were not solely benefiting from the longest interpulse intervals 共IPIs兲 and the instances of reduced rate by adding jitter, because the two types of pulse trains had the same longest IPI. The effect of jitter was studied using a physiologically-based model of auditory nerve and brainstem 共medial superior olive neurons兲. It was found that the random timing of the jittered pulses increased firing synchrony in the auditory periphery, which caused an improved rate-ITD tuning for the 600-pps pulse trains. These results suggest that a recovery from binaural adaptation induced by temporal jitter is possibly related to changes in the temporal firing pattern, not spectral changes. © 2009 Acoustical Society of America. 关DOI: 10.1121/1.3206584兴 PACS number共s兲: 43.66.Pn, 43.66.Ba, 43.66.Qp, 43.66.Mk 关RLF兴

I. INTRODUCTION

The experiments described here were motivated by recent work on interaural time difference 共ITD兲 sensitivity in cochlear-implant 共CI兲 users and past work on the binaural adaptation phenomenon observed in ITD perception of normal-hearing 共NH兲 listeners. Hafter and Dye 共1983兲 presented evidence that ITD sensitivity decreases for highfrequency modulated stimuli, like bandpass-filtered pulse trains, if the modulation rate is too high. By systematically varying the number and rate of pulses in a train, they found that increasing the pulse rate decreases the usefulness of the binaural information after the onset. Later, Hafter and Buell 共1990兲 showed that a recovery from binaural adaptation can be produced by inserting a change or “trigger” in the signal. They reported a recovery from adaptation when doubling or halving one or more intervals in a pulse train with a 2.5-ms interpulse interval 共IPI兲. They also reported a recovery from binaural adaptation to a pulse train by adding short trigger signals such as diotic sinusoids or diotic, monotic, or uncorrelated noise bursts. Hafter and Buell 共1990兲 concluded that the recovery effect from a trigger was most likely due to a temporary spectral change in the signal. The previously described studies were performed with a fixed number of pulses. In fact, even for a periodic stimulus with a fixed duration 共such as pulse trains, sinusoidally amplitude modulated tones, or transposed tones兲, there is decreasing ITD sensitivity with increasing modulation rate 共e.g., Bernstein and Trahiotis, 2002; Majdak and Laback, 2009兲. Recent work with CIs readdressed the binaural adaptation phenomenon and introduced a new method to cause a

a兲

Author to whom correspondence should be addressed. Electronic mail: [email protected]

J. Acoust. Soc. Am. 126 共5兲, November 2009

Pages: 2511–2521

recovery from binaural adaptation 共Laback and Majdak, 2008兲. CIs use high-rate electric pulses to encode acoustic information. Several recent studies have shown that, similar to NH listeners, ITD sensitivity in CI listeners rapidly decreases with increasing pulse rate beyond a few hundred pulses per second 共pps兲共Majdak et al., 2006; Laback et al., 2007; van Hoesel, 2007兲. Laback and Majdak 共2008兲 hypothesized that this pulse rate limitation is a form of binaural adaptation and showed that introducing binaurallysynchronized jitter 共referred to as binaural jitter兲 can substantially increase ITD sensitivity at rates of 800– 1515 pps. Because direct electric stimulation at one interaural electrode pair was used in that experiment, the jitter changed only the temporal properties of the stimuli, not the spectral. Therefore, they concluded that the recovery from binaural adaptation is caused by ongoing temporal changes in the signal. In this study, we examined if a similar improvement in ITD sensitivity could be achieved in acoustic hearing by introducing binaural jitter into high-frequency bandpassfiltered pulse trains. In experiment 1, we tested the effect of binaural jitter for 600-pps pulse trains, a pulse rate at which listeners normally have difficulty in detecting waveform ITDs 共Majdak and Laback, 2009兲. In experiment 2, we tested the hypothesis that the improvement in ITD sensitivity depends on only the longest IPIs of a jittered pulse train. We then modeled the response of the auditory periphery and brainstem to jittered pulse trains to observe the likely changes to the physiological firing patterns introduced by jitter in an attempt to understand the listeners’ ITD sensitivity. The effect of binaural jitter on ITD sensitivity has already been investigated in two earlier studies using sinusoids 共Nordmark, 1976; Blauert, 1981兲. Nordmark 共1976兲 reported surprisingly small just noticeable differences 共JNDs兲 around

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© 2009 Acoustical Society of America

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1.5 ␮s for a temporally-jittered 4-kHz carrier. Blauert 共1981兲 replicated Nordmark’s experiment and found JNDs that were two orders of magnitude larger 共around 170 ␮s兲. If the latter measurement is correct, this means that ITD JNDs for jittered sinusoids are comparable to other high-frequency stimuli that have an amplitude modulation 共AM兲共Henning, 1974兲 or a frequency modulation 共FM兲共Henning, 1980兲. This might be expected if a jittered sinusoid is viewed as a FM with a random modulation frequency. Note, however, the fundamental difference between the study by Nordmark 共1976兲 and Blauert 共1981兲 using jittered sinusoids, and both Laback and Majdak’s 共2008兲 study and the present study using pulse trains. The purpose of using jittered sinusoids in earlier studies was to present usable ITD information at high center frequencies. The purpose of this study is to investigate the effect of jitter on ITD rate limitations for pulsatile stimuli, which are commonly associated with CI processing strategies, and to more deeply understand how temporal jitter affects ITD sensitivity. II. EXPERIMENT 1 A. Listeners and equipment

Six listeners participated in this experiment. All listeners were between 24 and 37 years old and had normal hearing according to standard audiometric tests. Two listeners were authors of this study 共NH2 and NH10兲. All six listeners were experienced with virtual sound localization. Three listeners 共NH2, NH8, and NH10兲 had extensive experience in lateralizing pulse trains. From preliminary tests and training, we determined that listeners NH2, NH8, and NH10 could lateralize pulse trains with relatively small amounts of jitter compared to the other listeners. Therefore, we divided the listeners into a high-sensitivity group 共NH2, NH8, and NH10兲 and a low-sensitivity group 共NH12, NH14, and NH15兲. Also, NH8 was markedly more sensitive to ITD than the other five listeners. Thus, he was given smaller ITD values to lateralize to avoid ceiling effects. A personal computer system was used to control the experiment. The stimuli were output via a 24-bit stereo A/DD/A converter 共ADDA 2402, Digital Audio Denmark兲 using a sampling rate of 96 kHz/channel. The analog signals were sent through a headphone amplifier 共HB6, TDT兲 and an attenuator 共PA4, TDT兲. The signals were presented to the subjects via headphones 共HDA200, Sennheiser兲. Calibration of the headphone signals was performed using a sound level meter 共2260, Brüel & Kjær兲 connected to an artificial ear 共4153, Brüel & Kjær兲. B. Stimuli

The stimuli were 500-ms pulse trains composed of 10.4-␮s monophasic pulses, corresponding to one sampling interval at a sampling rate of 96 kHz. The pulse rate was 600 pps, which has an IPI of 1667 ␮s. A recent study by Majdak and Laback 共2009兲 showed that ITD sensitivity degrades to chance around 500 pps for most NH listeners, which is generally consistent with studies that use other types of modulated stimuli 共e.g., Bernstein and Trahiotis, 2512

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A)

Periodic Pulse Train Left Right

Binaurally-jittered Pulse Train

B) Left Right

FIG. 1. Examples of a periodic pulse train 共A兲 and a binaurally-jittered pulse train 共B兲. The arrows indicate that the ITD of the two signals is always constant between pulses, independent of the IPI of the pulses.

2002兲. Thus, stimuli with a 600-pps pulse rate have the property that there is substantial room for improvement in ITD sensitivity. A waveform ITD was introduced by delaying the temporal position of the pulses at one ear relative to the other ear. The ITD values were 100, 200, 400, and 600 ␮s for all but one listener. The other listener, who was unusually sensitive to ITDs, was tested with ITD values of 20, 50, 100, and 150 ␮s. To minimize the detection of ITD in the onset and offset of the stimulus, 150-ms linear ramping was applied to the pulse trains. The full-on duration of the stimuli was 200 ms. The −3-dB duration of the stimuli was 288 ms. Jitter in the timing of the pulses was applied to the stimuli. Periodic pulse trains 关Fig. 1共A兲兴 had a constant IPI, whereas the jittered pulse trains 关Fig. 1共B兲兴 had randomlyvaried IPIs. The nominal IPI corresponded to the average IPI over the stimulus duration. To preserve the ITD information in the pulse timing, the jitter was synchronized between the two ears 共indicated by the constant length of the arrows in Fig. 1兲. The jitter followed a rectangular distribution, where the parameter k defines the width of the distribution relative to the nominal IPI. The parameter k ranges from 0 共periodic, no jitter兲 to 1 共maximum jitter兲. A jittered pulse train was “constructed” pulse by pulse. For each pulse added, the IPI was varied within the range of IPI· 共1 ⫾ k兲. Thus, for k = 1, the largest possible IPI was twice the nominal IPI and the smallest possible IPI was zero. For the three high-sensitivity listeners, the jitter values were k = 0 共periodic condition, no jitter兲, 1 / 128, 1 / 32, 1 / 8, and 1 / 3. For the three lowsensitivity listeners, the jitter values were k = 0, 1 / 8, 1 / 3, 1 / 2, and 3 / 4.1 Each trial used a new random jitter manifestation. The pulse trains were passed through a digital sixthorder bandpass Butterworth filter. The spectral center frequency of the band was 4.6 kHz. The spectral bandwidth was 1.5 kHz. The A-weighted sound pressure level of the stimuli was 72 dB 共re: 20 ␮Pa兲. In a control condition, Gaussian white noises were used as stimuli, filtered by the same sixthorder Butterworth bandpass filter that was used for the jittered pulse trains. Binaurally-uncorrelated, low-pass filtered, white noise was used to mask low-frequency components that might contain useful binaural cues. The corner frequency was Goupell et al.: Temporal jitter and interaural time differences

FIG. 2. 共Color online兲 Results from experiment 1, the percentage of correct left-right discriminations for pulse trains with various jitter values and for noises. The high-sensitivity listeners are plotted in the top row, the low-sensitivity listeners in the bottom. Listener NH8 has smaller values of ITD than the other five listeners.

3500 Hz, with a 24-dB/oct roll-off, and the A-weighted sound pressure level of the noise was 61 dB. The sound pressure spectrum level at 2 kHz was 35.8 dB 共re: 20 ␮Pa in a 1-Hz band兲. C. Procedure

A two-interval, two-alternative forced-choice procedure was used in a lateralization discrimination test. The first interval contained a reference stimulus with zero ITD and zero k evoking a centralized auditory image. The second interval contained the target stimulus with non-zero ITD and one of the five values of k. The interstimulus interval was 400 ms. The listeners indicated whether the second stimulus was perceived to the left or to the right of the first stimulus by pressing a button. Visual response feedback was provided after each trial. The listeners controlled when the next trial began. For the pulse trains, a block contained 2000 trials consisting of 100 presentations of four ITD and five k values in a randomized order. For the noises, a block contained 400 trials consisting of 100 presentations of four different values of ITD. The 100 repetitions per condition were presented in a balanced format with 50 targets on the left and 50 targets on the right. The chance rate was 50%. Listeners took a break every 200–250 trials, which was approximately every 15 min. The order of the two blocks was balanced over listeners. Listeners were trained before the main test started. The training began with stimuli that had k = 1 / 3 and ITD= 600 ␮s. Values of k and/or ITD were decreased as listeners’performance improved. Training continued until J. Acoust. Soc. Am., Vol. 126, No. 5, November 2009

performance saturated. Listeners were separated into highsensitivity and low-sensitivity groups after the training. If a listener could left/right discriminate k = 1 / 3, ITD= 200-, 400-, and 600-␮s pulse trains more than 80% of the time, they were placed within the high-sensitivity group. The training period lasted between 4 and 8 h depending on the listener. D. Results

Figure 2 shows the results of the experiment. The highsensitivity listeners 共NH2, NH8, and NH10兲 are plotted in the top row. The low-sensitivity listeners 共NH12, NH14, and NH15兲 are plotted in the bottom row. Several of the psychometric functions asymptote well below 100% correct. Several of the listeners show a decrease in percent correct 共Pc兲 for the periodic 共k = 0兲 400-␮s condition where the ITD is ambiguous for a 600-pps pulse train. The data show that adding jitter to pulse trains increases ITD discrimination performance and eliminates the decreases in Pc due to the ITD ambiguity. The performance for the jittered pulse trains seems to be approximately limited by the performance for the bandpass-filtered noise stimuli. A two-way repeated-measures analysis of variance 共RM ANOVA兲共factors: ITD and k兲 was performed. The values of Pc were transformed using the rationalized arcsine transform proposed by Studebaker 共1985兲 to not violate the homogeneity of variance assumption required for an ANOVA. The RM ANOVA showed that the main effects were highly significant 共p ⬍ 0.0001 for both兲, but the interaction was not statistically significant 共p = 0.47兲. Tukey HSD post-hoc tests were performed separately for the two listener groups to determine Goupell et al.: Temporal jitter and interaural time differences

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TABLE I. JNDs calculated for experiment 1. JNDs that were not determinable are labeled “ND.” JNDs that were not measured for a given listener are labeled “—.” High-sensitivity

Low-sensitivity

k

NH2

NH8

NH10

NH12

NH14

NH15

0 1 / 128 1 / 32 1/8 1/3 1/2 3/4 Noise

ND ND 396.2 253.1 165.6 — — 60.3

83.9 65.0 89.9 45.1 27.2 — — 22.3

442.6 329.2 152.9 138.0 131.8 — — 81.6

ND — — ND 214.4 78.1 68.9 112.6

ND — — ND ND 137.6 128.7 201.8

ND — — ND ND 167.0 155.5 132.9

the value of k that shows a significant increase from the periodic condition. For the high-sensitivity listeners, k = 0 did not differ from k = 1 / 128 共p = 0.94兲 and k = 1 / 32 共p = 0.22兲; k = 0 significantly differed from k = 1 / 8 共p = 0.0004兲 and k = 1 / 3 共p ⬍ 0.0001兲. For the low-sensitivity listeners, k = 0 did not differ from k = 1 / 8 共p = 0.30兲; k = 0 significantly differed from k = 1 / 3 共p = 0.001兲, k = 1 / 2 共p ⬍ 0.0001兲, and k = 3 / 4 共p ⬍ 0.0001兲. To more easily compare our results to those of previous studies, JNDs were estimated for each listener.2 The threshold criterion was set to 70% and JNDs are reported in Table I. Some JNDs could not be computed because there were no Pc values above 70%. E. Discussion

The data in Fig. 2 show that introducing jitter to the pulse timing of an acoustic pulse train can substantially improve ITD discrimination performance. Depending on the sensitivity of the listener, the amount of jitter that increased ITD sensitivity was different. The high-sensitivity listeners showed significant improvements for jitter values as small as 1 / 8. The low-sensitivity listeners showed significant improvements for jitter values as small as 1 / 3. Listeners showed no or low sensitivity to ITD in the periodic 600-pps pulse trains, which was expected based on pilot tests. In many cases for low values of k, JNDs could not be determined 共ND in Table I兲, consistent with previous studies of ITD sensitivity at this rate 共Majdak and Laback, 2009兲. In contrast to our results, studies using comparable-rate pulse trains reported determinable JNDs 共Hafter and Dye, 1983; Dye and Hafter, 1984兲. This difference is most likely due to the fact that we used long 共150-ms兲 temporal ramping and thus avoided onset cues, which are known to be important at such high rates 共e.g., Saberi and Perrott, 1995; Laback et al., 2007兲. Binaurally-jittered pulse trains have not been tested before in acoustic hearing. Hafter and Buell 共1990兲 tested the effect of inserting one or three gaps of 5 or 7.5 ms in a regular pulse train with a standard IPI of 2.5 ms and observed improvements of ITD JNDs as large as a factor of 2. Even though this modification has some similarities with binaural jitter, a direct comparison to our results is hindered by the several differences in the stimuli, including the pulse 2514


rate, the signal duration, and the manner of IPI modification. Laback and Majdak 共2008兲 reported the effect of binaural jitter in electric pulse trains presented to CI listeners. They observed large improvements in ITD sensitivity similar to the improvements of the NH listeners in the current study. Again, a quantitative comparison between the two studies is hindered by differences in the stimuli, most importantly the difference between acoustic and electric hearing, but also the different pulse rates and the fact that the electric stimuli intentionally included a slowly-varying envelope modulation. Nordmark 共1976兲 and Blauert 共1981兲 measured ITD sensitivity to jittered sinusoids, which can produce random AM at the output of some auditory filters as a result of FMto-AM conversion. Thus, the jittered sinusoids may have similar temporal characteristics as our jittered pulse trains. Comparison of our JNDs to those for the previous two studies agrees with Blauert’s measurement, who found an average JND of 173 ␮s for 5% jitter. For our experiment, the average JND was 213 ␮s for the high-sensitivity listeners for k = 1 / 32= 3% jitter. The JNDs were not determinable for the low-sensitivity listeners for this jitter value. Our measurements may be slightly larger compared to Blauert because we used low-frequency masking noise, which could have increased JNDs 共Bernstein and Trahiotis, 2004兲. Blauert 共1981兲 measured an average JND of 35 ␮s for 1-octave noise centered at 4 kHz. Our average JND was 102 ␮s for a 1 / 2-octave noise. Assuming increasing sensitivity with increasing spectral bandwidth 共Bernstein and Trahiotis, 1994兲, our JNDs are expected to be larger than Blauert’s JNDs. As mentioned before, we included a lowfrequency masking noise, which could have further increased JNDs. The results show that ITD sensitivity increases as the amount of jitter increases. This gain appears to be limited to the performance achieved with the bandpass-filtered noise stimuli. A discussion of the similarities between noise and jittered pulse trains is provided in the general discussion. III. EXPERIMENT 2: HIGHER RATE AND PLACE

By introducing jitter, portions of the pulse trains have a relatively long instantaneous IPI, which decreases the instantaneous rate. At high center frequencies, low-rate modulated stimuli are easier to lateralize than unmodulated stimuli Goupell et al.: Temporal jitter and interaural time differences

共Henning, 1974兲, or high-rate modulated stimuli 共Bernstein and Trahiotis, 2002兲. It could be that the increase in ITD sensitivity with jitter was due to the listeners more effectively utilizing the long IPIs in the pulse train compared to the short IPIs. This hypothesis has two forms. The first form is that listeners utilized the IPIs longer than some critical absolute value. The second form is that listeners utilized the IPIs relatively longer than the surrounding IPIs. In this experiment, we tested the first form of this hypothesis. To do this, we used periodic 600-pps pulse trains and jittered 1200-pps pulse trains 共k = 1兲. If the performance at 1200 pps with jitter exceeds the performance at 600 pps without jitter, then the absolute length of the IPI cannot be the sole signal property that causes the increased ITD sensitivity with increasing jitter. This is because the maximum IPI for a 1200-pps pulse train with k = 1 is precisely the IPI for a 600-pps pulse train without jitter. To keep the number of resolved harmonics constant and the spectral bandwidth approximately constant in terms of critical bands 关an equivalent rectangular bandwidth of approximately 2.3 at both center frequencies 共Moore and Glasberg, 1983兲兴, the spectral center frequency and bandwidth of the 1200-pps stimulus were increased by a factor of 2 relative to the 4.6-kHz pulse train. As control conditions, a 600-pps pulse train was tested at a 9.2-kHz center frequency and a 1200-pps pulse train was tested at 4.6 kHz. This allowed us to further study the effects of the rate and place parameters. A. Methods

This experiment used the same methods as experiment 1 and tested three conditions. The first condition used stimuli that had a spectral center frequency of 4.6 kHz and a bandwidth of 1.5 kHz, like those of experiment 1, but with a pulse rate of 1200 pps. The jitter value was either k = 0 or 1. The second and third conditions used stimuli that had a center frequency of 9.2 kHz and a bandwidth of 3 kHz. The second condition had 600-pps stimuli with k = 0 or 1 / 3 for the high-sensitivity listeners or k = 0 or 3 / 4 for the lowsensitivity listeners. These values of k matched the largest values of k for the 600-pps data tested in experiment 1 for particular listener groups. The third condition had 1200-pps stimuli with k = 0 or 1 for all the listeners. The A-weighted sound pressure level was 72 dB for all of the stimuli. The masking noise was the same as used in experiment 1. The same six listeners participated in this experiment. For listener NH8, ITD values of 50 and 100 ␮s were tested. For the other listeners, the ITD values of 200 and 400 ␮s were tested. B. Results

Figure 3 shows the results for experiment 2. The 4.6-kHz, 600-pps data are repeated from experiment 1. From the figure, it can be easily seen that for any specific condition the performance for the jittered pulse trains was always greater than for the periodic pulse trains. For the periodic conditions, there appear to be substantial floor effects as most of the Pc values are near 50%. For some jittered conditions and listeners, there appear to be some ceiling effects. J. Acoust. Soc. Am., Vol. 126, No. 5, November 2009

FIG. 3. Results from experiment 2. The high-performance listeners are plotted in the top three rows, the low-performance in the bottom three. Listener NH8 had smaller values of ITD 共small ITD= 50 ␮s and large ITD = 100 ␮s兲 than the other five listeners 共small ITD= 200 ␮s and large ITD = 400 ␮s兲. The high-sensitivity listeners were presented jittered 600-pps pulse trains with k = 1 / 3. The low-sensitivity listeners were presented jittered 600-pps pulse trains with k = 3 / 4. All six listeners were presented jittered 1200-pps pulse trains with k = 1. The results for the 4.6-kHz 600-pps pulse trains are replotted from experiment 1.

To determine the effects of place and rate, specific cases were compared with a RM ANOVA. The values of k = 1 / 3, 3 / 4, or 1 were considered as a single condition with jitter for the statistical analysis. This is reasonable because the highperformance listeners in experiment 1 seemed to show a saturation of performance 共approximately the performance for the bandpass noise兲 at k = 1 / 3 and the low-performance listeners at k = 3 / 4. It is assumed that a value of k = 1 would only marginally improve the performance. First, one of the most important comparisons for this experiment is between Goupell et al.: Temporal jitter and interaural time differences

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jittered 1200-pps pulse trains at 9.2 kHz and periodic 600-pps pulse trains at 4.6 kHz. There was a significant difference between these two conditions 共p ⬍ 0.0001兲. This indicates that the absolute length of the IPIs due to jittering pulse trains does not cause the observed improvements in ITD sensitivity. However, the comparison between these two conditions might be confounded by the effect of the different places and bandwidths. The effect of place was tested using a RM ANOVA including only conditions with jitter to avoid floor effects. There was a significant decrease in performance with increasing place 共p = 0.001兲. Thus, even though there was an effect of place, it does not confound the conclusion of a larger performance for the jittered 9.2-kHz pulse trains compared to the periodic 4.6-kHz pulse trains. Rather, the effect of place reduces the difference. It is possible that the increased sensitivity for the jittered 1200-pps pulse trains at 9.2 kHz compared to the periodic 600-pps pulse trains at 4.6 kHz is due to the increased spectral bandwidth used at 9.2 kHz. Therefore, we compared jittered 1200-pps pulse trains to periodic 600-pps pulse trains for a fixed place of 4.6 kHz. There was a significant difference between these two conditions 共p ⬍ 0.0001兲. Since the jittered 1200-pps pulse trains showed a higher performance than the periodic 600-pps pulse trains for a constant spectral bandwidth, it stands to reason that it was not the increased bandwidth that increased the performance when the place was changed. C. Discussion

This experiment tested the hypothesis that jitter increases ITD sensitivity because it increases some IPIs beyond some absolute duration. Long IPIs may provide a benefit to listeners due to the refractoriness of some auditory neurons. This hypothesis can be rejected because it was shown that it was much easier to lateralize jittered 1200-pps pulse trains than periodic 600-pps pulse trains while systematically varying the rate and place parameters. Varying both parameters was necessary because by changing the rate, the number of resolved harmonics in the stimulus changed. The comparisons showed that place and rate had a comparatively small effect on ITD sensitivity compared to the jittering of pulse timing. IV. MODELING OF NEURAL RESPONSE

Physiological measurements of responses of ventral cochlear-nucleus 共VCN兲 chopper cells to maximum length sequence pulse trains 共essentially jittered pulse trains兲 have been performed by Burkard and Palmer 共1997兲. Their measurements showed that jitter increases the probability of a VCN neuron firing at certain time instances. Although spherical bushy VCN cells, not chopper VCN cells, project to the medial superior olive 共MSO兲共Smith et al., 1993兲, insight may be gained from Burkard and Palmer’s 共1997兲 measurements. We hypothesized that the responses of the auditory nerve 共AN兲 fibers, the input of the VCN, would become more synchronous after the introduction of jitter. We also hypothesized that increased synchrony will cause a 2516


FIG. 4. Example PSTHs for 100-pps 关panel 共A兲兴 and 600-pps pulse trains 关panels 共B兲 and 共C兲兴. Stimuli are either periodic 共k = 0兲 or jittered 共k = 0.9兲. Only one manifestation is shown for each type of stimulus. The examples shown in panels 共A兲 and 共B兲 are from a 100-ms section from the steady state portions of the different types of stimuli. Panel 共C兲 shows a 20-ms section for the 600-pps pulse train with a different vertical scale.

sharpening of rate-ITD tuning. We assumed that sharpening of rate-ITD tuning is related to improvements in ITD sensitivity. Therefore, we modeled AN and MSO responses to binaurally-jittered pulse trains. A. AN model

The model of the auditory periphery that was used was developed by Meddis 共2006兲. We will briefly describe the model. A physical acoustic stimulus was filtered by a human outer and middle ear model based on Huber et al. 共2001兲. The filtering of a human basilar membrane was modeled with a dual-resonance non-linear filter with parameters based on Tables II and III in Lopez-Poveda and Meddis 共2001兲. The inner-hair cell 共IHC兲 cilia, IHC presynapse, and AN synapse parameters were from Tables II, III, and IV of Meddis 共2006兲, respectively. Only high-spontaneous rate fibers were modeled. The refractory time for the AN fibers was 0.75 ms. The model sampling rate was 10 kHz. The input stimuli had the same parameters 共level, duration, rise-fall time, etc.兲 as the stimuli used in the experiments. Figure 4 shows sample post-stimulus time histograms 共PSTHs兲 for periodic and jittered 共k = 0.9兲 100-pps and 600-pps pulse trains with a 4.6-kHz center frequency. The auditory filter was centered at 4.6 kHz. The 100-pps pulse trains show synchronous responses to both the periodic and jittered conditions, and there is little noticeable difference in the PSTHs with the exception for the expected aperiodic timing of peaks for the jittered pulse train. In contrast, for the periodic 600-pps pulse trains, the synchrony is not evident. Additionally, the jittered 600-pps pulse train shows noticeably higher peaks in the PSTH compared to the periodic 600-pps pulse train, which can easily be seen in Fig. 4共C兲. We measured the firing rate and synchrony of the AN fibers’ responses. Each measurement was made over 50 unique PSTHs. All calculations were made over the entire 500-ms stimulus duration. Figure 5 shows the average firing rate and the correlation index 共CIn兲共described below兲 for the average of five pulse train manifestations for five pulse rates 共100, 300, 600, 900, and 1200 pps兲 as a function of k 共0, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, and 1兲. The responses of two filters with best frequencies 共BFs兲 of 4.6 and 9.2 kHz were modeled. The AN firing rates for the 100-pps pulse trains are around 50– 70 spikes/ s. Theoretically, the firing rate should be near 100 spikes/ s. As stated before, because of the long temporal onset and offset ramps, the −3-dB duration of the Goupell et al.: Temporal jitter and interaural time differences

FIG. 6. AN firing rate and CIn as a function of auditory filter BF. The stimuli were periodic 共k = 0兲 and jittered 共k = 0.9兲 600-pps pulse trains with a 4.6-kHz center frequency. Each point shows the average AN firing rate or CIn over the five manifestations of jitter. The error bars show ⫾1 standard deviation over the five manifestations. Several points have error bars smaller than the size of the data point.

FIG. 5. The average AN firing rates and the CIn for five pulse rates as a function of k. The left panels are for the 4.6-kHz pulse trains. The right panels are for the 9.2-kHz pulse trains. Each point shows the average AN firing rate or CIn over the five manifestations of jitter. The error bars show ⫾1 standard deviation over the five manifestations. The dotted lines show the value of the CIn for k = 0 to more easily identify changes for increasing k.

stimuli was only 288 ms. If the temporal ramping was omitted from the input stimuli, the firing rates would be higher. The other pulse rates have a higher firing rate, limited by the refractory time of the AN fibers. For both center frequencies and all pulse rates, the AN firing rate decreases slightly with jitter. For the higher pulse rates, a small decrease in firing rate may be expected with jitter because, after short IPIs, pulses will be missed because of the refractory effects. This will not necessarily be compensated by the longer IPIs because it will depend on the lengths of the surrounding IPIs. We quantitatively measured the change in synchrony when jitter was added to a pulse train. Since jittered pulse trains are aperiodic, a common metric like the synchronization index is not appropriate. Instead, we used a metric to allow for aperiodic stimuli, called the CIn 共Joris et al., 2006兲. The CIn is based on the counting of neural response spike coincidences from multiple presentations of the same stimulus. Mathematically, the CIn is CIn =

2Nc , M共M − 1兲r␻T

where Nc is the number of individual neuron firing coincidences, r is the average firing rate, M is the number of presentations, ␻ is the coincidence window duration, and T is the duration of the stimulus. The factor of 2 is necessary because we used the number of unordered pairs for our calculation, not the number of ordered pairs as in Joris et al. 共2006兲. For our modeling, we used ␻ = 100 ␮s and M = 50 presentations. The CIn has a value of 1 for an uncorrelated response, a value greater than 1 for a correlated response, J. Acoust. Soc. Am., Vol. 126, No. 5, November 2009

and a value of 0 for an anticorrelated response. The bottom row of Fig. 5 shows the CIn. The dotted lines show the CIn for k = 0. For an increase in jitter, both center frequencies and all pulse rates show an increase in CIn, hence more synchronous firing. The 100- and 300-pps pulse trains show increases for k greater than or equal to 0.5. In contrast, the higher pulse rates show an increase in CIn for values of k as small as 0.05. For a condition that showed a significant increase in ITD sensitivity in experiment 1 共highsensitivity listeners兲, namely, the 600-pps pulse trains for k = 1 / 8 = 0.125, there is an increase in firing synchrony. Blauert 共1981兲 postulated that the increase in ITD sensitivity to jittered sine tones was due to FM-to-AM conversion of the signal, which may happen due to the steep slopes of the auditory bandpass filters. He postulated this especially for off-frequency filters toward higher frequencies. To investigate the use of off-frequency cues for ITD sensitivity, we modeled the response of auditory filters with BFs from 3 to 9 kHz. We used periodic and jittered 共k = 0.9兲 600-pps pulse trains, all with a 4.6-kHz spectral center frequency. Like before, we averaged our results over five different jitter manifestations. Figure 6 shows the results of varying the BF of the auditory filter. The jittered pulse trains always have a slightly smaller firing rate than the periodic pulse trains for all auditory filters modeled, although this difference is approximately constant for all BFs. The jittered pulse trains always have a larger CIn than the periodic pulse trains for all auditory filters modeled. The largest differences were for auditory filters away from the center frequency of the stimulus, in line with Blauert’s 共1981兲 notion that the AM in offfrequency filters could be important for detecting ITDs. Another explanation for the larger CIn 共hence improved synchrony兲 with increasing auditory filter BF would be that the basilar membrane impulse response becomes shorter with increasing center frequency because the auditory filter bandwidth increases. The importance of the length of the basilar membrane impulse response is also supported by the results for periodic pulse trains in Fig. 5; the CIn for the 9.2-kHz band is consistently higher than the CIn for the 4.6-kHz band. B. MSO coincidence model

Because we observed an increase in AN firing synchrony with an increase in jitter, we wondered if such an Goupell et al.: Temporal jitter and interaural time differences

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FIG. 7. MSO rate-ITD tuning curves for auditory filters with differing BF. The stimuli were periodic 共k = 0兲 and jittered 共k = 0.9兲 600-pps pulse trains with a 4.6-kHz center frequency. Each point shows the average firing rate or CIn over the five manifestations of jitter. Error bars representing ⫾1 standard deviation are all smaller than the data points.

increase could be utilized by the MSO to improve ITD perception. We simply used the response of the AN as the MSO input because it is presently unknown exactly how primarylike spherical bushy VCN cells alter the AN firing pattern. The modeled MSO neuron was a simple excitatoryexcitatory coincidence counter. Thirty excitatory synapses 共15 per side兲 provided the input to the cell. The cell fired if there was a coincident firing from the left and right inputs within a 100-␮s window. One-hundred unique PSTHs were made and 30 共15 for each side兲 were randomly selected without replacement as the input to the MSO cell.3 After a coincidence, the cell went into a refractory state where no firing occurred for 1 ms 共Scott et al., 2005; Scott et al., 2007兲.4 Each MSO measurement was repeated 100 times using different random sets of 30 PSTHs, chosen from the same pool of 100 PSTHs. To show how an increased firing synchrony could translate to increased ITD sensitivity, we calculated MSO firing rates for binaural AN inputs with a range of ITDs. To support the psychophysical data, we expect sharper rate-ITD tuning for jittered pulse trains. The model MSO neuron had a best ITD of 0 ␮s. Figure 7 shows the rate-ITD curves for responses of auditory filters with BFs between 4 and 9 kHz. The input stimuli were a periodic and a jittered 共k = 0.9兲 600-pps pulse train with a 4.6-kHz center frequency. Little difference in the tuning could be seen between the shapes of the curves for the periodic and jittered pulse trains at 4 and 5 kHz. At higher BFs, the periodic nature of the rate-ITD tuning curves is apparent for the periodic pulse trains. This periodic nature is not seen for the jittered pulse trains. As expected, because the CIn is larger for the jittered pulse trains, there was sharper rate-ITD tuning. The MSO firing rate decreases for all ITDs for best auditory filter frequencies of 6 kHz and higher. This is due to the decreasing firing rate in the AN with increasing BF, seen in Fig. 6共A兲. V. GENERAL DISCUSSION

These experiments were inspired by previous studies on the binaural adaptation phenomenon 共Hafter and Dye, 1983; 2518


Hafter and Buell, 1990兲. The results show that introducing binaurally-synchronized jitter into the timing of highfrequency filtered pulse trains considerably improves ITD sensitivity of NH listeners, consistent with the hypothesis that a change in the ongoing signal causes a recovery from binaural adaptation. However, while Hafter and Buell 共1990兲 and Hafter 共1997兲 argued that the recovery effect is mediated by a discernible short-term change to the spectrum, the study by Laback and Majdak 共2008兲 on the effect of binaural jitter on ITD sensitivity in CI listeners suggests that temporal changes alone can cause a recovery. Direct electrical stimulation at a single interaural electrode pair allowed the introduction of jitter to the pulse timing without concomitant spectral changes. The improvements in ITD sensitivity by binaural jitter in electrical hearing were similar to those observed in the present study with acoustic hearing. Of course, it is possible that different mechanisms are responsible for the improvements in electric and acoustic hearing. Hence, we cannot entirely dismiss the possibility that spectral changes also contributed to the recovery effect in acoustic hearing. It is worth noting that jitter, created by randomly modulating the rate of pulses, will cause an additional AM signal due to FM-to-AM conversion from auditory filtering in NH listeners. In contrast, in CI listeners, the auditory filters are bypassed. However, additional AM is probably created in both NH and CI listeners in the auditory system via synaptic transmission properties and neural membrane time constants. In experiment 2, we hypothesized that the improvement in ITD sensitivity was due to only the introduction of long IPIs. Long IPIs could reduce the instantaneous modulation rate below the lowpass cutoff of a modulation filter or allow temporary recovery from refractoriness in auditory neurons. The data showed higher performance for jittered 1200-pps pulse trains compared to periodic 600-pps pulse trains. Since the pulse trains for the two different rates had longest IPIs of the same duration, this implies that the absolute length of the IPI is not as important as the relative IPI in the context of the surrounding pulses. Similar results can be found using electric stimulation 共Laback and Majdak, 2008兲. Two listeners for which comparable data are available showed significantly higher percent correct scores for jittered pulse trains 共k = 3 / 4兲 at 1515 pps compared to the scores for periodic pulse trains at 800 pps for an ITD of 600 ␮s. Nevertheless, there is no reason to assume that long IPIs do not improve ITD sensitivity. However, having only long IPIs is not sufficient to improve ITD sensitivity. Rather, the temporal jitter, which combines both long and short IPIs, seems to be the necessary condition for improved ITD sensitivity. We modeled the neural response characteristics in order to determine if response changes in the auditory periphery and brainstem might reflect the behavioral changes in ITD sensitivity. The results indicate that jitter increases the synchrony in the neural spike pattern of the ongoing signal. This is especially the case for auditory filters with BFs higher than the center frequency of the stimulus. It is quite likely that the increased synchrony makes it easier for the binaural system to detect an ITD, given that the jitter is synchronized between the two ears. Goupell et al.: Temporal jitter and interaural time differences

Modeling the basic operation of MSO neurons, we also showed improved rate-ITD tuning for auditory filters with BFs higher than the center frequency of the stimulus. While the simple MSO model was able to capture some of the expected trends in the data, numerous improvements could be made to the modeling, which might show a greater contrast between the rate-ITD tuning curves for periodic and jittered signals. For example, inclusion of spherical bushy VCN cells, which act as the input to the MSO, may act as monaural coincidence detectors 共Carney, 1990兲. Also, a true physiological model of the MSO could be used 共Han and Colburn, 1993兲, particularly one that includes elements that improve timing aspects, such as the inclusion of dendrites 共Agmon-Snir et al., 1998兲. VCN bushy cells and MSO principle neurons contain low-threshold potassium channels, which are thought to play a role in coincidence detection 共Manis and Marx, 1991; Smith, 1995兲. High-rate pulse trains, which would produce a relatively constant synaptic input to these neurons, may produce sustained activation of the low-threshold potassium channels, which, if included in the model, would suppress neuron repolarization and block firing 共Colburn et al., 2008兲. Also, inclusion of inhibitory effects in the VCN 共Burkard and Palmer, 1997兲 or at higher centers like the inferior colliculus 共Smith and Delgutte, 2008兲 may also help the use of models to understand the jitter effect. The modeling results provide an explanation for the jitter effect in terms of increased synchrony of the neural response at the level of the AN, which is not inconsistent with recent ITD sensitivity measurements in CI listeners by van Hoesel 共2008兲. This explanation is somewhat different from the hypothesis proposed by Hafter and Buell 共1990兲 that the recovery from binaural adaptation induced by inserting a change 共trigger兲 in a pulse train is an active process involving some kind of change detector. Hafter and Buell 共1990兲 reported that other types of changes applied to the ongoing part of a pulse train, such as the insertion of short trigger signals 共either monotic or diotic兲, cause recovery. The question arises if the effect of these changes could also be explained by an increase in synchrony. The answer is probably no, since a monotic or a diotic trigger signal in the spectral frequency region of the pulse train could disrupt the ITD. This is because the changes in the neural firing pattern would be unassociated with the ITD. This seems to imply that the recovery effect observed by Hafter and Buell 共1990兲 with those triggers is mediated via another mechanism, which may involve a true change detector. However, our modeling results do not necessarily rule out the restarting explanation of Hafter and Buell 共1990兲, and further work needs to be done to investigate the underlying mechanisms of recovery from binaural adaptation. An interesting aspect of the data obtained in this study, which was also seen for electric hearing in Laback and Majdak 共2008兲, is that binaural jitter resolves the ambiguity in the ongoing ITD cue that occurs whenever the ITD exceeds one-quarter of the IPI. Majdak et al. 共2006兲 showed that CI listeners lateralize periodic pulse trains to the wrong 共lagging兲 side for fine-structure ITDs exceeding one-half of the IPI. However, in our study, for jittered pulse trains, lisJ. Acoust. Soc. Am., Vol. 126, No. 5, November 2009

teners lateralize to the correct side, even for ITDs that approach or exceed one-half of the IPI. For example, the NH listeners lateralized jittered 1200-pps pulse trains 共IPI = 833 ␮s兲 with a 400-␮s ITD, which is about one-half IPI, to the correct 共leading兲 side in nearly all the trials. The CI listeners in Laback and Majdak 共2008兲 correctly lateralized jittered pulse trains at rates from 800 to 1515 pps with ITDs falling within the range of one-quarter to one IPI. There are at least two possible explanations of how binaural jitter could resolve the ITD ambiguity. First, the auditory system could process and analyze the jittered pulse trains as a temporal structure, thus integrating information across time. For a pulse train with an ITD of one-half of the IPI, the classical cross-correlation model of binaural interaction 共e.g., Colburn, 1977兲 predicts an ambiguous pair of peaks in case of a periodic pulse train. However, in the case of a jittered pulse train, the “wrong” peak disappears and only the peak corresponding to the correct ITD remains. Second, the auditory system could pick out interaural pulse pairs with a large IPI to adjacent pairs. This corresponds to a so-called multiple looks model 共Viemeister and Wakefield, 1991兲, where the auditory system stores samples or “looks” of the signal in memory and accesses and processes them selectively. Finally, based on these findings, we would like to reconsider the interpretation of experiments on the ITD sensitivity to high-frequency bandpass-filtered white noise. In particular, Bernstein and Trahiotis 共1994兲 showed that the ITD JND for bandpass-filtered noise centered at 4 kHz is independent of noise bandwidth up to a bandwidth of at least 800 Hz. The mean envelope rate in filtered noise corresponds to about 64% of the bandwidth 共Rice, 1953兲. Thus, the 800-Hz bandwidth corresponds to a modulation rate of 512 Hz. For sinusoidal AM tones, two-tone complexes, or transposed tones, ITD JNDs could not be measured at modulation rates of 512 Hz or greater 共Bernstein and Trahiotis, 1994, 2002兲. In order to explain the comparatively high ITD sensitivity for the noise, Bernstein and Trahiotis 共1994兲 suggested that the listeners may shift their attention to lower-frequency “internal filters” or critical bands, which would result in a narrower critical bandwidth and consequently a lower rate of envelope fluctuation. Bernstein and Trahiotis 共1994兲 also noted that this strategy reduces the rate of envelope fluctuation with no loss in depth of modulation. In light of the results presented in this study, an alternative explanation for the comparatively high sensitivity to filtered noise is the temporal jitter in the envelope.5 In other words, we propose that it is the random temporal variation in envelope maxima and minima that causes the high ITD sensitivity for noise rather than the strategy of down-shifting the internal filters. Note that down-shifting of filters cannot explain our results as our pulse trains had a constant spectral bandwidth for all amounts of jitter, including the periodic condition. Naturally, it is also possible that the variation in the amplitudes of the envelope maxima is a relevant factor in case of filtered noise. Due to the similar performance for jittered pulse trains and filtered noise in our study, we assume that the temporal variation is the more important factor. Goupell et al.: Temporal jitter and interaural time differences

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ACKNOWLEDGMENTS

We would like to thank Mr. Michael Mihocic for running experiments and our listeners. We would like to thank the associate editor Dr. Richard Freyman and two anonymous reviewers for numerous improvements to this work. We would like to thank Dr. Brian Moore, Dr. Zachery Smith, Dr. Andrew Brughera, Dr. Laurel Carney, and Dr. Philip Joris for useful discussions about the binaural jitter phenomenon. We would like to thank Dr. Raymond Meddis for help using his model. We would like to particularly thank Dr. Bertrand Delgutte and Dr. Kenneth Hancock for helping us to understand the pertinent physiology. This study was funded in part by the Austrian Science Fund 共FWF Project No. P18401B15兲. The k = 1 / 3 value was really 516/ 1667= 0.31. We intended to use k = 1 / 4 but there was a mistake in the experimental program. 2 JNDs were estimated from a maximum-likelihood cumulative Gaussian fit to the Pc data using PSIGNIFIT version 2.5.41 共see http://bootstrapsoftware.org/psignifit/, Last viewed 6/18/09兲, a software package for fitting psychometric functions to psychophysical data 共Wichmann and Hill, 2001a, 2001b兲. The function used was a Weibull function. 3 Due to the extremely large amount of time needed to compute 30 000 AN firing patterns 共30 AN fibers ⫻100 MSO measurements兲 per condition, we assumed that 30 AN fiber PSTHs randomly chosen from a pool of 100 were sufficient to represent variance of 30 000 PSTHs. 4 Refractory times of 2 and 4 ms were also tried. The different refractory times resulted in the same basic trends in the data. 5 Perceptually, periodic pulse trains have a tonal quality. Jitter introduces a noisy or scratchy quality to the pulse trains. The physical and perceptual qualities of temporally-jittered pulse trains and noise were summarized in Pierce et al. 共1977兲. In that study, it is stated that “… the central limit theorem tells us that at high enough rates, for which many pulses do overlap, the 关jittered pulse train兴 approaches Gaussian noise.” Hence, the ITD sensitivity for jittered pulse trains being bounded by the performance for noise seems consistent with the fact that jittered pulse trains become physically and perceptually similar to noises. 1

Agmon-Snir, H., Carr, C. E., and Rinzel, J. 共1998兲. “The role of dendrites in auditory coincidence detection,” Nature 共London兲 393, 268–272. Bernstein, L. R., and Trahiotis, C. 共1994兲. “Detection of interaural delay in high-frequency sinusoidally amplitude-modulated tones, two-tone complexes, and bands of noise,” J. Acoust. Soc. Am. 95, 3561–3567. Bernstein, L. R., and Trahiotis, C. 共2002兲. “Enhancing sensitivity to interaural delays at high frequencies by using ‘transposed stimuli’,” J. Acoust. Soc. Am. 112, 1026–1036. Bernstein, L. R., and Trahiotis, C. 共2004兲. “The apparent immunity of highfrequency ‘transposed’ stimuli to low-frequency binaural interference,” J. Acoust. Soc. Am. 116, 3062–3069. Blauert, J. 共1981兲. “Lateralization of jittered tones,” J. Acoust. Soc. Am. 70, 694–698. Burkard, R., and Palmer, A. R. 共1997兲. “Responses of chopper units in the ventral cochlear nucleus of the anaesthetised guinea pig to clicks-in-noise and click trains,” Hear. Res. 110, 234–250. Carney, L. H. 共1990兲. “Sensitivities of cells in anteroventral cochlear nucleus of cat to spatiotemporal discharge patterns across primary afferents,” J. Neurophysiol. 64, 437–456. Colburn, H. S. 共1977兲. “Theory of binaural interaction based on auditorynerve data. II. Detection of tones in noise,” J. Acoust. Soc. Am. 61, 525– 533. Colburn, H. S., Chung, Y., Zhou, Y., and Brughera, A. 共2008兲. “Models of brainstem responses to bilateral electrical stimulation,” J. Assoc. Res. Otolaryngol. 10, 91–110. Dye, R. H., Jr., and Hafter, E. R. 共1984兲. “The effects of intensity on the detection of interaural differences of time in high-frequency trains of clicks,” J. Acoust. Soc. Am. 75, 1593–1598. 2520


Hafter, E. R. 共1997兲. “Binaural adaptation and the effectiveness of a stimulus beyond its onset,” in Binaural and Spatial Hearing in Real and Virtual Environments, edited by R. H. Gilkey and T. R. Anderson 共Earlbaum, Hillsdale, NJ兲, pp. 211–232. Hafter, E. R., and Buell, T. N. 共1990兲. “Restarting the adapted binaural system,” J. Acoust. Soc. Am. 88, 806–812. Hafter, E. R., and Dye, R. H., Jr. 共1983兲. “Detection of interaural differences of time in trains of high-frequency clicks as a function of interclick interval and number,” J. Acoust. Soc. Am. 73, 644–651. Han, Y., and Colburn, H. S. 共1993兲. “Point-neuron model for binaural interaction in MSO,” Hear. Res. 68, 115–130. Henning, G. B. 共1974兲. “Detectability of interaural delay in high-frequency complex waveforms,” J. Acoust. Soc. Am. 55, 84–90. Henning, G. B. 共1980兲. “Some observations on the lateralization of complex waveforms,” J. Acoust. Soc. Am. 68, 446–454. Huber, A., Linder, T., Ferrazzini, M., Schmid, S., Dillier, N., Stoeckli, S., and Fisch, U. 共2001兲. “Intraoperative assessment of stapes movement,” Ann. Otol. Rhinol. Laryngol. 110, 31–35. Joris, P. X., Louage, D. H., Cardoen, L., and van der Heijden, M. 共2006兲. “Correlation index: A new metric to quantify temporal coding,” Hear. Res. 216–217, 19–30. Laback, B., and Majdak, P. 共2008兲. “Binaural jitter improves interaural timedifference sensitivity of cochlear implantees at high pulse rates,” Proc. Natl. Acad. Sci. U.S.A. 105, 814–817. Laback, B., Majdak, P., and Baumgartner, W. D. 共2007兲. “Lateralization discrimination of interaural time delays in four-pulse sequences in electric and acoustic hearing,” J. Acoust. Soc. Am. 121, 2182–2191. Lopez-Poveda, E. A., and Meddis, R. 共2001兲. “A human nonlinear cochlear filterbank,” J. Acoust. Soc. Am. 110, 3107–3118. Majdak, P., and Laback, B. 共2009兲. “Effects of center frequency and rate on the sensitivity to interaural delay in high-frequency clicks,” J. Acoust. Soc. Am. 125, 3903–3913. Majdak, P., Laback, B., and Baumgartner, W. D. 共2006兲. “Effects of interaural time differences in fine structure and envelope on lateral discrimination in electric hearing,” J. Acoust. Soc. Am. 120, 2190–2201. Manis, P. B., and Marx, S. O. 共1991兲. “Outward currents in isolated ventral cochlear nucleus neurons,” J. Neurosci. 11, 2865–2880. Meddis, R. 共2006兲. “Auditory-nerve first-spike latency and auditory absolute threshold: A computer model,” J. Acoust. Soc. Am. 119, 406–417. Moore, B. C., and Glasberg, B. R. 共1983兲. “Suggested formulae for calculating auditory-filter bandwidths and excitation patterns,” J. Acoust. Soc. Am. 74, 750–753. Nordmark, J. O. 共1976兲. “Binaural time discrimination,” J. Acoust. Soc. Am. 60, 870–880. Pierce, J. R., Lipes, R., and Cheetham, C. 共1977兲. “Uncertainty concerning the direct use of time information in hearing: Place clues in white-spectra stimuli,” J. Acoust. Soc. Am. 61, 1609–1621. Rice, S. O. 共1953兲. “Mathematical analysis of random noise,” in Selected Papers on Noise and Stochastic Processes, edited by N. Wax 共Dover, New York兲, pp. 133–294. Saberi, K., and Perrott, D. R. 共1995兲. “Lateralization of trains of clicks with opposing onset and ongoing interaural delays,” Acustica 81, 272–275. Scott, L. L., Hage, T. A., and Golding, N. L. 共2007兲. “Weak action potential backpropagation is associated with high-frequency axonal firing capability in principal neurons of the gerbil medial superior olive,” J. Physiol. 583, 647–661. Scott, L. L., Mathews, P. J., and Golding, N. L. 共2005兲. “Posthearing developmental refinement of temporal processing in principal neurons of the medial superior olive,” J. Neurosci. 25, 7887–7895. Smith, P. H. 共1995兲. “Structural and functional differences distinguish principal from nonprincipal cells in the guinea pig MSO slice,” J. Neurophysiol. 73, 1653–1667. Smith, Z. M., and Delgutte, B. 共2008兲. “Sensitivity of inferior colliculus neurons to interaural time differences in the envelope versus the fine structure with bilateral cochlear implants,” J. Neurophysiol. 99, 2390–2407. Smith, P. H., Joris, P. X., and Yin, T. C. 共1993兲. “Projections of physiologically characterized spherical bushy cell axons from the cochlear nucleus of the cat: Evidence for delay lines to the medial superior olive,” J. Comp. Neurol. 331, 245–260. Studebaker, G. A. 共1985兲. “A ‘rationalized’ arcsine transform,” J. Speech Hear. Res. 28, 455–462. van Hoesel, R. J. M. 共2007兲. “Sensitivity to binaural timing in bilateral cochlear implant users,” J. Acoust. Soc. Am. 121, 2192–2206. Goupell et al.: Temporal jitter and interaural time differences

van Hoesel, R. J. M. 共2008兲. “Observer weighting of level and timing cues in bilateral cochlear implant users,” J. Acoust. Soc. Am. 124, 3861–3872. Viemeister, N. F., and Wakefield, G. H. 共1991兲. “Temporal integration and multiple looks,” J. Acoust. Soc. Am. 90, 858–865. Wichmann, F. A., and Hill, N. J. 共2001a兲. “The psychometric function: I.


Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293– 1313. Wichmann, F. A., and Hill, N. J. 共2001b兲. “The psychometric function: II. Bootstrap-based confidence intervals and sampling,” Percept. Psychophys. 63, 1314–1329.

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