measurement of the two-click threshold

4.6• 4.7 Received 1 June 1970

Measurement of the Two-Click Threshold

BARRY LESHOWITZ*

Department of Psychology, University of California, San Diego, La Jolla, California 92037

Observers were asked to discriminate between a pair of 10-t•sec pulses and a single 20-t•sec pulse having the same total energy. The independent variable was the time, AT, between the two 10-•sec pulses. The stimuli were also presented as elements in a periodic pulse train. The AT required for resolution of two clicks (two- click threshold) was 10 t•sec. Whereas the addition of a steady background noise produced a remarkably small change in the magnitude of the two-click threshold, performance deteriorated markedly when the pulses were low-pass filtered. It appears that discrimination of slight changes in the energy spectrum of the two transient signals, especially in the high-frequency region (8000 Hz and above), underlies the ear's sensitivity to a temporal discontinuity.

INTRODUCTION

In a recent pilot study, listeners were asked to discriminate between a pair of 10-tzsec pulses and a single 20-tzsec pulse having the same total energy. The aim of the experiment was to determine the size of the temporal interval between the two 10-tzsec pulses necessary for reliable discrimination of the pulse doublet from the single pulse. The two-click threshold was found to be surprisingly small--less than 10 tzsec. This value is in the same range as the separation needed to lateralize clicks delivered to the two ears (Klumpp and Eady, 1956) and is about three orders smaller than the temporal interval needed to hear two clicks as distinctly separate (Wallach, Newman, and Rosen- zweig, 1949).

Pollack (1967, 1969) has recently amassed a considerable body of evidence demonstrating that listeners can discriminate minute temporal perturbations in auditory waveforms. Detection of temporal gaps and pulse jitter in the low-microsecond region are common- place in Pollack's work. Pollack has suggested that, since nerve-impulse transmission has precision in the time domain in the millisecond region, some sort of preneural (mechanical) spectral analysis combined with a neural sharpening mechanism underlies the exquisite temporal acuity of the ear.

Unfortunately, specification of the spectral cues underlying discriminability of temporal discontinuities in Pollack's pulse trains is difficult, inasmuch as the stimuli just do not have simple frequency representa- tions. To overcome this difficulty, the present work

sought to measure the limits of temporal acuity and/or frequency resolution using transient stimuli having well-understood energy spectra, namely, the familiar sin2x/x 2 function. Specifically, the aim of the experiments was to demonstrate that frequency analysis in the very-high-frequency region of the audible spectrum governs the detectability of a temporal gap interposed between a pair of pressure pulses.

i. PROCEDURE

Thresholds were measured using a two-interval forced-choice procedure. On each trial, a standard 20-tzsec pulse and two 10-tzsec pulses separated in time by ZXT were presented. The two observation intervals were spaced 0.7 sec apart. Observers were instructed to choose the observation interval containing the doublet. Knowledge of the correct interval was provided immediately after the trial. The duration of a trial was 3.4 sec.

A 10-min experimental session consisted of a block of 100 trials. Each session was devoted to determining the percentage of correct responses, P(c), for a given value of ZXT. Time separations were chosen in an effort to cover the range of the psychometric function. At least 200 observations were used to define a single value of P(c), and from 2 to 6 points were used to determine the shape and location of the psychometric function. Smooth curves were fitted by eye to the data, and the value of ZXT corresponding to P(c) = 75, defined here as the two-click threshold, was determined using visual interpolation. Two-click thresholds reported in

462 Volume 49 Number 2 (Part 2) 1971

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MEASUREMENT OF THE TWO-CLICK THRESHOLD

this paper represent the average performance of two observers. Differences between the two-click thresh-

olds for the two observers were less than 10% in all conditions.

Electrical pulses were delivered via an attenuator, low-pass filter (Allison 2BR), and power amplifier to binaural headsets (TDH-39 headphones mounted in Grason-Stadler No. 00! headsets). The unfiltered pulses measured at the earphones were 1.25 V, with rise-fall times of about 2 tzsec. For conditions in which the pulses were low-pass filtered, the amplitude of the filtered pulses was adjusted such that their amplitude in the 500-Hz spectral region was 10 dB greater than that for the unfiltered condition. A General Radio 1900

wave analyzer was used to measure the amplitude spectra of the pulses.

II. RESULTS AND DISCUSSION

A. Energy Spectra

The spectral content of a transient stimulus is described by its energy spectrum. The energy spectrum of a rectangular pulse of unit amplitude is

rs • sin•(oors/2) IF½)I'= ,

(rs/2)'

where rs is the duration of the pulse and o• is radian frequency. A doublet has a similar spectrum and is

ro • sin=(•ro/2) IF(w) I'--F2+2 cos(o•dT)'] , (2)

(•o/2)'

where dT refers to the delay of the second pulse with respect to onset of the first pulse. (Note that dT is not identical to the quantity AT, the time between the

__z • DOUBLE PULSE

• -8 -

•- •_• --- PULSE DELAY • I • • 10 4'0 ' '- \

-16 -- TIME { ftse½) ' I I I I

o 4000 8ooo 12 ooo •6 ooo 2o ooo

FREQUENCY [Hz)

Fro. 1. Amplitude spectra for a single 20-/•sec pulse and a pair of 10-t•sec pulses separated in time by 10/•sec (see insert).

60 • SINGLE PULSE (Ho=65) - 50- '•/ DOUBLE PLSE (Ho=65) _

•j ß > .

- 40 •X - •- 30 -

20 -

LD I0 -

0 -

I 1 o 4000 8000 12 000 16 00o

FREQUENCY (Uz)

Fro. 2. Amplitude spectra for a single 20-•sec pulse and a pair of 10-•sec pulses separated in time by l0 •sec, as measured at t•e output of t•e listener's earphone by a General Radio type 1551-C sound-level meter in an ASA type 1 coupler. T•e spectrum level (power/unit bandwidth) of t•e pulses is plotted on t•e ordinate. T•e parameter is t•e spectrum level (tto) of the pulse. absolute t•res•old curve of SDia, a,d WNte (1933) is plotted terms of sound-pressure level of t•e continuous sinusDid.

two 10-tzsec pulses.) What is important to note here is that, whereas the single pulse has its first spectral zero at the reciprocal of its duration (i.e., at 1/rs), the first zero of the doublet occurs at 1/(2dT). Thus, although the singlet and doublet pulses have the same total energy, differences in the location of their spectral zeros give rise to amplitude differences throughout the entire spectrum.

Singlet and doublet pulses were also presented as elements in a periodic pulse train. The amplitude spectrum of a periodic pulse train consists of a series of components at the harmonic frequencies of the reciprocal of the repetition period. What is important to note here is that the spectral envelope of the pulse train (i.e., the magnitude of each discrete frequency component) is identical, except for a proportionality constant, to the continuous energy spectrum character- izing the nonperiodic function.

Figure 1 shows the energy spectra in the audible region of the spectrum for the condition where the pulse pair is just discriminable (i.e., AT=10 usec). The singlet and doublet pulses have spectral zeros at 50 kHz and 25 kHz, respectively. Observe that appreci- able amplitude differences exist in the high-frequency region (i.e., 2 dB at 12 kHz). A much more realistic description of the spectral composition of the stimuli, which incorporates an approximation to the response of the TDH-39 earphones, is shown in Fig. 2 together with the audiogram of Sivian and White (1933). The parameter /-/0 is the spectrum level (power/unit bandwidth) of the pulses. We observe that the relative differences (in decibels) between the spectra for the singlet and doublet pulses are unaffected by the response

The Journal of the Acoustical Society of America 463


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B. LESHOWITZ

65 45 25

I I i

19- -

17- -

ß •RANDOM AMPLITUDE

.I---

13 --

/RANDOT,', AMPLITUDE (6dB) ///

NO NOISE 65 85

TOTAL .NOISE LEVEL (SPL)

Fie.. 3. Two-pulse threshold as a function of the sensation level of the pulses. Sensation level was varied either by adding a wide- band background noise (lower abscissa and filled circles) or by attenuating the pulses (upper abscissa and untilled circles). The average spectrum level of the noise was approximately 45 dB below the sound-pressure level of the wide-band noise.

of the transducer. It is important to note that, since the audiogram of Sivian and White was obtained with continuous sinusolds, quantitative comparisons of the audiogram and the spectra describing transient signals cannot be made. Arguing on a qualitative level, the point to be made is that differences in the energy spectra can serve as perceptual cues only to the extent that these differences occur in audible regions of the spectrum. With reference to the present experiment, we should expect then that experimental manipulations limiting the availability of high-frequency information must adversely affect performance.

B. Two-Pulse Threshold as a Function

of Sensation Level

As a working hypothesis, we propose that the basis for two-pulse discrimination is the presence of small energy differences in the 10-kHz frequency region. To test this hypothesis, several experiments were conducted. In the first experiment, two-click thresholds were measured at several sensation levels. Sensation

level was varied either by partially masking the clicks with wide-band noise or by attenuating the pulses. For the two conditions,//o=25 dB and N--85 dB (rightmost points in Fig. 3), the clicks were about 10 dB above "masked" threshold. Inspection of Fig. 3 reveals that, while the addition of a continuous background noise produces little change in threshold

(lower abscissa), attenuation causes a marked decline in performance.

The effects of sensation level on two-pulse discrimination can easily be understood in terms of our spectral- analysis hypothesis. From Fig. 2, it is seen that when the clicks are 10 dB above absolute threshold (i.e., //b=25 dB) the 10-kHz region is inaudible. Conse- quently, amplitude differences here can no longer serve as the basis for discrimination. In order to

reinstate spectral differences in an audible spectral region, the time separation between the two pulses must be increased. Hence, we observe an increase in the two-click threshold. Partially masking the pulses with white noise, on the other hand, does not differen- tially lower the signal-to-noise ratio in any particular frequency region. Hence, discriminability remains unchanged.

In a second study, singlet and doublet pulses were presented as a periodic pulse train in quiet. The amplitude of elements in the pulse train was 1.25 V, and the duration of the pulse train was 320 msec. Two-click thresholds as a function of the basic repetition rate are drawn in Fig. 4. At all repetition rates, the threshold was found to be about 5 #sec, which is about half that obtained in the first experiment with nonrepeated pulses of comparable amplitude.

C. Low-Pass-Filtered Pulses

Additional confirmation of the spectral-analysis hypothesis comes from a second experiment in which the clicks were low-pass filtered (Allison 2BR filter). The results are presented in Fig. 5, where it is seen that sensitivity deteriorates significantly as the high-pass cutoff is lowered. Of interest is the observation that for

the wide-band condition (cutoff=21120 Hz) a 1.5-dB difference occurs at 10 kHz; for the cutoff equal to 2640 Hz, a 1.5-dB difference occurs at 2.5 kHz. These results seem to suggest that a 1-2-dB difference in the

9 - ' i i

RANDOM AMPLITUDE

I I I 0.2 2 20

PULSE PERIOD (msec)

Fio. 4. Two-pulse threshold for pulses presented as elements in a periodic pulse rate. The abscissa is the reciprocal of the basic repetition rate.

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MEASUREMENT OF THE TWO-CLICK THRESHOLD

"high"-frequency region is necessary for discriminating a pulse doublet. Examination of the amplitude spectra for the singlet and doublets shown in Fig. ! reveals the existence of relative energy differences in the order of 2 dB at high frequencies. And the results of conventional intensity-discrimination experiments indicate that differences of this magnitude ought to be discriminable.

D. Two-Pulse Threshold for Random-Amplitude Pulses

As an alternative explanation of the present data, we might suppose that listeners do not perform any spectral analysis of the stimuli, but instead listen wide- band. Discrimination of the doublet, then, is accom- plished by assessing the over-all energy in the frequency region below 15 kHz. For example, for the condition depicted in Fig. 1 (AT-- 10 usec) the over-all difference in energy between the singlet and doublet in the audible frequency region is approximately 0.75 dB. In view of the fact that investigations of difference limens for clicks show that increments smaller than

2 dB are not reliably detected (Raab and Taub, 1969), it is highly unlikely that wide-band amplitude discrimination is responsible for resolution of a pulse doublet presented in the nonrepeated mode. However, the improvement in gap sensitivity for pulses presented as a pulse train does suggest that differences in over-all intensity may be a relevant cue in the two-pulse discrimination task. This conclusion follows from the

observation that a 0.75-dB increment, which is approximately the difference in intensity for the singlet and doublet, has been shown to be detectable for 200-msec tone bursts (Henning, 1969).

In order to assess the importance of over-all intensive cues in the two-pulse discrimination experiment, two- click thresholds were measured using pulses whose amplitude was varied randomly across observation intervals. Randomizing pulse amplitude precludes use of wide-band as well as narrow-band amplitude differences in detecting a temporal gap.

In the first study, two-click thresholds were measured for nonrepeated random-amplitude singlet and doublet pulses. At maximum amplitude, the spectrum level H0 was 65 dB. The six equally likely levels of attenuation covered a range of 6 dB in one condition and 12 dB in another. It can be seen in Fig. 3 that, when all intensive cues are eliminated by randomizing the amplitude over a range of 6 dB, the two-click threshold is ab- solutely unchanged. For the 12-dB condition, however, we observe that performance is worse than that measured in the original constant-amplitude experiment. The two-click threshold for a periodic pulse train (500-Hz repetition rate) whose amplitude was varied over a range of 12 dB is shown in Fig. 4. The threshold is approximately 10 usec and is somewhat greater than that measured with pulse trains of constant amplitude.

I -- [ - - 60 -

50

40

30

20 -

10

2640 5280 I0 560 21 120

HIGH CUTOFF

FIO. 5. Two-pulse threshold for low-pass-filtered pulses. The experimental variable is the high cutoff of the filter.

The finding that randomizing the amplitude of brief transients does not markedly lower performance suggests that observers are able to appreciate in some detail the profile of the energy spectrum. Knowledge of the spectral profile requires that the listener monitor the output of at least two bandpass filters--one centered in the low-frequency region and the other in the high-frequency region. The ratio of the outputs of the two filters, defined here as the "spectral profile," provides a representation of the spectrum that is, of course, independent of over-all level. Such a quantity, then, can serve as a reliable cue in the two-pulse detection task in the face of considerable random

variation in over-all level. The surprising result that the two-click threshold for random-amplitude stimuli is only slightly higher than that measured under constant- amplitude conditions provides important information about the ability of listeners to assess small differences in the contour of the energy spectrum.

In conclusion, the data collected in the present experiment demonstrate that the auditory system is extremely sensitive to small spectral differences. More- over, these differences may exist in high-frequency regions of the audible spectrum, which have heretofore been ignored by most investigators. Although the notion of the ear as a frequency analyzer is firmly established, there has been little work devoted to studying discrimination of spectral contours or profiles. Research that has been conducted has mainly been concerned with detection of irregularities in the spectrum of continuous white noise (Flanagan, 1965, p. 215). In light of the ear's exquisite sensitivity to the form of the energy spectrum, experiments on differential discriminability of spectral shape should provide

The Journal of the Acoustical Society of America 465


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B. LESHOWITZ

important information on the properties of the frequency analyzer of the auditory system.

ACKNOWLEDGMENTS

The author would like to express his gratitude to Dr. David M. Green and Dr. Larry Feth for critically reading an earlier draft of this manuscript. The assist-

ance of Dr. Frederic Wightman, who helped in setting up the equipment, is gratefully acknowledged.

This investigation was supported in part by a grant from the National Institute of Health, U.S. Public Health Service, and by a U.S. Public Health Service Postdoctoral Fellowship.

* Present address: Department of Psychology, Arizona State University, Tempe, Ariz. 85281.

REFERENCES

FLANAOAN, J. L. (1965). Speech Analysis, Synthesis and Perception (Academic, New York). HENNINO/ G. B., and PSOT•CA, J. (1969). "Effect of Duration on Amplitude Discrimination in Noise," J. Acoust. Soc. Amer. 45, 1008-1013.

KLU•PP, R. G., and EAD¾, H. R. (1956). "Some Measurements of Interaural Time Difference Thresholds," J. Acoust. Soc. Amer. 28, 859-860. Po•x.a½rq I. (1967). "Asynchrony: The Perception of Temporal Gaps Within Auditory Pulse Patterns," J. Acoust. Soc. Amer. 42, 1335-1340.

POLLAC•C, I. (1969). "Submicrosecond Auditory Jitter Discrimina- tion Thresholds," J. Acoust. Soc. Amer. 45, 1058-1059.

RAA•, D. H., and TAtre, H. B. "Click-Intensity Discrimination with and without a Background Noise," J. Acoust. Soc. Amer. 46, 965-968.

StYtAN, L. J., and WmTv., S. D. (1933). "On Minimum Audible Sound Fidds," J. Acoust. Soc. Amer. 4, 288-321.

WALLACH, H., NEWMAN, E. B., and ROSENZWEIG, M. R. (1949). "The Precedence Effect in Sound Localization," Amer. J. Psych. 52, 315-336.

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measurement of the two-click threshold

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