interaural phase effects in the masking of signals of different durations

4.3, 4.7, 4.8, 4.11, 4.15 Received 12 November 19õ5

Interaural Phase Effects in the Masking of Signals of Different Durations

DAvm M.

Department of Psychology, University of Pennsylvania, Philadelphia, Pennsylvania

The detectability of a pulsed, 250-cps sinusold in noise was measured under three interaural phase conditions and at three durations. The conditions were (1) signal and noise in one ear only, StuNre, (2) signal in one ear and the same in-phase noise in both ears, StuN0, (3) signal in both ears, but with a 180 ø phase difference, and the same in-phase noise in both ears, S•N0. The detectability of the signal was about 9 dB better in Condition 2 than in Condition 1, and about 7 dB better in Condition 3 than in Condition 2. The difference in detectability is slightly dependent on signal duration, the largest difference appearing at the shortest duration. The psychometric functions were essentially the same in all conditions, except for an attenuation constant. The results are contrasted with two theories used to account for the binaural effects; some discrepancy between both theories and the results are noted.

INTRODUCTION

NE of the more intriguing phenomena of psychoacoustics is the profound effect the interaural phase of the masker and the signal have on the detectability of the signal. Specifically, if one compares a monaural condition and a binaural condition in which

the noise is the same in both ears, but the signal is 180 ø out of phase at the two ears, then the signal-to- noise (S/N) level needed to achieve the same level of detectability is reduced by as much as 16 dB in the binaural condition. The magnitude of this difference in masking effectiveness, sometimes called a MLD (masking-level difference), depends on several factors. (1) The noise waveforms in the two ears must be identical to

achieve the maximum effect. If independent noise waveforms are used, the effect is zero. (2) The frequency of the signal must be low to yield larger differences; for a 250-cps signal, the difference is 16 dB, whereas for a 4000-cps signal it is only 3 dB. (3) The magnitude of the effect depends very slightly on signal duration.

The phenomenon was first reported by Licklider • and Hirsh, •' and a review of the data, along with a theoretical account, has been published by Jeffress, Blodgett,

x J. C. R. Licklider, "The Influence of Interaural Phase Re- lations upon the Masking of Speech by White Noise," J. Acoust. Soc. Am. 20, 150-159 (1948).

"I. J. Hirsh, "The Influence of Interaural Phase on Interaural Summation and Inhibition," J. Acoust. Soc. Am. 20, 536-544 (1948).

Sandel, and Wood? More recently, a model based on a simple equalization and cancellation process has been proposed by Durlach. 4 The study reported here was designed to find out how signal duration affects the magnitude of the MLD and to determine the shape of the psychometric function in the simple monaural condition and in the two heterophasic conditions.

I. PROCEDURE

The signal was a 250-cps sinusold pulsed for either 1/100, 1/10, or 1 sec. The signal, which was gated to begin and end at a zero crossing, had a rise time of 2.5 msec. The masking noise was continuously present in the observer's earphones. Wide-band Gaussian noise was used with a high-frequency cutoff of 20 000 cps so that the effective noise filter was, in fact, the PDR-8 earphone. The phones were wired in parallel to drive in phase. The spectrum level of the noise was 55 dB. The six observers, all young males of college age, listened for 2 h a day, 5 days a week for about 2 months.

The data were collected in a two-alternative forced-

choice procedure. For each condition of the experiment, the signal level was varied in 2-dB steps to determine a

a L. A. Jeffress, H. C. Blodgett, T. T. Sandel, and C. L. Wood, III, "Masking of Tonal Signals," J. Acoust. Soc. Am. 28, 416-426 (1956).

4 N. I. Durlach, "Equalization and Cancellation Theory of Binaural Masking-Level Differences," J. Acoust. Soc. Am. 35, 1206-1213 (1963).

720 volume 39 number 4 1966

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INTERAURAL PHASE EFFECTS AND DURATION

psychometric function, i.e., the percentage of correct decisions versus the ratio of the signal energy to noise power density. Each signal level was repeated three times during the experiment, at each occurrence of the signal 100 trials were conducted; thus 300 observations define each point on the psychometric function for each subject. The resulting data points were fit with a theoretical function that was displaced to the right or left until a best fit appeared to result. The main dependent variable of the paper is 10 times the logarithm of signal energy to noise power density for the observer to achieve 75% correct responses. [-We use the following notation to refer to this variable' 8--•0 = 10 log•0E/N0, where E is signal energy, measured at a 1-f• impedance point and No is the noise power density (noise power in a 1-cps band) measured at the same impedance point as the signal.]

Using the convention that m denotes monaural, 0 denotes no phase difference, and ,r denotes a phase difference of 180 ø, the three interaural phase relations were (a) SmNm, monaural condition--signal and noise in one ear, nothing in the other ear; (b) SmN0, monaural signal--in-phase noise in both ears--that is, the same noise waveform in both ears; and (c) S•N0, 180 ø out- of-phase binaural signal-- in-phase binaural noise--that is, the same noise waveform in both ears.

II. RESULTS--PSYCHOMETRIC FUNCTIONS

Fiõures 1 (a)-(c) show the average, (i.e., mean-percent correct over the six observers) psychometric functions for the three interaural phase conditions at the three durations. The solid curves are theoretical functions based

on an energy-detection modelS: namely, •I,(kE/No), where cb is the cumulative normal (or Gaussian) function from --o• to kE/No, F. is the signal energy, No is the noise power density, and k is a free parameter. On the logarithmic abscissa of these Figures, changes in k correspond to translations to the left or right. The mean data presented in Fig. 1 summarize what appears to be true of each individual's psychometric function: namely, the interaural phase and signal duration have very slight effect on the shape of the psychometric function. Moreover, the individual functions also suggest that the fitted function is not exactly correct; the slope of the theoretical function is consistently shallower than needed to fit the data points.

III. MASKING-LEVEL DIFFERENCES

Figure 2 shows how the effects of interaural phase and signal duration are related. The points are the difference in the detectability of the signal between the heterophasic condition and the homophasic condition at the three signal durations. The signal level needed to obtain about 75% correct detection is some 9 dB higher in the SmNm condition than the StuN0 and about

5 D. M. Green and J. A. Swets, "Signal Detection Theory and Psychophysics," NASA Rept. No. 1244 (Apr. 1965).

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Fro. 1. Average psychometric function for indicated condition and duration. g--•0 is 10 log•0E/N0, where No is the noise power density, and E is signal energy. Mean percent correct over 6 subjects. Signal frequency 250 cps.[SignaL*.duration (a) 1/100 sec; (b) •o sec; (c) 1.0 sec.

the journal of the Acoustical Society of America 721


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D. M. GREEN

20

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FIG. 2. The difference in 8--9Z0 needed in the monaural condition and the indicated antiphasic condition for the subject to achieve 75% correct in the two-alternative forced-choice task. Signal frequency: 250 cps. Observers 1(©), 2(O), 3(A), 4(A), 5(I), 6([:]). -->: Mean.

16 dB higher in the SmNm than in the S,N0. Even though the signal duration was varied by a factor of 100, the change in magnitude of the interaural phase effects is small. Specifically, the MLD is about 2 dB larger at 1/100 than at 1/10 and 1 sec. The last result is con- sistent, both in direction and size, with the result reported by Jeffress, Blodgett, and Taylor. 6

IV. DISCUSSION

Another way to examine the slight change in the MLD at 1/100 sec is to consider the relation of time and intensity for the two conditions. As Fig. 1 shows, practically no change in 8--9Z0 is needed to maintain the same level of detectability form 1/10 to 1/100 sec for the S,N0 and StuN0 conditions. That is, in both heterophasic conditions almost perfect power summation exists from 1/10 to 1/100 sec. In the simple homophasic condition, however, about 2 dB more energy is needed at 1/100 sec than at 1/10 sec to maintain the same level of detectability. Such departures from perfect power summation for short duration pulse are well-known and presumably are due to the spread of energy caused by gating the signal for a very short duration. TM At short durations, some of the signal en-

6 H. C. Blodgett, L. A. Jeffress, and R. W. Taylor, "Relation of Masked•Thresholds to Signal-Duration for Various Interaural Phases-Combinations," Am. J. Psychol. 66, 283-290 (1958).

7 W. R. Garner, "The Effect of Frequency Spectrum on Tem- poral Integration_of. Energy in the Ear," J. Acoust. Soc. Am. 19, 808-815 (1947).

8 p.M. Hamilton, "Noise Masked Thresholds as a Function of Tonal Duration and MaskinglNoise Bandwidth," J. Acoust. Soc. Am. 506-511 (1957).

• D. M. Green, T. G. Birdsall, and W. P. Tanner, Jr., "Signal Detection as a Function of Signal Intensity and Duration," J. Acoust. Soc. Am. 29, 523-531 (1957).

ergy falls outside the critical band. The anamolous result is that this same spread of energy does not affect the heterophasic conditions as much as the homophasic conditions. Jeffress, Blodgett, and Taylor, in a much more extensive study, found essentially the same discrepancy for their homophasic and heterophasic conditions. One possible conclusion is that the critical band is larger in the heterophasic than the homophasic conditions. Another explanation of this result can be obtained by applying a detection-theory analysis to Dur- lach's equalization and cancellation model. A paper is in preparation on this analysis.

Next, let us consider the apparent invariance of the shape of the psychometric function over the various conditions of the experiment.

First we must discuss whether the invariance might be simply a result of our averaging over observers. That is, suppose that the psychometric function is, in fact, slightly different in the various experiments; are we likely to detect the change when we average the data? The answer depends both on the size and consistency of the change as compared to other sources of variability included in the average. It is conceivable that each subject has a moderately steep psychometric function, but that the signal energy corresponding to 75% correct responses differs slightly for each subject. The average curve would then rise more slowly than any individual function, the amount of the reduction in slope depending upon the distribution of sensitivity of the individuals within the group. This could effectively obscure any changes across conditions of the experiment. But this is not the explanation. The data for each individual subject were analyzed separately, using least-squares pro- gram to fit each individual psychometric function with two parameters. One parameter was a measure of sensitivity--i.e., the energy needed for 750/0 correct--and the second parameter was related to the slope of the function. Analysis of the slope parameter indicated no significant changes over conditions or durations.

Nevertheless, a problem remains because the data of the individual psychometric functions are the average of points measured on different days and perhaps this obscures changes in individual psychometric functions in much the same way that differences among individuals might have obscured changes in group psychometric functions. Post hoc, statistical analysis of the data, does not support such a:conclusion, but there is no really satisfactory test of the hypothesis. I would not, therefore, consider the apparent invariance of the shape of the psychometric function as strong evidence against a model that said otherwise. On the other hand, the shape cannot be markedly different in the?arious conditions since there are circumstances (e.g., detection of an increment in a sine wave) in which changes_of slope are consistently seen?

10 D. Mo Green, "Psychoacoustics and Detection Theory," J. Acoust. Soc. Am. 32, 1189-1203 (1960).



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INTERAURAL PHASE EFFECTS AND DURATION

Second, given that the slopes of the psychometric function really are the same, what implication does this finding have for theories of the interaural detection process? • According to Jeffress, Blodgett, Sandel, and Wood, detection is limited by statistical fluctuations that obscure the addition of a small signal to the noise. In the monaural condition, the observer is assumed to monitor fluctuations in the envelope of the output of a critical band centered at the signal frequency. It is known that a Gaussian-noise input produces an output envelope that has a Rayleigh distribution. •2 For the heterophasic condition, the observer monitors the output of two such bands, one from each ear, and he attempts to detect the slight change in phase caused by adding the signal to one ear StuN0, or at different phases in both ears, S•N0. The limiting distribution in this case presumably arises from slight error in neural processing. According to Jeffress, Watson, Rilling, and Bourbon, •a the noise distribution for the homophasic and the heterophasic conditions are quite different. Watson et al. 14 have recently presented some data that show that the rES-NO ROC curve is quite different in the two experimental situations.

The psychometric function in a two-alternative forced-choice task is presumably generated because the observer samples from a fluctuating statistical process during the two observation intervals, determines the larger observation, and selects the interval corresponding to that observation. He is correct when the sample from the signal distribution xs is larger than the noise sample an. Thus the probability of his being correct is the probability that xs>x,•. This probability is determined by the distribution of Xn and the distribution of The shape of the psychometric function is determined by how the signal distribution changes as a function of

As the signal energy increases, the density for the signal plus noise changes and, thus, the probability that 3Cs> 3On increases.

The variation in P(xs>x.) as a function of signal energy E is the psychometric function. Now, the results appear to indicate that, except for an attenuation constant, this variation is the same for both antiphasic and homophasic conditions and for all three signal durations. Thus, if we plot on a scale of kE, the psychometric functions are all the same, only the value of k changes from one condition to another. If x• has a different distribution in the homophasic than in the heterophasic

• J.P. Egan, "Masking-Level Differences as a Function of Interaural D•sparities •n Intensity of S•gnal and of No•se," J. Acoust. Soc. Am. 36, 1992(A) (1964). Egan also concludes the slopes are the same.

• L. A. Jeffress, "Stimulus-Oriented Approach to Detection," J. Acoust. Soc. Am. 36, 766-774 (1964).

• L. A. Jeffress, C. S. Watson, M. E. Rilling, and W. T. Bourbon, "Theoretical and Obtained ROC Curves for Antiphas[c Stimulation," J. Acoust. Soc. Am. 36, 1991(A) (1964).

• C. S. Watson, M. E. Rilling, and W. T. Bourbon, "Receiver- Operating Characteristics by Rating Scale for Antiphasic Stimu- lation," J. Acoust. Soc. Am. 36, 1991(A) (1964).

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Fro. 3. The d•fference •n g--•0 needed in the two antiphasic conditions for the subject to achieve 75% correct in the two- alternative forced-choice task. Observers 1(©), 2(¸), 3(A), 4(/x), 5(i), 6([51).--• ' Mean.

condition, it seems remarkable that the variation between P(x•>x.) and E should be the same except for the single constant, k. Logically, this could happen but it seems to be a remarkable coincidence. The observed

invariance of the psychometric function does not appear to have an obvious explanation within the Jeffress el al. model.

According to Durlach, the observer combines linearly the waveform at the two ears after first scaling their amplitudes and shifting their time bases appropriately. Each of these processes is subject to slight errors. Presently, Durlach's theory is based on a S/N ratio analysis. Thus, in predicting results for a variety of monaural and binaural tasks, the theory calculates the differences in signal level needed to maintain the same S/N level and hence, presumably, the same level of detection performance. Because of the linear nature of the processing, it is entirely plausible that the psychometric function--that is, the relation between percent correct and signal level--will be the same, except for an attenuation constant, in the three tasks explored in the experimental section. The exact statistical character of the errors introduced by the equalization and cancellation is of some relevance also, but it should not be surprising to find that if the processing errors are assumed to be Gaussian one can show that the psychometric function is of the same form for both monaural

and antiphasic listening. Using Durlach's estimate of internal noise, S•N0 should be about 8 dB better than S•N•. The obtained difference is 7 dB at 1 sec, 7 dB at • sec and 10.5 dB at 1/100•'sec. The difference between S•N0 and StuN0 is easy to determine. In both cases, the waveforms at the two ears are subtracted in an attempt to cancel the noise, but because of im- perfections in the equalization process, the cancellation is not complete and so some small amount of noise remains. If the signal is monaural, S•, then the signal is present in the noise; if the signal is present in both

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D. M. GREEN

ears but 180 ø out of phase, then twice the monaural signal is present in the noise after subtraction. Thus, we expect the difference between StuN0 and S•N0 to be 6 dB. The actual difference is about 7 dB, according to Fig. 3, although some subjects show much larger differences. According to Durlach's model, the largest possible difference independent of the amount of internal noise, is a factor of 4, or 6 dB (Ref. 15). Thus, no appeal to individual differences in this parameter could account for the rather sizable differences obtained

with most of the subjects (see Fig. 3).

•5 The actual improvement predicted by Durlach is 5.7 dB. See Ref. 4, Eq. 20, p. 1212. Note that there is a small misprint in Eq. 20' the term (! q-•,•') should be the denominator of a fraction.

In summary, then, the invariance of slope of the psychometric function favors Durlach's model over that of Jeffress, Blodgett, Sandel, and Wood, but the magnitude of the difference between S•N0 and Sr, N0 seems somewhat greater than Durlach's model would predict.

ACKNOWLEDGMENT

This research was supported in part by the National Institutes of Health, Public Health Service, U.S. De- partment of Health, Education, and Welfare, and by the National Science Foundation. I wish to thank and

acknowledge the assistance of L. A. Jeffress, N. I. Durlach, R. D. Luce, and G. B. Henning, for their comments on earlier drafts of this paper.



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interaural phase effects in the masking of signals of different durations

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