Temporal modulation transfer functions obtained using sinusoidal ...

Temporal modulation transfer functions obtained using sinusoidal carriers with normally hearing and hearing-impaired listeners Brian C. J. Moorea) and Brian R. Glasberg Department of Experimental Psychology, University of Cambridge, Downing Street, Cambridge CB2 3EB, United Kingdom

共Received 3 May 2001; revised 15 May 2001; accepted 17 May 2001兲 Temporal modulation transfer functions were obtained using sinusoidal carriers for four normally hearing subjects and three subjects with mild to moderate cochlear hearing loss. Carrier frequencies were 1000, 2000 and 5000 Hz, and modulation frequencies ranged from 10 to 640 Hz in one-octave steps. The normally hearing subjects were tested using levels of 30 and 80 dB SPL. For the higher level, modulation detection thresholds varied only slightly with modulation frequency for frequencies up to 80 Hz, but decreased for high modulation frequencies. The decrease can be attributed to the detection of spectral sidebands. For the lower level, thresholds varied little with modulation frequency for all three carrier frequencies. The absence of a decrease in the threshold for large modulation frequencies can be explained by the low sensation level of the spectral sidebands. The hearing-impaired subjects were tested at 80 dB SPL, except for two cases where the absolute threshold at the carrier frequency was greater than 70 dB SPL; in these cases a level of 90 dB was used. The results were consistent with the idea that spectral sidebands were less detectable for the hearing-impaired than for the normally hearing subjects. For the two lower carrier frequencies, there were no large decreases in threshold with increasing modulation frequency, and where decreases did occur, this happened only between 320 and 640 Hz. For the 5000-Hz carrier, thresholds were roughly constant for modulation frequencies from 10 to 80 or 160 Hz, and then increased monotonically, becoming unmeasurable at 640 Hz. The results for this carrier may reflect ‘‘pure’’ effects of temporal resolution, without any influence from the detection of spectral sidebands. The results suggest that temporal resolution for deterministic stimuli is similar for normally hearing and hearing-impaired listeners. © 2001 Acoustical Society of America. 关DOI: 10.1121/1.1385177兴 PACS numbers: 43.66.Mk, 43.66.Dc, 43.66.Sr 关SPB兴

I. INTRODUCTION

One way of characterizing the temporal resolution of the auditory system is to measure the threshold for detecting changes in the amplitude of a sound as a function of the rapidity of the changes. In the simplest case, white noise is sinusoidally amplitude modulated, and the threshold for detecting the modulation is determined as a function of modulation frequency 共Rodenburg, 1977; Viemeister, 1977, 1979兲. The function relating threshold to modulation frequency is known as a temporal modulation transfer function 共TMTF兲. Modulation of white noise does not change its long-term magnitude spectrum, so one can be reasonably confident that the pattern of results depends on temporal resolution per se. TMTFs obtained in this way generally show a reasonably flat section for low modulation frequencies. Performance for this section is presumably determined mainly by the amplitude resolution of the auditory system. For modulation frequencies above about 50 Hz, sensitivity declines 共Rodenburg, 1977; Viemeister, 1977, 1979; Bacon and Viemeister, 1985; Formby and Muir, 1988; Strickland and Viemeister, 1997兲. a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

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The decline is usually interpreted as a measure of the limited ability of the auditory system to follow rapid amplitude fluctuations. TMTFs have also been measured using sinusoidal carriers 共Zwicker, 1952; Viemeister, 1979; Sek, 1994; Fassel and Kohlrausch, 1995; Dau et al., 1997a; Strickland and Viemeister, 1997; Kohlrausch et al., 2000兲. In this case, the interpretation of the results is complicated by the fact that the modulation introduces spectral sidebands, which may be detected as separate components if they are sufficiently far in frequency from the carrier frequency 共Sek and Moore, 1994; Kohlrausch et al., 2000兲. Even when the sidebands are not detectable, the results may be influenced by ‘‘off-frequency listening,’’ i.e., the use of the output of an auditory filter that is not centered at the carrier frequency. This can happen in two ways. First, the effective modulation depth at the outputs of the auditory filters might be greater for a filter centered close to the frequency of one of the sidebands than for a filter centered at the carrier frequency. Subjects may be able to select the filter with the highest modulation at its output. The extent of the difference between the on-frequency and offfrequency filters would vary with the frequency separation of the carrier and sidebands, and hence with modulation frequency 共Dau, 1996兲, so this form of off-frequency listening would influence the shape of the TMTF. Second, even when the frequency separation of the carrier and sidebands is very

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small, subjects may make use of the outputs of auditory filters tuned well above the signal frequency 共the highfrequency side of the excitation pattern兲, for which there is less compression than for filters tuned close to the signal frequency 共Zwicker, 1956, 1970; Robles et al., 1986; Nelson and Schroder, 1997; Moore and Oxenham, 1998兲; the effective modulation depth would be greater on the highfrequency side of the excitation pattern. However, since the compression appears to be very fast-acting 共Robles et al., 1986; Recio et al., 1998兲, this form of off-frequency listening would not be expected to influence the shape of the TMTF, at least for the range of modulation frequencies where sidebands are not detectable. When the carrier frequency is high, the effects of resolution of sidebands and off-frequency listening of the first type are likely to be small for modulation frequencies up to a few hundred Hertz. For example, for a carrier frequency of 5000 Hz, the equivalent rectangular bandwidth 共ERB兲 of the auditory filter is about 560 Hz 共Glasberg and Moore, 1990兲, and the ‘‘edge’’ components in complex tones need to be separated by more than about 0.75 ERB from neighboring components to be ‘‘heard out’’ as separate tones, even when all components have equal amplitude 共Moore and Ohgushi, 1993兲. Thus, the results obtained for low modulation frequencies are likely to reflect temporal resolution rather than spectral resolution or off-frequency listening. Consistent with this, TMTFs for high carrier frequencies generally show an initial flat portion 共sensitivity independent of modulation frequency兲, a portion where sensitivity decreases with increasing modulation frequency, presumably reflecting the limits of temporal resolution, and then a portion where sensitivity increases again, presumably reflecting the detection of spectral sidebands 共Kohlrausch et al., 2000兲. The ‘‘transition’’ modulation frequency, at which sensitivity is worst, increases with increasing carrier frequency, and typically is about 5%– 6% of the carrier frequency 共about 0.5 ERB兲 共Kohlrausch et al., 2000兲. The initial flat portion of the TMTF extends to about 100–120 Hz for sinusoidal carriers, but only to 50 or 60 Hz for a broadband noise carrier. It has been suggested that the discrepancy occurs because of the inherent amplitude fluctuations in a noise carrier, which limit the detectability of the imposed modulation 共Fleischer, 1982; Dau, 1996; Dau et al., 1997a, 1997b, 1999兲. The effect of the inherent fluctuations depends upon their similarity to the imposed modulation. When a narrowband noise carrier is used, which has relatively slow inherent amplitude fluctuations, TMTFs show the poorest sensitivity for low modulation frequencies 共Fleischer, 1982; Dau et al., 1997a兲. In principle, then, TMTFs obtained using sinusoidal carriers provide a better measure of the inherent temporal resolution of the auditory system than TMTFs obtained using noise carriers, provided that the modulation frequency is within the range where spectral resolution does not play a major role. The present study compares TMTFs obtained using sinusoidal carriers for normally hearing subjects and for subjects with cochlear hearing loss. The latter have reduced frequency selectivity 共Pick et al., 1977; Glasberg and Moore, 1068

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1986; for a review, see Moore, 1998兲 and so the modulation frequency at which spectral resolution starts to play a role should be higher than for normally hearing subjects. Thus, for subjects with cochlear hearing loss, TMTFs for sinusoidal carriers should be influenced mainly by temporal resolution over a relatively wide range of modulation frequencies. Several previous studies measuring TMTFs for hearingimpaired subjects have used broadband noise carriers. These studies showed that hearing-impaired listeners were generally less sensitive to high frequencies of modulation than normal listeners 共Formby, 1982; Lamore et al., 1984; Bacon and Viemeister, 1985兲. However, this may have been largely a consequence of the fact that high frequencies were inaudible to the impaired listeners 共Bacon and Viemeister, 1985兲; most of the subjects used had greater hearing losses at high frequencies than at low. Bacon and Gleitman 共1992兲 measured TMTFs for broadband noise using subjects with relatively flat hearing losses. They found that at equal 共high兲 SPLs performance was similar for hearing-impaired and normally hearing subjects. At equal 共low兲 SLs, the hearingimpaired subjects tended to perform better than the normally hearing subjects. Moore et al. 共1992兲 controlled for the effects of listening bandwidth by measuring TMTFs for an octave-wide noise band centered at 2 kHz, using subjects with unilateral and bilateral cochlear hearing loss. Over the frequency range covered by the noise, the subjects had reasonably constant thresholds as a function of frequency, both in their normal and their impaired ears. This ensured that there were no differences between subjects or ears in terms of the range of audible frequencies in the noise. To ensure that subjects were not making use of information from frequencies outside the nominal passband of the noise, the modulated carrier was presented in an unmodulated broadband noise background. For the subjects with unilateral impairments, performance was similar for the normal and impaired ears, both at equal SPL and equal SL. The present study was intended to provide more information about temporal resolution for listeners with cochlear hearing loss, using carriers without inherent fluctuations, i.e., sinusoids. This is important since the inherent fluctuations in a noise carrier may have different effects for normally hearing and hearing-impaired subjects. For example, loudness recruitment appears to have the effect of magnifying the perceived fluctuation of a modulated sound 共Moore et al., 1996兲, and this may have adverse effects on temporal resolution, at least for the task of gap detection 共Moore and Glasberg, 1988; Glasberg and Moore, 1992; Moore et al., 2001兲; see, however, Hall et al. 共1998兲. In addition, we wished to clarify the role of spectral sidebands in modulation detection by hearing-impaired subjects. We anticipated that the reduced frequency selectivity of listeners with cochlear hearing loss would lead to poorer resolution of spectral sidebands, allowing temporal resolution per se to be measured over a relatively wide range of modulation frequencies. B. C. J. Moore and B. R. Glasberg: TMTFs for sinusoidal carriers

TABLE I. Absolute thresholds for the test ears of the hearing-impaired subjects, measured in two ways: 共1兲 using conventional manual audiometry, and expressed in dB HL; 共2兲 using a three-alternative forced-choice procedure, and in dB SPL.

Subject GW TT AR

Frequency 共Hz兲 2000 4000

250

500

1000

HL SPL

40

50

60 66.5

55 65.5

65

HL SPL

40

35 44.9

50 65.3

60

HL SPL

30

40 51.1

45 65.2

50

35 35

II. THE EXPERIMENT: TMTFs FOR SINUSOIDAL CARRIERS A. Procedure

Thresholds for the detection of sinusoidal amplitude modulation 共AM兲 of a sinusoidal carrier were measured using a three-alternative forced-choice three-down one-up procedure tracking the 79.4% point on the psychometric function. The carrier was gated, and it was unmodulated in two of the intervals and modulated in the other; subjects had to indicate the interval containing the modulated carrier. Observation intervals were marked by lights on the response box and feedback was provided after each trial by a light indicating the correct interval. Twelve turnpoints were obtained in a given run, and the threshold estimate for that run was taken as the mean value of 20 log m at the last eight turnpoints 共where m is the modulation index兲. The step size 共defined in terms of 20 log m兲 was 5 dB up to the first four turnpoints, and 2 dB thereafter. At least three runs were obtained for each condition.

5000

8000 70

74.9 65 77.2 50 61.2

quency response of the HD580 at the eardrum was estimated using a KEMAR manikin 共Burkhard and Sachs, 1975兲, averaging the results for the large and small ears. C. Subjects

Four normally hearing subjects were tested, with ages ranging from 23 to 54 years. One was author BG. All had absolute thresholds better than 15 dB HL at all audiometric frequencies in the ear tested. Three subjects with symmetrical mild to moderate cochlear hearing loss were tested. Their ages in years were 84 共GW兲, 80 共TT兲, and 70 共AR兲. Their absolute thresholds for the test ear, measured using manual audiometry 共Grason–Stadler GSI-16 audiometer兲 are given in Table I. Table I also gives thresholds in dB SPL at the test frequencies, estimated using a three-alternative forcedchoice, three-down one-up procedure. Impedance audiometry revealed normal middle-ear function. All subjects were trained until their performance appeared to be stable. This took only a few hours. All subjects except BG were paid for their services.

B. Stimuli

The carrier frequency was 1000, 2000, or 5000 Hz. The modulation frequency was 10, 20, 40, 80, 160, 320, or 640 Hz. Each carrier burst lasted 540 ms, including 20 ms raisedcosine rise/fall ramps. The interval between bursts within a trial was 500 ms. The overall level of the modulated and unmodulated stimuli was the same, regardless of modulation depth. The normally hearing subjects were tested using levels of 30 and 80 dB SPL. The hearing-impaired subjects were, in most cases, tested only using a level of 80 dB SPL. For two subjects, GW and TT, the absolute thresholds at 5000 Hz were above 70 dB SPL, and a level of 90 dB was used for this frequency. At the levels used, the sensation levels were in a similar range to those for the normally hearing subjects tested at 30 dB SPL, i.e., 15–30 dB SL. Stimuli were digitally generated using a Tucker–Davis Technologies 共TDT兲 system with a 16-bit digital-to-analog converter 共DD1, 50-kHz sampling rate兲, lowpass filtered at 20 kHz 共Kemo VBF8, mark 4兲, attenuated 共TDT PA4兲, passed through a headphone buffer 共TDT HB6兲, and delivered to a double-walled sound attenuating booth. Stimuli were delivered to one earpiece of a Sennheiser HD580 headphone via a final manual attenuator 共Hatfield 2125兲. Sound levels are specified as levels close to the eardrum; the freJ. Acoust. Soc. Am., Vol. 110, No. 2, Aug. 2001

III. RESULTS

Individual results for the normally hearing subjects are shown in Fig. 1. Note that the results are plotted with worst performance at the top of the y axis, opposite to the way in which TMTFs are often plotted. To avoid clutter, error bars are not shown. The standard deviation of the three threshold estimates for a given subject and condition was typically about 1 dB. The pattern of results was similar across subjects, and mean data are shown in Fig. 2. Performance was better for the higher carrier level 共open symbols兲, than for the lower level, which is consistent with earlier work 共Riesz, 1928; Zwicker, 1952; Kohlrausch et al., 2000兲. The effect of level for low modulation frequencies can be attributed to two factors. First, at high levels the excitation pattern spreads over a greater range of center frequencies. Subjects can probably combine information from different parts of the pattern 共i.e., across auditory filters兲 in order to improve performance 共Florentine and Buus, 1981; Moore and Sek, 1994兲. Second, as noted earlier, at high levels subjects can use information from the high-frequency side of the excitation pattern, for which there is less compression than at the peak of the pattern 共Zwicker, 1956; Zwicker, 1970; Nelson and Schroder, 1997; Moore and Oxenham, 1998兲. B. C. J. Moore and B. R. Glasberg: TMTFs for sinusoidal carriers

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FIG. 1. Individual results for the four normally hearing subjects. The modulation detection threshold 共20 log m兲 is plotted as a function of modulation frequency. The parameters are level and carrier frequency, as indicated in the key. Each panel shows results for one subject.

For high modulation frequencies, performance at the high level improved markedly for the two lower carrier frequencies, and the improvement started at a lower modulation frequency for the 1000-Hz carrier 共circles兲 than for the 2000-Hz carrier 共squares兲. For the 5000-Hz carrier frequency 共triangles兲, performance tended to worsen slightly as the modulation frequency was increased from 80 to 320 Hz, and then improved slightly for the highest modulation frequency. The improvement in performance with increasing modulation frequency almost certainly reflects the detection of spec-

FIG. 2. Mean results for the four normally hearing subjects. Otherwise as in Fig. 1. 1070

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tral sidebands. For the 1000-Hz carrier, these appear to be clearly detectable for the modulation frequency of 160 Hz, while for the 2000-Hz carrier they are detectable for the modulation frequency of 320 Hz. For the lower carrier level, thresholds did not vary markedly with modulation frequency, except at 640 Hz, where there was a small increase in threshold for the 5000-Hz carrier and a small decrease for the 2000-Hz carrier. Mean performance was slightly better for the 1000-Hz carrier than for the other two carriers, probably reflecting the fact that the average SL was slightly higher at 1000 Hz 共26 dB SL兲 than at 2000 Hz 共19 dB SL兲 or 5000 Hz 共19 dB SL兲. Even though thresholds did not vary markedly with modulation frequency, the mechanism underlying modulation detection presumably did change. The failure of thresholds to decrease for the large modulation frequencies presumably reflects the low SL of the stimuli. The value of 20 log m at threshold was typically around ⫺16 dB for the 1000-Hz carrier, which means that each sideband had a level 22 dB below the carrier level. Thus, each sideband had a level of about 8 dB SPL, which was just above the mean absolute threshold of 4 dB SPL 共at 1000 Hz兲. For the 2000- and 4000-Hz carriers, the sideband level was about 12 dB SPL, again, just above the mean absolute threshold of 11 dB SPL. Modulation detection thresholds for the highest modulation frequencies were presumably mediated by sideband detection for the two lower carrier frequencies, but the low overall level of the stimuli did not allow thresholds to fall below about ⫺12 to ⫺16 dB. The small rise in threshold for the 5000-Hz carrier for the 640-Hz modulation frequency probably occurred because temporal resolution was relatively poor at that frequency, but the spectral sidebands were not sufficiently separated from the carrier to be easily detectable. Consistent with this, calB. C. J. Moore and B. R. Glasberg: TMTFs for sinusoidal carriers

culations based on the excitation-pattern program published by Glasberg and Moore 共1990兲 indicate that the excitation level produced by a 30-dB SPL 5000-Hz tone is only about 10 dB down from the peak excitation level for frequencies 640 Hz on either side of 5000 Hz. To be detectable, each sideband would have to have a level comparable to the excitation level of the carrier, which would require a value of 20 log m of about ⫺4. This is close to the observed threshold values. The individual results for the hearing-impaired subjects are shown in Fig. 3. Symbols with up-pointing arrows indicate cases where thresholds could not be measured, as even m⫽1 共100% modulation兲 did not lead to sufficient detectability. For low modulation frequencies, the thresholds are similar to those for the normally hearing subjects with the carrier level of 80 dB SPL, and are generally lower 共better兲 than the thresholds obtained for the carrier level of 30 dB SPL. Since the SLs of the stimuli for the hearing-impaired subjects were similar to those for the normally hearing subjects for the 30-dB carrier level, the results indicate that the hearing-impaired subjects were better than the normally hearing subjects at AM detection when the stimuli were at

FIG. 3. Individual results for the hearing-impaired subjects. The modulation detection threshold 共20 log m兲 is plotted as a function of modulation frequency. The parameter is carrier frequency, as indicated in the key. The level was 80 dB SPL, except for the 5000-Hz carrier for subjects GW and TT, where the level was 90 dB SPL. Error bars indicate ⫾ one standard deviation. They are omitted when they would be smaller than the size of the symbol used to represent a given point. J. Acoust. Soc. Am., Vol. 110, No. 2, Aug. 2001

similar SLs. This is consistent with previous research indicating that at equal low SLs amplitude resolution can be better for subjects with cochlear hearing loss than for normally hearing subjects 共Jerger et al., 1959; Buus et al., 1982a, 1982b; Moore, 1995兲. Consider first the results for the 1000-Hz carrier. For TT, who had the smallest hearing loss at this frequency 共see Table I兲, the pattern of results resembles that found for the normally hearing listeners at the 30-dB SPL carrier level; the thresholds varied only slightly with modulation frequency. For subject AR, who has a slightly greater hearing loss at this frequency, the thresholds decreased by about 5 dB as the modulation frequency was increased from 10 to 40 Hz, remained constant up to 160 Hz, increased at 320 Hz, and then decreased by about 4 dB at 640 Hz. The increase at 320 Hz presumably reflects the effects of temporal resolution, while the decrease at 640 Hz reflects detection of a spectral sideband; probably it was the lower sideband that was detected, as AR had only a mild hearing loss for frequencies below 1000 Hz. For the modulation frequency of 160 Hz, it is very unlikely that spectral sidebands were detectable; at the modulation detection threshold, each sideband would have had a level of 44 dB SPL, which would have been below the absolute threshold. Thus, the results for AR indicate that temporal resolution is as good for a modulation frequency of 160 Hz as it is for lower modulation frequencies. The thresholds for GW for the 1000-Hz carrier rose slightly as the modulation frequency was increased from 10 to 20 Hz, remained roughly constant for frequencies from 20 to 80 Hz, increased slightly as the frequency increased to 160 and 320 Hz, and then decreased slightly at 640 Hz. The decrease at 640 Hz presumably reflects detection of a spectral sideband; the level of each sideband was 61 dB SPL, which would have been just above the absolute threshold at 360 Hz 共but below the absolute threshold at 1640 Hz兲. Again, the results suggest relatively good temporal resolution for modulation frequencies up to 160 Hz. Consider next the results for the 2000-Hz carrier 共squares兲. For all three subjects, thresholds were roughly constant for modulation frequencies up to 80 Hz, and increased with increasing modulation frequency from 80 to 320 Hz. This increase probably reflects the effects of temporal resolution. For the modulation frequency of 640 Hz, threshold was unmeasurable for GW. She was probably unable to detect the AM per se at this modulation frequency, while at the same time she was unable to detect the spectral sidebands, either because of poor frequency selectivity, or because the sidebands were too close to absolute threshold, or both. For subject AR, the threshold for the modulation frequency of 640 Hz was only slightly higher than that for the frequency of 320 Hz. Probably, the threshold for the 640-Hz frequency was determined by detection of the spectral sideband at 1360 Hz, whose level of 57 dB would have been just above the absolute threshold. For subject TT, the threshold for the modulation frequency of 640 Hz was slightly lower than that for the frequency of 320 Hz, presumably reflecting his ability to detect the spectral sideband at 1360 Hz, whose level of 59 dB would again have been somewhat above the absolute threshold. B. C. J. Moore and B. R. Glasberg: TMTFs for sinusoidal carriers

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Finally, consider the results for the 5000-Hz carrier 共triangles兲. Recall that for this carrier, GW and TT were tested at a level of 90 dB SPL. The pattern of results was similar for all three subjects. Thresholds were roughly independent of modulation frequency for frequencies up to 80 Hz 共GW and AR兲 or 160 Hz 共TT兲, and increased for modulation frequencies above that. Threshold could not be determined for any subject for the 640-Hz modulation frequency. The results for the 5000-Hz carrier probably reflect ‘‘pure’’ effects of temporal resolution, free from any influence of the detection of spectral sidebands. IV. DISCUSSION

The results are consistent with the idea that, for high modulation rates, spectral sidebands were less detectable for the hearing-impaired than for the normally hearing subjects. Indeed, for the 5000-Hz carrier, it appears that spectral sidebands were not detectable at all for the hearing-impaired subjects. It is noteworthy that, for this carrier frequency, the hearing-impaired subjects could not detect the modulation for the 640-Hz modulation frequency. However, this may partly reflect the relatively low SL of the stimuli, since performance on several measures of temporal resolution worsens at very low SLs. These measures include TMTFs 共Bacon and Viemeister, 1985; Kohlrausch et al., 2000兲, gap detection 共Plomp, 1964; Shailer and Moore, 1983兲, and the rate of recovery from forward masking 共Glasberg et al. 1987兲. Hearing-impaired subjects might be able to detect 640-Hz AM at higher overall levels. Bacon and Gleitman 共1992兲 have presented data consistent with this idea. They measured TMTFs with a broadband noise carrier, using normally hearing subjects and subjects with relatively flat hearing losses. When the SL of the carrier was about 20 dB, the normally hearing subjects could not detect AM at frequencies above 256 Hz, whereas when the SL was increased to 30 dB they could detect AM at frequencies up to 1024 Hz. The results for their hearing-impaired subjects showed individual variability, but also tended to improve with increasing SL. At the SL of 20 dB, the modulation thresholds for the hearingimpaired subjects were often lower 共better兲 than for the normally hearing subjects, which is consistent with our own results. It should be noted that the shapes of TMTFs for noise carriers do not vary markedly with level. Sensation level seems mainly to affect amplitude resolution, as reflected in the asymptotic modulation detection threshold for low modulation frequencies. We have interpreted the results for the normally hearing subjects as resulting from the combined effects of detection of the modulation per se and detection of spectral sidebands at large modulation rates. However, it is also possible that, for the 80-dB carrier level, the normally hearing subjects detected a distortion component at the modulation frequency. Evidence for the existence of such a distortion product, when bandpass noise carriers are used, has been provided by Wiegrebe and Patterson 共1999兲. For a bandpass filtered noise carrier with a level per ERB 共Glasberg and Moore, 1990兲 of about 72 dB SPL, modulated with m⫽1 共20 log m⫽0 dB兲, they estimated the level of the distortion product to be about 20 dB SPL, i.e., about 52 dB below the effective level of the 1072

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carrier. The modulation thresholds measured in our experiment for the normally hearing subjects for the 80-dB carrier were mostly below ⫺20 dB for modulation frequencies of 160 Hz and below, corresponding to m⫽0.1; for higher modulation frequencies the thresholds were even lower. At these reduced modulation depths, we would expect the relative level of the distortion product at the modulation frequency to be at least 20 dB lower, i.e., 72 dB or more below the carrier level. Thus, the effective level of the distortion product at the modulation frequency is expected to be 8 dB SPL or less. Since the absolute thresholds of our subjects at low frequencies 共160 Hz and below兲 were well above 8 dB SPL, it seems unlikely that our results were influenced by detection of a distortion product at the modulation frequency. Temporal resolution measured using TMTFs is often characterized by a time constant, ␶, defined as 1/(2 ␲ f c ), where f c is the frequency at which sensitivity has declined by 3 dB relative to that measured for low modulation frequencies. Such a measure cannot be applied to the data for our normally hearing subjects, as, in most cases, there was not a 3-dB decline in sensitivity at any modulation frequency. The failure to find a decline presumably reflects the ability of the subjects to detect spectral sidebands at high modulation frequencies. However, TMTFs obtained using sinusoidal carriers do sometimes show a region of decreased sensitivity for normally hearing subjects, especially when a very high carrier frequency is used 共Kohlrausch et al., 2000兲; sensitivity at first decreases and then increases again for very large modulation frequencies. The value of f c in such cases is typically about 150 to 200 Hz, giving a value of ␶ of about 1.1 to 0.8 ms. For the mean data of our hearing-impaired subjects obtained with the 5000-Hz carrier, the value of f c was 155 Hz 共␶ ⬇1 ms兲. Thus, there is no indication of reduced temporal resolution in our hearing-impaired subjects. V. CONCLUSIONS

共1兲 The TMTFs obtained using sinusoidal carriers with normally hearing subjects resemble those found by previous researchers. Modulation detection thresholds for low modulation rates reflect the effects of both amplitude resolution and temporal resolution. Modulation detection thresholds for high modulation rates reflect the detection of spectral sidebands. The modulation rate at which the spectral sidebands first become detectable increases with increasing carrier frequency. Performance was better for a carrier level of 80 dB SPL than for a carrier level of 30 dB SPL, especially at high modulation rates. 共2兲 For low modulation rates, modulation detection thresholds for the hearing-impaired subjects tested at 80 dB SPL were similar to those for the normally hearing subjects at 80 dB SPL, and lower 共better兲 than for the normally hearing subjects at 30 dB SPL. This indicates that, at similar SLs, hearing-impaired subjects perform better than normally hearing subjects. 共3兲 For high modulation rates, thresholds for the hearing-impaired subjects usually did not decline with increasing modulation rate, and when they did, the decreased was small. This suggests that spectral sidebands were less detectable for the hearing-impaired than for the normally B. C. J. Moore and B. R. Glasberg: TMTFs for sinusoidal carriers

hearing subjects. For the 5000-Hz carrier, it appears that spectral sidebands were not detectable at all, as performance worsened monotonically with increasing modulation rate. 共4兲 For the 5000-Hz carrier, the cutoff frequency of the TMTF was about 155 Hz, corresponding to a time constant of about 1 ms. These values are similar to those for normally hearing subjects. Thus, the results suggest that temporal resolution for deterministic stimuli is similar for hearingimpaired and for normally hearing subjects. ACKNOWLEDGMENTS

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