Research Note MODULATION TRANSFER FUNCTIONS: A COMPARISON OF THE RESULTS OF THREE METHODS

Transcription

1 Journal of Speech and Hearing Research, Volume 33, , June 1990 Research Note MODULATION TRANSFER FUNCTIONS: A COMPARISON OF THE RESULTS OF THREE METHODS DIANE M. SCOTT LARRY E. HUMES Division of Hearing and Speech Sciences, Vanderbilt University School of Medicine Modulation transfer functions (MTFs) were measured with three different psychoacoustical paradigms in the same normalhearing subjects. In the temporal-probe method, the threshold of a 4-ms probe tone (frequencies of 1000 and 4000 Hz) was measured at various envelope phases within a 100% sinusoidally amplitude-modulated (SAM) noise at modulation frequencies from 2 to 256 Hz. For the derived-mtf method, the threshold of a 500-ms tone at 1000 and 4000 Hz was measured in the same noise at the same modulation frequencies. For the modulation-detection paradigm, modulation thresholds were measured as a function of modulation frequency for bandpass filtered SAM noise centered at 1000 and 4000 Hz. MTFs with lowpass shapes were observed with all three methods. Differences were observed in the cutoff frequencies and/or attenuation rates when the data were fitted with lowpass filter transfer functions. Factors influencing those differences are discussed. KEY WORDS: psychoacoustical, modulation transfer functions, temporal processing Psychoacoustic modulation transfer functions (MTFs) represent one approach to the study of temporal processing. Several methods have been reported for measuring MTFs. These methods have in common the measurement or representation of threshold in terms of depth of modulation (m). A series of threshold estimates are made and plotted as a function of modulation frequency (f,,r) to produce a MTF. In this report we consider three methods of measuring MTFs that yield different patterns of results. These methods include the temporal-probe, the derived- MTF, and the modulation-detection paradigms. The temporal-probe paradigm measures the detectability of a brief pure tone, or probe signal, as a function of the sinusoidal phase of a 100% amplitude-modulated noise. The derived- MTF method measures the threshold of a longer duration (500 ms) tone masked by continuous 100% sinusoidally amplitude-modulated (SAM) noise. The most commonly used technique to obtain MTFs is the modulation-detection method. This procedure searches for the depth of modulation (m) that makes the modulated signal just discriminable from an unmodulated signal. Viemeister (1973a) described one of the first temporalprobe experiments in which a wideband noise at 65 db SPL was 90% sinusoidally amplitude modulated. A click (of unspecified nature) was presented at several different phases of a single modulation cycle. For each modulation frequency studied, a sine wave was fit to the click threshold data to show masked threshold as a function of the phase of the modulating sinusoid. From these curves Viemeister derived the amplitude and phase characteristics of the MTF. The cutoff frequencies derived from the data ranged from Hz. Viemeister (1977) showed that the primary limitation of the temporal-probe procedure is the use of finite-duration probes. The temporal "smearing" effects of such signals preclude direct interpretation of the observed MTF as a true transfer function. Viemeister (1977) demonstrated that the attenuation rate of the lowpass MTF derived with this method varied between 6 and 10 db/octave depending on probe duration. Buunen (1976) measured MTFs using the derived-mtf method with a 100% amplitude-modulated broadband noise carrier and pure-tone signals of 500, 1000, 2000, and 4000 Hz. He obtained lowpass cutoff frequencies of 30, 38, 55, and 85 Hz, respectively. Cutoff frequency increased with signal frequency. The asymptotic attenuation rate of the MTFs was about 6 db/octave at the lower frequencies. Weber (1977) utilized the same procedure with a 2000-Hz signal and three noise spectrum levels. His derived MTF had a cutoff frequency of 40 Hz and an attenuation rate of about 12 db/octave. He found that the cutoff frequency increased slightly with spectrum level. Viemeister (1973b, 1977, 1979) conducted a series of experiments on modulation detection. He concluded that: (a) MTFs were relatively independent of presentation level above a spectrum level of 20 db SPL; (b) the time constant of the MTF decreased as the center frequency of the bandlimited modulated noise was increased (however, change in carrier bandwidth was a confounding factor); and (c) the attenuation characteristic of the MTF (i.e., 3-4 db/octave) is not consistent with that of a simple lowpass filter (attenuation rate = 6 db/octave), but a model incorporating such a filter (with a time constant of 2.5 ms) can describe the data for broadband noise carriers. Because all of the methods considered here yield MTFs with a more or less lowpass shape, investigators have found it useful to describe the MTFs in terms that an engineer might use to quantify the transfer function for a lowpass filter. This lowpass-filter approach to MTFs provides a simple and convenient framework for the comparison of MTFs obtained with the several methods. Estimates of the lowpass-filter cutoff frequencies, as determined by various studies using MTFs, have ranged C 1990, American Speech-Language-Hearing Association /90/ $0 1.00/0

2 SCOTT & HUMES: Comparison of Three MTF Methods 391 from 15 to 100 Hz with the temporal-probe paradigm, 30 to 85 Hz with the derived-mtf method, and 5 to 55 Hz with the modulation-detection procedure (Scott, 1986). The attenuation rate of the best-fitting lowpass filter has also varied generally between 6 and 12 db/octave for the temporal-probe and derived-mtf paradigms. Most MTFs based on modulation-detection thresholds have consistently shown attenuation rates of less than 6 db/octave. The variability of the results may reflect the wide variety of stimulus parameters used in each study, the use of different groups of listeners, and the use of different methods. Given this variability, it is difficult to determine if the different MTF paradigms provide equivalent estimates of temporal resolution in the auditory system. The present study compared the MTFs for each paradigm in the same group of subjects for similar stimulus parameters. EXPERIMENT I (TEMPORAL-PROBE PARADIGM) Subjects METHOD Five normal-hearing adults (27-39 years of age) served as subjects. Each subject had hearing thresholds no poorer than 15 db HL (ANSI, 1970) bilaterally at octave intervals from 250 to 8000 Hz. They also had normal middle-ear function (middle-ear pressure dapa and contralateral acoustic reflexes present at 100 db HL from 500 to 4000 Hz). Testing time for each subject was about hours. All subjects were volunteers. Apparatus An LSI-11/23 laboratory minicomputer generated a dc-shifted cosine modulator with specified frequency, amplitude, rise/fall time, and starting phase. The modulation frequencies were 2, 4, 8, 16, 32, 64, 128, and 256 Hz. A white noise lowpass filtered at 10 khz was multiplied by the modulator to produce 100% sinusoidally amplitude-modulated (SAM) noise. The 4-ms probe signal was formed by gating a continuous tone with a triangular window. An oscillator generated and 4000-Hz pure tones and a rise/fall gate provided a linear 2-ms rise/decay function for the triangular gating. A timer controlled the temporal location of the probe tone within the phase of the SAM noise. The probe tone was presented 248 ms into a 500-ms observation interval. The stimulus was presented to the left earphone (TDH- 49P) for each subject. The nominal spectrum level of the noise at the earphone was about 31 db/hz. Procedure Each subject practiced 2 hours before data collection began. An adaptive two-interval forced-choice (2IFC) paradigm was used to measure probe threshold. Presentation of the probe occurred as illustrated in Figure la. The spectra of the probe and the SAM masker are also shown schematically in the right-hand portion of the figure. At the offset of the warning light, a burst of modulated noise was presented. Each burst lasted 2500 ms (beginning 500 ms before the first observation interval and ending 500 ms after the second observation interval). Lights were activated to indicate each of the observation a) Temporal probe 21FC Temporal Structure I II PIT Off t of & Morning light mac I II Spectrum 70 db SPL or 31 db/hz f Hz PIP Ofw t o wmkg light moo b) DerivedX MTF l Offeet of 5 wrnng light 1 I mo 11 detection 0 f c) Uodulmlon 1/ / // L//4// dtction Offlt of warning light moom ime I l II 11dB/Jzj-r---c 70 db SPL or 31 db/hz fs Hz fl f f Hz Froqueeny FIGURE 1. Schematic representation of the temporal structure of the test paradigm (left) and the spectra of the signals in each of the three experiments. For all experiments, the signal is represented as occurring in the first interval of a 2IFC paradigm. PIT represents a 4-ms tone presented in the trough of the SAM noise, whereas PIP represents a 4-ms tone presented in the peak of the SAM noise.

3 392 Journal of Speech and Hearing Research intervals. Once the burst of modulated noise was completed, a fourth light was activated to allow the subject to choose the signal interval. After the subject responded, feedback was provided. The probe was presented in a peak or trough of the SAM noise for modulation frequencies 2 through 8 Hz and was presented in all conditions at the same time relative to the start of the SAM noise. Pilot data indicated that the maximum and minimum probe threshold at modulation frequencies > 8 Hz did not appear at the points of maximum and minimum carrier amplitude, as was the case for lower modulation frequencies. It was therefore necessary to determine the degree of the phase shift within the auditory system. For modulation frequencies from 16 Hz to 256 Hz, the probe was presented as a function of the phase of the sinusoidal modulator in 30 steps from 0 to 360. Probe threshold was measured for each phase condition. The level of the tone was adjusted adaptively according to the subject's responses to estimate 70.7% correct signal detections (Levitt, 1971). A total of 14 reversals in signal level determined a single run. Threshold was estimated by averaging the last 10 reversals. An 8-dB step size was used for the first three reversals; the step size for the remaining reversals was 2 db. Average probe-tone threshold was obtained from three runs. Whenever the standard deviation over three runs was greater than 3.0 db, a fourth run was made, and the threshold most different from the mean of the four runs was discarded. The order of presentation of modulation frequency was varied randomly for each subject, but all measurements at a given June 1990 modulation frequency were completed before proceeding to a new frequency. RESULTS Individual masked thresholds obtained with the Hz probe signal have been pooled for the five listeners; average data are shown in Figure 2. The data in the upper left panel for modulation frequencies 2 through 8 Hz indicate that: (a) the maximum threshold was roughly stable at 78 db SPL and appeared at a modulation phase of 0, and (b) minimum threshold increased from 40 to 52 db SPL as modulation frequency was increased from 2 to 8 Hz, and it appeared at a modulation phase of 180 As modulation frequency was increased above 8 Hz, several trends became apparent in the data. The maximum threshold no longer occurred at a modulation phase of 0. Maximum threshold remained at approximately 78 db SPL through 64 Hz, although it occurred at a different modulation phase for each of the modulation frequencies. The maximum threshold decreased to roughly 75 db SPL at 128 and 256 Hz. The minimum threshold did not occur at 1800 modulator phase. The phase value corresponding to the minimum decreased as fm increased. As modulation frequency was increased, the minimum threshold continued to increase such that the difference between maximum and minimum threshold disappeared at 256 Hz. The observations drawn from the data for 1000 Hz in Figure 2 were also apparent in the data for 4000 Hz. The data were essentially identical to those shown in Figure 2 3 -I C I0 am - 0 _c U 73 a 63 u X 0 X2 O -... l l lll l li l l odula o 2Pa (d Modulaior Phase (deg) M _ l 71 Im m i,... i _~Crr~y3 64 H- U M m 43 gl 73 M I'... A I. I I I l I I 3 U 1N 2a i Modulaator Phase _ ~~~~~~~~~~~~~~~~~~~~_ It (deg) 1233W. 41(_T I r i i I I I I I i ir a H WI U I 4 oda 1o 2Ph (dm Modulator Phase (dug) 73 a M.. : l ~~~~2, 2-4. i..... Modulat.or Pha (deg) 4 Modula 2P " (d Modulator Phase (deg) 4U 111i i Modulator Phase FIGURE 2. Mean temporal-probe thresholds at 1000 Hz as a function of modulation starting phase. The first panel shows the thresholds at modulation starting phases of 00 and 180' for modulation frequencies of 2, 4, and 8 Hz. The rest of the panels show threshold at modulation starting phases of 0 through 360 in 30-degree steps for modulation frequencies 16 through 256 Hz. (deg)

4 . SCOTT & HUMES: Comparison of Three MTF Methods 393 except that maximum probe threshold at 4000 Hz was 76 db SPL. This value was relatively stable for modulation frequencies 2 through 64 Hz, but decreased by approximately 3 db at 128 and 256 Hz. As modulation frequency increased, the minimum threshold again increased such that the difference between the maximum and minimum threshold diminished to near zero at 256 Hz. A cosine wave was fit to the data for modulation frequencies 16 through 256 Hz. The root-mean-square (RMS) error of the fitted wave ranged from 0.61 to 5.78 db, with most values below 2.67 db. AP, the difference between the maxima and minima of the cosine fitted data, was estimated to be twice the best-fitting cosine amplitude. By using the starting phase of the best-fitting cosine function, we were able to estimate the shift in temporal location of the maximum and minimum thresholds. The starting phase of the cosine function should have been radians when the maximum and minimum thresholds occurred at the maximum and minimum carrier amplitude, respectively. A starting phase other than radians indicated a phase shift. This analysis corroborated the shift in phase apparent in Figure 2. AP was then obtained, using the best-fitting cosine functions, as a function of modulation frequency. To calculate modulation depth (m) from P, the following formula was used: mxy = (Dxy - 1)/(Dxy + 1) (1) Where Dxy is 10 to the power of APxy/20, for probe-tone frequency (x) and modulation frequency (y). The modulation values calculated in this manner were plotted as an MTF in Figure 3. For both the and the 4000-Hz 'a data, modulation depth declined as modulation frequency increased. The temporal-probe paradigm permits an estimate of both the amplitude and phase characteristics of the MTF (see Figure 3). At both signal frequencies of 1000 and 4000 Hz no phase shift was evident through 8 Hz. At 16 Hz modulation frequency there was a slight phase shift of about radians. As modulation frequency increased further, the phase shift also increased to a maximum value of 3 radians at 128 Hz. This phase lead is consistent with that found earlier by Viemeister (1977). A phase lead indicates that the location of maximum and minimum probe thresholds leads the acoustic maximum and minimum in the modulator. EXPERIMENT II (DERIVED-MTF PARADIGM) Subjects METHOD The same five normal-hearing adults who served as subjects for the first experiment served as subjects for this experiment. The testing time required for each subject was approximately 6 hours. Procedures The derived-mtf method was identical to that of the temporal-probe method except that the probe-tone duration was 500 ms, rise/fall time was 20 ms, and an additional modulation frequency, 512 Hz, was presented. Figure lb illustrates schematically the 2IFC paradigm for this method, as well as the spectra of the noise masker and probe tone. RESULTS o a' 0o FIGURE 3. Modulation depth as a function of modulation frequency for both the and 4000-Hz signals for the temporalprobe paradigm. The circles connected by the solid line represent the results at 1000 Hz, whereas the circles connected by the dashed line represent the results at 4000 Hz. Phase shift as a function of modulation frequency is also indicated by the triangles and the right ordinate. The triangles connected by the solid line represent the phase shift at 1000 Hz and the triangles connected by the dashed line represent the phase shift at 4000 Hz. U) S a n Figure 4 shows the group mean thresholds for both a and 4000-Hz tone as a function of modulation frequency for the derived-mtf paradigm. The 1000-Hz thresholds (circles) were several db lower than the Hz thresholds (triangles) at most modulation frequencies. At 1000 Hz, the threshold was asymptotic at about 50 db SPL at 256 Hz. At 4000 Hz, the asymptote appeared at db. For three of the listeners, the threshold of the tone at 4000 Hz was essentially asymptotic by 256 Hz, but the thresholds for the other two listeners continued to increase through 512 Hz. For the derived-mtf method, an estimate of the depth of modulation at threshold was determined from the difference between the asymptotic threshold and the threshold at a given modulation frequency. Modulation depth was calculated from these values as follows:

5 394 Journal of Speech and Hearing Research June J mca I- I- MEAN EXPERIMENT III (MODULATION-DETECTION PARADIGM) Subjects METHOD 'a 0 -C f I Hz 4000 Hz A---- The same 5 normal-hearing adults who served as subjects for the first two experiments served as subjects for this experiment. The testing time was approximately 6 hours for each subject FIGURE 4. Thresholds obtained using the derived-mtf paradigm as a function of modulation frequency. The circles represent the thresholds for the 1000-Hz signal, whereas the triangles represent the thresholds for the 4000-Hz signal. mxy = 1 - (Pmry/Pax) (2) Where mxy is as before, Pmy is the threshold sound pressure at modulation frequency (y) and probe frequency (x), whereas Pax is the asymptotic sound pressure for probe frequency (x). Modulation depth is plotted as a function of modulation frequency in Figure 5 for signal frequencies of 1000 and 4000 Hz. At 1000 Hz, the MTF shows only a slight decline through 8 Hz followed by a more rapid decline in modulation depth from 16 to 256 Hz. At 4000 Hz, modulation depth remains relatively large out to 32 Hz with the largest decline occurring at modulation frequencies above 64 Hz. 4- C o n. r k. A I. I I. I I I.._... AN FIGuRE 5. Modulation depth as a function of modulation frequency for the derived-mtf paradigm. The circles represent the results for the 1000-Hz signal, whereas the triangles represent the results for the 4000-Hz signal. Apparatus Broadband noise was multiplied by dc-shifted sinusoids to produce SAM noise. The SAM noise was bandpass filtered after modulation to provide frequency-specific stimuli (bandpass noises at 1000 and 4000 Hz). By filtering after modulation, the spectrum of the signal was determined by the characteristics of the filter and, as with the broadband noise used in the previous two experiments, is invariant with changes in modulation frequency. Bandpass filtering after modulation can, however, alter the modulation depth when the modulation frequency is large relative to the bandwidth of the filter. Direct measurement of modulation depth for stimuli in this study revealed no effect of filtering on modulation depth. The sinusoidally modulated waveforms were attenuated by a factor of /1+m2) so that the average intensities of the two observation intervals were equal to one another. The frequencies of modulation were the same as were used in the temporal-probe paradigm. The spectrum level of the bandpass noise was 31 db/hz for both center frequencies, the same as for the broadband noise used in the earlier methods. The bandwidths of the noises were 1100 Hz for the 1000-Hz signal ( Hz) and 1850 Hz for the 4000-Hz signal ( Hz). A continuous broadband background masker served as an additional precaution to prevent off-frequency listening; the background masker served to prevent the subjects from using information outside the passbands of the SAM filtered noise. The signal-to-masker ratio (SMR) (signal spectrum level/background spectrum level) was 20 db for both bandpass noises. Viemeister (1979) concluded that MTFs based on modulation detection were relatively independent of sensation level above approximately 20 db, therefore the modulation detection data should not have been affected by SMR. The right-hand portion of Figure c provides a schematic illustration of the spectra of the stimuli. Procedure The procedure was similar to the one used with the two preceding methods. Subjects practiced for 2 hours before

6 SCOTT & HUMES: Comparison of Three MTF Methods 395 TABLE 1. Time constants (), cutoff frequencies (F,), and rejection rates (RR) for the 1000-Hz data. TP = Temporal-probe paradigm; DMTF = Derived-MTF paradigm; and MD = Modulation-detection paradigm. Subject T FC (Hz) RR (dbloct) GW TP DMTF MD RF TP DMTF MD CC TP DMTF MD LH TP DMTF MD RL TP DMTF MD MEAN TP DMTF MD TABLE 2. Time constants (), cutoff frequencies (Fc), and rejection rates (RR) for the 4000-Hz data. TP = Temporal-probe paradigm; DMTF = Derived-MTF paradigm; and MD = Modulation-detection paradigm. Subject T Fc (Hz) RR (dbloct) GW TP DMTF MD RF TP DMTF MD CC TP DMTF MD LH TP DMTF MD RL TP DMTF MD MEAN TP DMTF MD data collection began. The left-hand portion of Figure c provides a schematic illustration of the 2IFC paradigm used for this method. Following the offset of the warning light, an unmodulated bandpass noise was presented. During one of the 500-ms observation intervals, the noise was sinusoidally modulated. Thus, the noise was on for 2500 ms with 500 ms of the noise being amplitude modulated. Modulation-detection thresholds were obtained in a background of continuous unmodulated broadband noise. The amplitude of the modulating sinusoid (Am) was varied adaptively to estimate 70.7% correct detection of modulation (Levitt, 1971). The computer controlled the amplitude of modulation using a 4-dB step size for the first 3 reversals and then a 2-dB step size for the remaining 11 reversals. Otherwise, threshold determination was the same as in the two preceding methods. RESULTS For this paradigm, threshold was the just-detectable modulation depth, m. This was calculated as follows: mxy = Amxy/D (3) Where D is the DC level to which the sinusoidal modulation is added and Amxy is the peak amplitude of the modulator for carrier frequency (x) and modulator frequency (y). The thresholds obtained for modulation detection are plotted in Figure 6 as 20 log m (db) versus modulation frequency. At most modulation frequencies, except 2 Hz, the modulation thresholds for the 4000-Hz condition (triangles) were consistently better (by about 5 db) than those found for the 1000-Hz condition. For both conditions, modulation thresholds were lowest at 8 Hz and progressively deteriorated with increasing frequency. DISCUSSION This study was designed to compare three methods for measuring modulation transfer functions. Modulation depth is plotted as a function of modulation frequency for all three paradigms in Figure 7. The dashed and dotted lines are plots from the first two experiments taken from Figures 3 and 5, whereas the solid line represents the modulation detection experiment. In the modulationdetection paradigm, as modulation frequency increased, it became more difficult for the listener to discriminate between modulated and unmodulated noise. From these data we can estimate the time constant of hearing to evaluate auditory temporal resolution. This process begins by determining the cutoff frequencies of the lowpass MTFs. A curve was fit to graphs of modulation depth (m) versus modulation frequency (Figures 3 and 5) for each paradigm, except for the modulationdetection paradigm (Figure 7), for which (l-m) was used. It was assumed, based on previous studies, that a firstorder or second-order lowpass filter would provide a good description of the dependence of m on modulation frequency. According to Schroeder (1981), the dependence of m on modulation frequency, F, for a first-order filter can be described as follows:

7 396 Journal of Speech and Hearing Research T E 08 0o 0N c.j O FIGURE 6. Modulation-detection thresholds as a function of modulation frequency at 1000 Hz (circles) and 4000 Hz (triangles). Thresholds are plotted as 20 log m, where m is modulation depth. m(w) = [1 + (wr) 2 ] (4) Where w = 2nF and r is the time constant in seconds. The best-fitting i value was determined using a least-squares criterion. The corresponding cutoff frequency, F(c), was determined by 1/2rT = F(c) (Carlson, 1975) (5) Tables 1 and 2 list, for each subject, the best-fitting time constant (T), cutoff frequency [F(c)], and attenuation rate determined using this equation. Only first-order (6 db/ octave) and second-order (12 db/octave) lowpass filters were considered in this analysis, so the actual attenuation rate for a given paradigm may not have been either 6 or 12 db/octave exactly. An analysis of variance (paradigm by signal frequency by subject) was performed on the cutoff frequencies appearing in Tables 1 and 2. The ANOVA revealed a significant F(2,8) = 16.70, p <.01 paradigm by signal frequency interaction, as well as main effects of both signal frequency and paradigm. In analyzing the simple effect of signal frequency, there was no significant difference in cutoff frequency at the two signal frequencies for the temporal-probe paradigm. For the derived-mtf and modulation-detection paradigms, on the other hand, the 4000-Hz cutoff frequency was significantly higher (shorter time constant at 4000 Hz). In analyzing the simple effect of paradigm, there was no significant difference in the cutoff frequency provided by all three paradigms at 1000 Hz. At 4000 Hz, the modulation-detection paradigm had the highest mean cutoff frequency, followed by values from both the derived-mtf and temporal-probe paradigms. The cutoff frequencies provided by the latter two paradigms were not significantly different from one another June 1990 The individual cutoff frequencies determined with the temporal-probe and derived-mtf paradigms in this study were in agreement with those found in earlier studies using this method, at both 1000 and 4000 Hz (Ahlstrom, 1984; Buunen, 1976; Rodenburg, 1977; Viemeister, 1973a). Because the derived-mtf paradigm made use of a broadband noise masker, it is possible that the results could have been influenced by a phenomenon known as comodulation masking release. This possibility was investigated using 2 subjects, and found not to have had any effect on the determination of modulation depth in the derived-mtf paradigm (see Scott, 1986). For the modulation-detection method, the cutoff frequencies for a NBN centered at 1000 Hz have been reported to be near Hz (Rodenburg, 1977; Viemeister, 1979). The mean value of 82 Hz observed in this study was somewhat higher than that reported previously. This could be due, in part, to the broader bandwidth used in the present study. The cutoff frequencies in this study for a 4000-Hz bandpass noise, however, were much higher than those found with a wideband noise carrier, which usually provides the highest cutoff frequency obtainable. The background masker used in this paradigm to restrict listening to the bandpass noises has not been used in previous studies. This may explain the higher cutoff frequencies obtained in the present study. In previous reports sensation levels of 20 db have produced asymptotic levels of performance (Viemeister, 1979). The signal-to-masker ratio used in the third experiment was 20 db. Thus, it would appear that the SMR should have not affected the modulation detection thresholds measured. In addition, a phase shift was demonstrated when using the temporal-probe paradigm. The present data indicate that the location of maximum and minimum probe thresholds in this paradigm will shift as modulation frequency increases above 16 to 32 Hz. One cannot simply measure threshold at the acoustic maximum and minimum in the modulator and assume this provides an estimate of maximum and minimum threshold. In summary, the characteristics of the "typical" MTF obtained from normal hearing listeners depend, in part, on the psychophysical method used to measure the MTF. When the MTF is characterized as a lowpass-filter transfer function, significant differences in both the cutoff frequency and the attenuation rate of the lowpass filter can be observed due to the use of different measurement paradigms. The temporal-probe and derived-mtf methods yield similar results. The modulation-detection paradigm produces lowpass MTFs with higher cutoff frequencies and shallower attenuation rates than either of the other methods. ACKNOWLEDGMENTS The authors express their gratitude to Judy Wallace and Debbie Hettinger for assistance in typing the manuscript and to Donald Riggs for assistance with some of the illustrations. Thanks are also expressed to Wes Grantham for providing

8 SCOTT & HUMES: Comparison of Three MTF Methods z L E )1 o F F F -0.2 ' ,: = & Al J 70 & ve -0.2 Modulator Frequency (Hz) FIGURE 7. Modulation depth as a function of modulation frequency for the 1000-Hz signal (left panel) and 4000-Hz signal (right panel) for each of the paradigms. The triangles represent the results from the temporal-probe (TP) paradigm, the squares represent the results from the derived-mtf (DMTF) paradigm, and the Xs represent the results from the modulation-detection (MD) paradigm. assistance in the setup of the equipment for the three experiments. This work was supported, in part, by an RCDA awarded by NIH to the second author. Portions of this paper were presented at the American Speech-Language-Hearing Association Convention in New Orleans, November, REFERENCES American National Standards Institute. (1970). American National Standard specifications for audiometers. (ANSI S ). New York: ANSI. AHLSTROM, C. (1984). Psychoacoustical modulation transfer functions and speech recognition in listeners with normal hearing. Unpublished doctoral dissertation, Vanderbilt University, Nashville, TN. BUUNEN, T. J. F. (1976). On the perception of phase difference in acoustic signals. Unpublished doctoral dissertation, Delft University of Technology, Delft, The Netherlands. CARLSON, A. B. (1975). Communication systems: An introduction to signals and noise in electrical communication. (2nd ed.). New York: McGraw-Hill. LEVITT, H. (1971). Transformed up-down methods in psychoacoustics. Journal of the Acoustical Society of America, 49, RODENBURG, M. (1977). Investigation of temporal effects with amplitude modulated signals. In E. F. Evans & J. P. Wilson (Eds.), Psychophysics and physiology of hearing (pp ). New York: Academic Press. SCHROEDER, M. R. (1981). Modulation transfer functions: Definition and measurement. Acustica, 49, SCOTT, D. M. (1986). Measurement of temporal resolution in the auditory system. Unpublished doctoral dissertation, Vanderbilt University, Nashville, TN. VIEMEISTER, N. F. (1973a). In minimum integration time. In A. R. Moller (Ed.), Basic mechanisms in hearing (pp ). New York: Academic Press. VIEMEISTER, N. F. (1973b). Temporal modulation transfer function for audition. Journal of the Acoustical Society of America, 53, 312 (A). VIEMEISTER, N. F. (1977). Temporal factors in audition: A system analysis approach. In E. F. Evans & J. P. Wilson (Eds.), Psychophysics and physiology of hearing (pp ). New York: Academic Press. VIEMEISTER, N. F. (1979). Temporal modulation transfer functions based upon modulation thresholds. Journal of the Acoustical Society of America, 66, WEBER, D. L. (1977). Auditory MTF derived with modulated noise. Journal of the Acoustical Society of America, 61 (Suppl. 1), S88. Received August 1, 1988 Accepted September 29, 1989 Requests for reprints should be sent to Diane M. Scott, Department of Audiology and Speech Sciences, Michigan State University, East Lansing, MI