Cochlear hearing loss and the detection of sinusoidal versus random amplitude modulation

Abstract

This study assessed the effect of cochlear hearing loss on detection of random and sinusoidal amplitude modulation. Listeners with hearing loss and normal-hearing listeners (eight per group) generated temporal modulation transfer functions (TMTFs) for envelope fluctuations carried by a 2000-Hz pure tone. TMTFs for the two groups were similar at low modulation rates but diverged at higher rates presumably because of differences in frequency selectivity. For both groups, detection of random modulation was poorer than for sinusoidal modulation at lower rates but the reverse occurred at higher rates. No evidence was found that cochlear hearing loss, per se, affects modulation detection.

1. Introduction

Cochlear hearing impairment is often characterized by diminished nonlinear functioning of the inner ear. This loss of nonlinearity contributes not only to elevated absolute thresholds, but also to a broadening of auditory filters and a general loss of amplitude compression (for review, see Moore, 1996; Oxenham and Bacon, 2003). Because of the loss of amplitude compression, the internal representation of a fluctuating stimulus could, in theory, be more pronounced in the hearing impaired (HI) ear than in the normal-hearing (NH) ear. This latter notion gives rise to the expectation that the more pronounced internal representation of fluctuation in HI ears should be beneficial to tasks involving envelope processing. There is some evidence for this in tasks of suprathreshold envelope processing: (1) for listeners with unilateral hearing impairment, less modulation depth is required for a fluctuating stimulus presented to the impaired ear than to the normal ear to obtain perceptual equivalence of fluctuation across ears (Moore et al., 1996); (2) for narrow bands of noise with perceptually pronounced inherent fluctuations, gap detection is poorer for HI listeners presumably because of the greater propensity for confusion between the imposed gap and the inherent fluctuations (Grose et al., 1989); and (3) masking period patterns are usually more shallow for HI ears than NH ears (Wojtczak et al., 2001).

It is less clear whether the benefit of a more pronounced internal representation of fluctuation in HI ears extends to tasks involving the detection of modulation. Some studies have found no effect of HI on the detection of modulation (Grose and Hall, 1994; Moore and Glasberg, 2001; Koopman et al., 2008), some studies have found poorer performance for HI listeners (Grant et al., 1998), and yet other studies have reported superior performance for HI listeners (Ernst and Moore, 2012; Shen, 2014; Sek et al., 2015). Even within a particular study, the effect of hearing impairment on modulation detection can be varied (cf. Desloge et al., 2011). Comparisons across these studies are complicated by confounding factors of age and presentation level. One purpose of this study was to add clarity to the issue of the effect of hearing impairment on modulation detection.

The studies of modulation detection cited above all used deterministic modulators (sinusoids or square waves). It might be hypothesized that detection of random modulation should be more acute than detection of deterministic modulation in the HI ear with compromised compression. The basis of this speculation is that random modulation with the same average depth and rate as a sinusoidal modulation contains sporadic large peaks that, if uncompressed, might aid detection if sensitivity to envelope peaks is important for detection amplitude modulation. However, evidence relevant to this suggestion is both sparse and conflicting. Studies of NH listeners show similar thresholds for random and deterministic modulation—at least for lower average rates of modulation (Mendoza et al., 1995; Ozimek et al., 1998; Sek et al., 2015). Thus, in ears with normal compression there is no suggestion of a detection benefit associated with the sporadic large peaks of random modulation. In terms of HI ears, Shen and Lentz (2010) measured modulation detection thresholds for random envelopes carried by a 500-Hz pure tone carrier and found that detection thresholds were quite similar for HI and NH listeners, suggesting that loss of compression does not confer a benefit for the detection of random modulation. Logically, therefore, since modulation detection thresholds are similar for random and sinusoidal modulation in the NH ear, and modulation detection thresholds are similar for random modulation for HI and NH ears, it follows that modulation detection thresholds should be similar for random and sinusoidal modulation in the HI ear. This reasoning runs counter to the speculation that the sporadic large peaks associated with random modulation might aid detection in the (non-compressing) HI ear. However, the detection of random and sinusoidal modulation has not been compared for the HI ear, to our knowledge. A second purpose of this study, therefore, was to address this lacuna in the literature.

In summary, the purpose of this study was to measure temporal modulation transfer functions (TMTFs) in HI and NH ears for both deterministic (sinusoidal) and random modulation. The objectives were to further clarify the effect of HI on modulation detection, and to determine whether the presumed absence of compression in the HI ear confers any benefit for the detection of random modulation.

2. Method

2.1. Participants

Eight listeners with mild-to-moderate sensorineural hearing loss and eight listeners with normal hearing participated. The NH listeners had pure tone thresholds ≤20 dB hearing level (HL) at octave frequencies from 250 to 8000 Hz. Air conduction thresholds for the test ear of each HI listener (HI1–HI8) are shown in Table 1. In order to avoid the age confound that is present in some earlier studies of modulation detection by HI listeners, care was taken to have substantial age overlap between the two groups. The HI group had a mean age of 50 years (standard deviation = 14 years), and the NH group had a mean age of 47 years (standard deviation = 12 years).

Table 1.

Air conduction thresholds (dB HL) for the test ear of listeners with cochlear hearing loss. Group mean and standard deviation (SD) is also shown for each audiometric frequency.

Listener	Frequency (Hz)
	250	500	1000	2000	4000	8000
HI1	20	30	50	40	35	15
HI2	25	15	20	50	60	65
HI3	10	20	35	45	60	60
HI4	50	45	40	30	55	60
HI5	30	35	45	40	25	50
HI6	35	30	35	45	35	60
HI7	35	35	45	55	50	50
HI8	35	45	45	45	45	60
Mean	30.0	31.9	39.4	43.8	45.6	52.5
SD	12.0	10.7	9.4	7.4	12.9	16.0

2.2. Stimuli

The signal was an amplitude modulated (AM) sinusoid with a carrier frequency ($f_c$) of 2000 Hz. The modulator was either a raised sinusoid or the raised envelope of a narrow band of Gaussian noise. The two types of AM stimuli will be referred to as sinusoidal AM (SAM) and Gaussian AM (GAM).

To generate SAM, the carrier tone was multiplied by a DC-shifted modulator using the equation

$$s\left(t\right)=\left[1+m*\hspace{0.17em}\text{sin}\left(2\pi f_{m}t+\frac{3\pi }{2}\right)\right]*\hspace{0.17em}\text{sin}\left(2\pi f_{c}t+\theta \right),$$ (1)

where m is the modulation index, and the modulator frequency ($f_m$) was either 8, 16, 32, 64, 128, or 256 Hz. The starting phase of the modulator was fixed at 3π/2 radians whereas the starting phase of the carrier ($\theta$) was randomly selected for each presentation. To maintain a constant output level of the SAM prior to final stage attenuation, the amplitude of the signal waveform was scaled as a function of modulation depth by the factor

$$\frac{1}{\sqrt{1+\frac{m^2}{2}}}.$$ (2)

To generate GAM, the 2000-Hz carrier tone was modulated by the envelope of a narrow band of noise. A range of noise bandwidths was selected to yield average modulation rates that coincided with the SAM frequencies (8, 16, 32, 64, 128, and 256 Hz) based on the principle that the average modulation rate of a narrow band of Gaussian noise is approximately 0.64 times the bandwidth (Rice, 1954). To construct a GAM signal having a particular average modulation rate and a particular modulation depth, the stipulated narrow band of noise was first digitally generated and the Hilbert envelope extracted. This envelope was then down-shifted to have a mean amplitude of zero, and subsequently normalized to have a root mean square (RMS) amplitude of $1/\sqrt{2}$ (equivalent to the RMS amplitude of a pure tone with peak amplitude = 1). To vary the depth of modulation, this normalized envelope was multiplied by a factor of $m$. The adjusted envelope was then up-shifted by a constant of 1.0 and multiplied by the carrier to obtain the desired GAM signal. Finally, the GAM signal was scaled to maintain a constant output level prior to final stage attenuation.

For each type of AM, a new stimulus sample was generated for each and every presentation at a sampling rate of 24 414 Hz. Each stimulus was 400 ms in duration, including 50-ms raised cosine rise/fall ramps, and presented at a constant output level of 85 dB sound pressure level (SPL).

2.3. Procedure

Modulation detection thresholds were measured with a three-alternative, forced-choice procedure (3AFC) that incorporated a three-down, one-up stepping rule to converge on the 79.4% correct point. Lights on a response box indicated observation intervals and, following each trial, feedback was provided to participants by illuminating the correct interval. The initial step size for modulation depth adjustment was 4 dB [in units of $20\hspace{0.17em}\text{log}\hspace{0.17em}(m)$], and this was halved after the second and fourth reversals to result in a final step size of 1 dB. A threshold estimation track was terminated after ten reversals, and the mean of the modulation depths at the final six reversal points was taken as the threshold estimate. At least three estimates of threshold were obtained for each modulation rate, with a fourth obtained if the range of the first three exceeded 3 dB. All estimates obtained were averaged to give the final threshold value.

2.4. Statistical analyses

Repeated measures analyses of variance (ANOVAs) were used to assess group differences between conditions and interactions within variables. Greenhouse-Geisser corrections were applied when Mauchly's tests indicated violations of sphericity. Significant interactions were assessed using simple effects testing. Cohen's d was used as a measure of effect size, in which values of 0.20, 0.50, and 0.80 designate small, medium, and large effect sizes, respectively (Cohen, 1992).

3. Results

Performance was reasonably similar within each group and is well represented by the group means. The results are shown in Fig. 1, where the data have been broken down into separate panels, with some replication across panels, in order to highlight particular features.

Fig. 1.

Mean modulation detection thresholds plotted as a function of modulation rate. (A) Summary TMTFs for SAM (circles) and GAM (triangles) for NH (filled symbols) and HI (open symbols) listeners; (B) TMTFs for SAM for NH listeners; present data (filled circles) and comparable data from Moore and Glasberg (2001) (filled squares); (C) TMTFs for SAM (filled circles) and GAM (filled triangles) for NH listeners at 85 dB SPL, with supplemental data at 65 dB SPL (small open symbols); (D) TMTFs for SAM for NH listeners (filled circles) and HI listeners (open circles); (E) TMTFs for GAM for NH listeners (filled triangles), HI listeners (open triangles), and data from Shen and Lentz (2010) (hashed squares). Error bars, when present, indicate 1 standard deviation.

Figure 1(A) provides a general overview of the data pattern, showing the mean data for both groups and modulation types. This portrayal highlights that for both SAM (circles) and GAM (triangles), HI listeners (open symbols) and NH listeners (filled symbols) had similar modulation sensitivity for lower modulation rates. However, performance for NH listeners improved at higher rates, whereas that for HI listeners remained relatively stable. For SAM the divergence occurred at 256 Hz; for GAM the divergence occurred at 128 Hz. At these higher rates, the two listener groups also showed a difference in behavior: whereas the NH listeners exhibited greater sensitivity to GAM than SAM at the two highest rates, the HI listeners exhibited relatively similar sensitivity to the two modulation types. For both listener groups, sensitivity to modulation was more acute at the lower rates for SAM than for GAM.

Figure 1(B) depicts the average TMTF for the sinusoidal modulators for the NH listeners (circles). Also shown are SAM data for NH listeners from Moore and Glasberg (2001) for a 2-kHz carrier (squares). Although the modulation rates, stimulus durations (400 ms vs 540 ms), and presentation levels (85 dB SPL vs 80 dB SPL) differed across studies, the resulting form of the TMTF was similar. Detection thresholds were relatively stable for modulation rates less than about 160 Hz and then improved markedly for the highest rate.

Figure 1(C) shows the SAM (filled circles) and GAM (filled triangles) detection thresholds for the NH listeners. (The smaller open symbols are supplemental data collected at a lower presentation level and are discussed later.) Unlike the SAM data, the GAM thresholds improved monotonically with increasing modulation rate. The SAM and GAM functions crossed, such that the GAM thresholds were poorer than SAM thresholds for lower modulation rates but better than SAM thresholds at higher rates. Statistical analysis showed a significant effect of modulation type [F(1,7) = 5.70; p = 0.048, d = 1.00], a significant effect of modulation rate [F(1.65,11.51) = 67.22; p < 0.001, d = 3.10], and a significant interaction between these two factors [F(5,35) = 25.84; p < 0.001, d = 1.92)]. The interaction was further evaluated, revealing that the SAM and GAM thresholds were significantly different at each modulation rate (p ≤ 0.03, d = 0.96–2.92].

Figure 1(D) shows the SAM detection thresholds for both the HI listeners (open circles) and NH listeners (filled circles). There is a close correspondence between mean thresholds across listener groups for all of the modulation rates except the highest rate of 256 Hz. Here, the NH listeners showed a marked improvement relative to lower modulation rates whereas the HI listeners showed a slight worsening. This pattern of results was confirmed with analyses revealing no significant effect of group [F(1,14) = 3.36, p = 0.088, d = 0.49], a significant effect of modulation rate [F(3.15,44.12)= 8.25; p < 0.001, d = 0.77], and a significant interaction between these two factors [F(3.15,44.12) = 4.50; p = 0.007, d = 0.57]. The interaction term was assessed, and only the threshold difference at the highest modulation rate was statistically significant [F(1,14) = 23.21; p < 0.001, d = 2.40].

Figure 1(E) shows the GAM detection thresholds for both the HI listeners (open triangles) and the NH listeners (filled triangles). [The hatched square symbols show data from Shen and Lentz (2010), and are discussed later.] Similar to the SAM data, there was a close correspondence between mean thresholds across listener groups for the lower modulation rates but then a divergence occurred – here, for the highest two rates. Statistical analyses revealed a significant effect of group [F(1,14) = 6.89; p = 0.020, d = 0.70], a significant effect of modulation rate [F(2.40,33.53) = 92.55; p < 0.001, d = 2.58], and a significant interaction between these two factors [F(2.40,33.53) = 12.33; p < 0.001, d = 0.94]. Assessment of the interaction revealed that the two groups did not differ for the lower modulation rates but did for the rates of 128 Hz [F(1,14) = 8.25; p = 0.12, d = 1.44] and 256 Hz [F(1,14) = 66.94; p < 0.001, d = 4.09].

4. Discussion

The data pattern for SAM conformed to expectations based on previous work. For NH listeners, detection thresholds remained relatively stable across low modulation frequencies but then reached an inflection point above which thresholds improved markedly. This improvement at the highest rate reflects audibility of the now-resolved modulation sidebands, wherein the task transitions from one of modulation detection to one of pure tone (sideband) detection. The modulation rate at which this occurs depends on the carrier frequency (Kohlrausch and Fassel, 2000). Because the bandwidths of auditory filters (expressed in Hz) increase with increasing center frequency, the modulation rate at which the side bands become resolved increases with carrier frequency. The fact that the HI listeners did not improve at the highest rate for either SAM or GAM supports the interpretation that their auditory filters in the 2-kHz region were abnormally wide, such that the modulation sidebands remained unresolved at the highest rate tested here (cf. Moore and Glasberg, 2001).

Some aspects of the GAM data pattern also conformed to expectations. As just noted, the presumably greater frequency selectivity of the NH listeners enabled them to benefit from sideband detection at the highest modulation rates, unlike the HI listeners, leading to a divergence in thresholds across the two groups at these rates. Sideband detection also likely accounts for the superior thresholds for GAM relative to SAM at the highest modulation rates for the NH listeners. Because of the random fluctuations in frequency of the modulation sidebands for the GAM stimuli, these sidebands would sporadically become resolved at lower average modulation rates than for fixed-rate SAM with the same average rate; in addition, the frequency-modulating nature of these GAM sidebands might enhance their salience and consequently their detectability. Ozimek et al. (1998) also found better detection thresholds for GAM than for SAM at high modulation rates.

The factor of frequency selectivity, however, raises an important issue with respect to the presentation level used in this study. Because auditory filter bandwidth is known to be level dependent (e.g., Glasberg and Moore, 2000), the relatively high presentation level of 85 dB SPL likely resulted in the NH listeners functioning with broader effective auditory filters than would have been the case at more moderate presentation levels. Integrally related to this, the 85-dB SPL presentation level possibly also resulted in the NH listeners operating within a less compressive range of the cochlear input/output function since there is some psychophysical evidence suggesting that normal auditory function transitions to a more linear mode at high input levels (e.g., Oxenham and Plack, 1997). In consequence, the compressive characteristics of the NH and HI listeners might not have been as dissimilar as would have been the case had the NH listeners been tested at a lower level. To assess this, supplemental data were collected at a presentation level of 65 dB SPL for three NH listeners, two of whom had participated in the main study. These data are shown as small, open symbols in Fig. 1(C). For SAM there appeared to be little effect of presentation level. The similarity of the SAM thresholds at the higher modulation rates suggests that any benefit of increased audibility of the resolved sidebands for the 85-dB SPL presentation level relative to the 65-dB SPL level was offset by the reduced frequency resolution at the higher level. For GAM, there was little effect of level at the two lowest modulation frequencies; however, modulation detection thresholds for the 65-dB SPL stimuli became progressively poorer than for their higher-level counterparts as the modulation rate increased. This suggests that, with the wider frequency dispersion of the modulation sidebands associated with the GAM stimuli, the benefit of increased audibility of the resolved sidebands at the 85-dB SPL presentation level was not completely offset by the reduced frequency resolution at that level.

Although the SAM data pattern and some aspects of the GAM data pattern for the full data set at 85 dB SPL conformed to expectations, other aspects of the GAM data pattern were not anticipated, particularly the poorer GAM thresholds at the lower modulation rates relative to the SAM thresholds. Although there is an indication in the results of Shen and Lentz (2010) of a decline in detection threshold as the average rate of a random modulator decreased for both NH and HI listeners, as shown by the hatched squares in Fig. 1(E) which are averages across both NH and HI listeners, their pattern is not as strikingly monotonic as in the present dataset. Comparison with their study is limited by the fact that they did not include sinusoidal modulation for reference. Normative tonal TMTFs measured by Ozimek et al. (1998) and Sek (1993) did not show a difference between sinusoidal and random modulation detection thresholds at lower modulation rates (i.e., ≤64 Hz). The reasons for this disparity at the lower modulation rates are not clear. One likely factor is the difference in the nature of the random modulator across studies. In the present experiment, the modulator was the envelope of a narrow band of noise. In the study of Sek (1993), and some conditions of the study of Ozimek et al. (1998), the envelope randomization was implemented by varying the period-to-period amplitude of a base sinusoidal modulator. The maintenance of constant zero crossings in the modulator imposes a uniform envelope rate. However, Ozimek et al. (1998) also varied both amplitude and frequency on a period-by-period basis in some conditions, and this did not have a pronounced effect at lower frequencies. The various studies also differed in terms of stimulus duration, which determines the number of modulation cycles in the stimulus. The duration of 400 ms employed here contrasts with the durations of 1000 ms and 1500 ms used by Ozimek et al. (1998) and Sek (1993), respectively. Further work is required to clarify the origin of these differences across studies.

5. Summary and conclusion

In summary, this study measured TMTFs for HI and NH listeners using both sinusoidal and random modulation carried by a pure tone. Similar performance was observed for the two listener groups at low modulation rates. At higher rates of modulation, there was a divergence between listener groups presumably because the greater frequency selectivity of the NH listeners allowed them to benefit from the detection of resolved sidebands, whereas these sidebands were less resolved for the HI listeners. In both groups of listeners, detection thresholds were poorer for random modulation than sinusoidal modulation at low modulation rates.