Effects of noise precursors on the detection of amplitude and frequency modulation for tones in noise

Juraj Mesik; Magdalena Wojtczak

doi:10.1121/10.0002879

. 2020 Dec 10;148(6):3581–3597. doi: 10.1121/10.0002879

Effects of noise precursors on the detection of amplitude and frequency modulation for tones in noise

Juraj Mesik ^1,^a),^✉, Magdalena Wojtczak ^1,^b)

PMCID: PMC8097715 PMID: 33379905

Abstract

Recent studies on amplitude modulation (AM) detection for tones in noise reported that AM-detection thresholds improve when the AM stimulus is preceded by a noise precursor. The physiological mechanisms underlying this AM unmasking are unknown. One possibility is that adaptation to the level of the noise precursor facilitates AM encoding by causing a shift in neural rate-level functions to optimize level encoding around the precursor level. The aims of this study were to investigate whether such a dynamic-range adaptation is a plausible mechanism for the AM unmasking and whether frequency modulation (FM), thought to be encoded via AM, also exhibits the unmasking effect. Detection thresholds for AM and FM of tones in noise were measured with and without a fixed-level precursor. Listeners showing the unmasking effect were then tested with the precursor level roved over a wide range to modulate the effect of adaptation to the precursor level on the detection of the subsequent AM. It was found that FM detection benefits from a precursor and the magnitude of FM unmasking correlates with that of AM unmasking. Moreover, consistent with dynamic-range adaptation, the unmasking magnitude weakens as the level difference between the precursor and simultaneous masker of the tone increases.

I. INTRODUCTION

Extraction of spectrotemporal modulation patterns present within natural acoustic inputs is a key function of the auditory system as these signals carry the meaningful information necessary for communication, object identification, and other auditory tasks. Importantly, in complex natural environments, signals of interest are often embedded in a rich mixture of acoustic signals that hinder the extraction of target information via energetic masking in the auditory periphery, as well as modulation masking (e.g., Bacon and Grantham, 1989; Dau et al., 1997a,b; Wojtczak, 2011) and informational masking in more central neural loci (e.g., Kidd et al., 2003; Roverud et al., 2016; Rennies et al., 2019). The auditory system needs to flexibly adjust response properties throughout its processing hierarchy to both enhance the representation fidelity of the target signals and suppress the representation of the interfering noise sources. Elucidation of the mechanisms involved in these functions is key for both understanding how acoustic signals are converted into perception and how their representation is altered by the presence of hearing loss or by bypassing the cochlea in cochlear-implant users.

Recently, a few studies have reported that amplitude modulation (AM) detection for tonal and narrowband-noise carriers presented in a simultaneous noise masker can be improved by the presentation of a noise precursor (Almishaal et al., 2017; Jennings et al., 2018; Marrufo-Pérez et al., 2018a; Wojtczak et al., 2019). Consistent with the idea that an improved AM representation in the target leads to better speech understanding (Jørgensen and Dau, 2011; Jørgensen et al., 2013; Jørgensen et al., 2015), it has been shown that delaying words from the onset of a background noise presented ipsilaterally (Ben-David et al., 2012; Ben-David et al., 2016; Marrufo-Pérez et al., 2018b; Marrufo-Pérez et al., 2020) and contralaterally (Marrufo-Pérez et al., 2018b) results in better word recognition than when onsets of words and noise maskers coincide.

Although frequency glides are ubiquitous in most environmental acoustic stimuli, including speech, the effect of precursors on frequency modulation (FM) detection has received much less attention. FM detection is thought to be based on detecting AM at the output of cochlear filters through which the stimulus sweeps during an FM cycle. This FM coding strategy has been referred to as FM-to-AM conversion (Zwicker, 1970; Moore and Sek, 1992, 1994, 1995; Whiteford and Oxenham, 2015; Moore et al., 2019). For low carrier frequencies, the FM-to-AM conversion is thought to be the dominant neural code for detecting fast-rate (≳10 Hz) FM because of a presumed sluggishness of temporal fine-structure processing (Grantham and Wightman, 1978; Moore and Sek, 1995, 1996). For high carrier frequencies, FM is thought to be detected via FM-to-AM conversion for all FM rates because temporal fine-structure cues are unreliable above the upper frequency limit of neural phase locking (Joris and Verschooten, 2013; Verschooten et al., 2019). Byrne et al. (2013) measured FM-detection thresholds for a 4-kHz tonal carrier and found that delaying the onset of FM relative to the onset of the carrier improved performance for FM delays up to a few hundred milliseconds. Effects of a noise precursor on FM detection for tones in noise, i.e., in conditions comparable to those used in the studies of the effect of a precursor on AM detection, have not been measured. Since the detection of FM is thought to be based on FM-to-AM conversion, FM detection should benefit from mechanisms facilitating AM detection at least for relatively high (≳10 Hz) FM rates.

The mechanisms involved in the facilitation of AM detection (referred to hereafter as AM unmasking) due to wideband precursors remain unknown. Wojtczak et al. (2019) provided evidence that auditory grouping (Bregman, 1990) based on the similarity of acoustic features between the simultaneous masker and the precursor could not explain this phenomenon. In that study, the unmasking effect was comparable in size for a precursor that consisted of a different sample of the same band of Gaussian noise as that used for the masker and for a precursor that was distinct from the masker (a seven-tone complex with different perceptual quality from the noise masker).

A frequently invoked mechanism of AM unmasking due to precursors is the activation of medial olivocochlear (MOC) efferent feedback. MOC efferents, which synapse directly onto outer hair cells in the cochlea, turn down cochlear gain after a sufficient amount of time is allowed for the medial olivocochlear reflex (MOCR) to build up (Backus and Guinan, 2006; Guinan, 2006; Lopez-Poveda, 2018). One of the main effects of the MOCR is to improve the representation of transient sounds presented in noise by adjusting the cochlear gain and restoring the dynamic range of auditory-nerve fibers (Winslow and Sachs, 1988; Kawase et al., 1993). The MOCR is hypothesized to play an important role for enhancing speech representation in noise as speech is rich in transients and envelope fluctuations. Indeed, the build-up time for MOCR strength appears to correspond to the time course of improvement in word recognition with an increased delay of words from the noise onset (Ben-David et al., 2016). In general, however, experimental support for the MOCR-based hypothesis is weak. While some studies show that greater MOCR suppression of otoacoustic emissions (indicating more effective cochlear gain control by the MOC efferent feedback) is related to better speech recognition in noise (Kumar and Vanaja, 2004; Mishra and Lutman, 2014; Bidelman and Bhagat, 2015), others report the opposite relationship (de Boer et al., 2012). Marrufo-Pérez et al. (2018b) and Marrufo-Pérez et al. (2019) showed that cochlear-implant users exhibit improvements in both AM detection and word recognition in noise due to a noise precursor, although MOCR effects on cochlear responses are absent in electric hearing. For words in noise, the size of the precursor effect was similar to that observed for normal-hearing listeners presented with tone-vocoded stimuli (Marrufo-Pérez et al., 2018b). For AM detection, the improvement in cochlear-implant users (Marrufo-Pérez et al., 2019) was comparable to or somewhat smaller than that in normal-hearing listeners (Almishaal et al., 2017; Jennings et al., 2018; Wojtczak et al., 2019). For AM tones presented in noise, Wojtczak et al. (2019) found no significant MOCR effects on stimulus-frequency otoacoustic emissions (SFOAEs) for stimuli comparable to those for which robust behavioral AM unmasking was observed in that study. The lack of a relationship between the presence of unmasking and the presence of MOCR effects suggests that other mechanisms must play a role.

An alternative explanation often considered in the context of AM unmasking is that neural adaptation to stimulus-level statistics, typically referred to as dynamic-range adaptation, facilitates AM coding when the AM stimulus is preceded by a precursor. Dynamic-range adaptation is characterized by a shift of neural rate-level functions toward the most common level in a dynamically varying acoustic stimulus. The shift allows an adapted neural fiber to encode a change in stimulus intensity that would otherwise be undetected due to saturation of the fiber's firing rate (e.g., see Fig. 1 in Dean et al., 2005). Studies using animal models have shown direct evidence of dynamic-range adaptation from neural recordings at different sites throughout the auditory pathway from the auditory nerve (Wen et al., 2009, 2012) through the inferior colliculus (IC; Dean et al., 2005; Dean et al., 2008; Robinson et al., 2016; Rocchi and Ramachandran, 2018) and the auditory cortex (Watkins and Barbour, 2008). Two recent studies investigated dynamic-range adaptation of cortical responses in humans using magnetoencephalographic (MEG; Herrmann et al., 2018) and electroencephalographic (EEG; Herrmann et al., 2020) measures. The latter study also incorporated a behavioral measure of AM detection, but because of differences in stimulus design, their results cannot be directly related to the AM unmasking by a fixed-level precursor immediately preceding the target AM sound.

This study was conducted with two aims. One aim was to investigate if the unmasking by a noise precursor extends to relatively brief bursts of FM. Our hypothesis was that for a FM tone presented with simultaneous noise, a noise precursor should facilitate AM detection in auditory filters swept by the stimulus frequency during each FM cycle and, thus, should have an unmasking effect on FM coded via FM-to-AM conversion. The second aim was to investigate the role of dynamic-range adaptation in AM unmasking by implementing a level-rove paradigm to manipulate a mismatch between the level of the precursor and the level of the simultaneous noise masker of an AM tone. Our hypothesis was that due to dynamic-range adaptation, a precursor level most similar to the level of the simultaneous noise masker should result in a shift in neural rate-level functions that optimizes coding of the AM of tones embedded in the masker. In contrast, precursor levels that are most mismatched with the level of the masker should lead to suboptimal shifts of neural rate-level functions and, consequently, diminished ability of the fibers to optimally encode the AM. These mismatched shifts should yield poorer AM-detection performance. The level-rove paradigm was designed to use different precursor levels that were fixed throughout the precursor duration. The underlying assumption was that each fixed-level precursor represents an adapting stimulus with an infinitesimally narrow level distribution that induces dynamic-range adaptation within each trial. In this design, trials with a precursor level matching the level of the masker mimicked conditions with a precursor used in previous behavioral studies on AM unmaking (Marrufo-Pérez et al., 2018a; Marrufo-Pérez et al., 2019; Wojtczak et al., 2019).

II. EXPERIMENT 1: DETECTION OF AM AND FM OF A TONE IN NOISE WITH AND WITHOUT A PRECURSOR

A. Rationale

For tones modulated in frequency, auditory filters swept through by the stimulus frequency over the course of the modulation cycle convert the frequency sweep into AM at the filters' outputs. It has been shown that FM-to-AM conversion is likely used as a code for FM detection for modulation rates above ∼10 Hz (e.g., Moore and Sek, 1994, 1995, 1996; Moore et al., 2019). This experiment was designed to test the hypothesis that for conditions in which detection of AM and FM is based on a shared code, i.e., AM at the output of cochlear filters, detection of both types of modulation can be improved by a noise precursor, and these improvements should be correlated with each other across listeners.

B. Methods

1. Listeners

A total of 70 normal-hearing listeners (22 male, 48 female), aged between 18 and 64 years old [mean = 22.69 yr, standard deviation (SD) = 8.17 yr, median = 20 yr], participated in the study. AM-detection tasks were completed by 61 of the recruited participants while 30 participants completed FM-detection tasks. Among these listeners, a smaller number (21) were able to commit to participation over a longer time period and completed both the AM and FM tasks. Participants were recruited from the population of students and employees at the University of Minnesota and were screened for normal hearing by administering pure-tone audiometry at octave frequencies between 250 and 8000 Hz prior to the beginning of the experiment. Normal hearing was defined by air-conduction thresholds ≤20 dB hearing level (HL) at all the octave frequencies. In this, and the subsequent experiment, all participants provided written informed consent, and the experimental procedures were approved by the Institutional Review Board of the University of Minnesota. Listeners received monetary compensation for their participation.

2. Stimuli

Threshold modulation depths needed for the detection of 20-Hz AM and 20-Hz FM were measured for pure-tone carriers with frequencies of 1 and 4 kHz. Because of the possibility that the temporal fine structure could contribute to FM coding at low to medium but not at high carrier frequencies, the 1-kHz carrier was used because it falls within the range of frequencies for which auditory-nerve fibers exhibit phase-locked responses, and the 4-kHz carrier was used because it likely falls above the limit of phase locking in humans (Joris and Verschooten, 2013; Verschooten et al., 2019). Based on studies by Moore and Sek (1992, 1995, 1996), the 20-Hz FM should be detected via FM-to-AM conversion for both carrier frequencies despite robust phase-locked neural responses at 1 kHz. The tonal carriers had a duration of 100 ms, including 5-ms Hanning onset and offset ramps and were modulated throughout their duration, thus comprising two modulation cycles. The starting phases of the modulations (AM and FM) were chosen randomly from a range of 0 − 2 $π$ radians. The carriers were presented at 55 dB sound pressure level (SPL) and were temporally centered in a 110-ms simultaneous two-octave-wide threshold equalizing noise (TEN; Moore et al., 2000). For both tonal carriers, the TEN was centered on the respective carrier frequency. In the precursor condition, the TEN masker followed a 250-ms TEN precursor (different noise sample) after a 15-ms silent interval. The masker and the precursor durations included 5-ms Hanning onset/offset ramps. For the AM detection, the level of the TEN was set individually for each participant to produce a relatively poor but below ceiling (<100% AM depth) performance. This was done to optimize the AM unmasking effect due to a precursor as our pilot data indicated that the effect tends to decrease or disappear when the AM-detection threshold measured in noise approaches that for the AM of the tones presented in quiet, leaving little or no room for AM unmasking. For many listeners, the signal-to-noise ratio (SNR) was set to 25 dB and remained at this level. However, some listeners (32 of 61) needed a lower SNR if their AM thresholds in the no-precursor condition were low (approaching the thresholds in quiet), and no reliable AM unmasking was observed at the SNR of 25 dB. A few listeners required a slightly higher SNR as they could not detect the full (100%) AM for the SNR of 25 dB. For each listener, the same SNR was used for conditions with and without the noise precursor. For FM detection, carriers were presented 15 dB above the level of the TEN (SNR = 15 dB) because a ceiling performance was not a concern as all listeners could detect the FM for frequency deviations that were a fraction of the carrier frequency.

All stimuli were generated in matlab (The MathWorks, Natick, MA) on a personal computer (PC) and played using an E22 soundcard (LynxStudio, Costa Mesa, CA) with 24-bit resolution and a sampling rate of 48 kHz. The stimuli were delivered to both ears (diotically) through Sennheiser HD650 headphones (Sennheiser, Old Lyme, CT).

3. Procedure

The AM- and FM-detection thresholds were measured using a two-interval two-alternative forced-choice (2AFC) procedure with a three-down one-up adaptive tracking technique, estimating the 79.4% correct point on the psychometric function (Levitt, 1971). The procedure was implemented in the AFC toolbox for matlab (The MathWorks, Natick, MA; Ewert, 2013; Ewert and Dau, 2017). In each trial, participants heard two tones embedded in TEN, separated by a 500-ms silent interstimulus interval. One interval was randomly selected to contain an unmodulated tone while the other interval contained an identical tone except it was modulated in amplitude (AM detection) or frequency (FM detection). Listeners were asked to indicate which of the two intervals contained modulation by a key press on the computer keyboard or via a mouse click. The observation intervals were marked by flashing colored boxes, and visual feedback, indicating the correct response, was provided after each trial.

For AM detection, the modulation depth was tracked by using steps in decibel units, $20 log (m)$ , where m is the modulation index with a value between 0 and 1. The adaptive track used steps of 6 dB for the first two reversals, 4 dB for the subsequent two reversals, and 2 dB for the remaining eight reversals. Modulation depths at the final eight reversals were averaged to compute the threshold from a single run. When the adaptive procedure called for a modulation depth greater than 0 dB (100% AM), the modulation depth was set to 0 dB and the track continued. Adaptive tracks that exceeded 100 trials in length were terminated and no threshold was recorded. The final AM-detection threshold was obtained by averaging thresholds from three runs. If the SD of the mean from the three runs exceeded 3 dB, three more runs were performed, and the final threshold estimate was obtained by averaging all single-run thresholds that were less than ±3 median absolute deviations (MADs) from the median threshold (i.e., excluding outlier thresholds). Utilizing MADs for outlier detection is preferable to using the SD, as the MAD metric is more robust to outliers (Leys et al., 2013).

For FM detection, the procedure was similar to that of the AM-detection task except the adaptive tracking was applied to a deviation from the carrier frequency defined in dB units as $10 log (Δ f)$ , where $Δ f$ indicates a deviation in Hz from the carrier frequency. The adaptive tracking used an initial step size of 3 dB, which was reduced to 1.5 dB after the first two reversals, and 0.75 dB after another two reversals. The 0.75-dB step was used for the remaining eight reversals that were then averaged to estimate the FM-detection threshold from each run. Thresholds from three runs were averaged to obtain the final estimate, and no exclusion criterion was applied as the thresholds were generally less variable across runs than those for AM detection. Both AM- and FM-detection thresholds were measured with and without the noise precursor at the two carrier frequencies, 1 and 4 kHz. The four conditions (two carrier frequencies × precursor/no-precursor) were presented in a random order for a given modulation type. Listeners who performed the tasks for both AM and FM completed the AM portion of the experiment prior to starting the FM conditions. During the experiment, listeners were seated comfortably in a single-walled sound-attenuating booth.

C. Results and discussion

Individual shifts in AM-detection thresholds due to the noise precursor are shown in Fig. 1 for the 1-kHz carrier [Fig. 1(a)] and the 4-kHz carrier [Fig. 1(b)]. Shifts in the negative direction indicate improvement in AM detection due to the precursor (AM unmasking), whereas shifts in the positive direction indicate a worse performance with than without the precursor. Note that a greater negative shift (lower negative number) indicates a greater unmasking effect. The majority of listeners exhibited AM unmasking with an average improvement in AM detection of ∼4 dB for the 1-kHz carrier and ∼2 dB for the 4-kHz carrier. These shifts in threshold are comparable to those observed by Marrufo-Pérez et al. (2018a) and Jennings et al. (2018) but are generally smaller than those reported by Almishaal et al. (2017) and Wojtczak et al. (2019) especially for the 4-kHz carrier frequency. A two-way repeated-measures analysis of variance (ANOVA) with main factors of condition (precursor vs no-precursor) and carrier frequency showed a significant effect of precursor [F(1,60) = 121.3, p < 0.001], indicating that the precursor facilitated AM detection. The effect of the carrier frequency was also significant [F(1,60) = 4.4, p = 0.04], indicating higher overall thresholds for the 4-kHz carrier. Finally, there was a significant interaction between the effects of the noise precursor and carrier frequency [F(1,60) = 30.4, p < 0.001]. A post hoc t-test showed that the interaction reflected a significantly greater unmasking for the 1-kHz carrier than for the 4-kHz carrier [t(60) = 5.5, p < 0.001].

The effect of carrier frequency on AM unmasking was not observed by Wojtczak et al. (2019). Different parameters of the stimuli may have contributed to this discrepancy. Specifically, both studies used two modulation cycles, but the modulation rate was lower in this study (20 Hz vs 40 Hz), resulting in a longer stimulus duration (100 ms vs 50 ms). A frequency-dependent decay time of the physiological effect underlying the AM unmasking could lead to these different outcomes. Dean et al. (2008) showed that the buildup time of dynamic-range adaptation was inversely related to the characteristic frequency (CF) of neurons in the IC. It is feasible that the decay time is similarly related to the CF. The dependence on frequency might be more easily observed for the longer stimuli used here as more recovery would occur over the course of their duration. In addition, in all of the previous studies of AM unmasking (Almishaal et al., 2017; Marrufo-Pérez et al., 2018a; Jennings et al., 2018; Wojtczak et al., 2019), there was no silent gap between the noise precursor and the masker with the modulated/unmodulated carrier. The longer carrier duration and the 15-ms silent gap used in this experiment might have facilitated a greater recovery from the precursor effect. The gap was introduced to ensure that AM unmasking can be observed for the temporal parameters of the stimuli used in experiment 2 in which the role of dynamic-range adaptation was investigated. This issue will be discussed in Sec. III B 2.

Although most listeners exhibited AM unmasking, a few exhibited no precursor effect or an effect in the opposite direction (a worse performance with a precursor). This pattern is consistent with previous studies, which reported significant effects of noise precursors at the group level, but a lack of effects or effects in the opposite direction in a subset of listeners (see Jennings et al., 2018; Marrufo-Pérez et al., 2018a). One reason for the lack of the effects could be a suboptimal choice of the SNR. In the study by Wojtczak et al. (2019), the SNR was adjusted to produce poor performance in the no-precursor condition because good performance resulted in little or no effect of the precursor. Similarly, for words in noise, Marrufo-Pérez et al. (2018b) showed that good performance in the no-precursor condition was associated with a smaller precursor effect. In this study, up to three SNR adjustments were performed for listeners whose thresholds in the no-precursor condition were low (indicating good performance), and no AM unmasking due to a precursor was observed. However, when thresholds in the no-precursor condition were high (in the range of −6 to −1.5 dB) and no AM unmasking or worsening of AM detection was observed, no attempts to optimize the SNR were made.

Figure 2 shows the relationship between AM-detection thresholds in the no-precursor condition and shifts in threshold due to the noise precursor. Note that to improve sensitivity to a possible linear relationship between the two measures, we identified outlier data points (ones differing from the median of each measure in either direction by more than three MADs) using matlab's “isoutlier” function and excluded them from analysis. This led to the exclusion of two data points from both the 1-kHz and 4-kHz data. In this and subsequent correlation plots, outlier points are shown as light red circles.

FIG. 2. — (Color online) The relationship between AM-detection thresholds without a noise precursor and threshold shifts due to a precursor for 1-kHz (a) and 4-kHz (b) carriers. The dashed lines denote the best fitting linear function relating the two measures. Faint red circles indicate outlier data points.

For the 1-kHz carrier, there was a significant negative correlation between the size of AM unmasking and the baseline (no-precursor) performance (r = −0.28, p = 0.029). However, despite a comparable range of thresholds in the baseline condition for the 4-kHz carrier, the effect of the precursor was independent of the baseline performance (r = −0.09, p = 0.49).

Overall, for the relatively long (100-ms) bursts of AM with the 20-Hz rate, the unmasking effect was observed both at 1 and 4 kHz, but the effect appeared less robust at the higher carrier frequency.

Individual shifts in FM-detection thresholds for the 1- and 4-kHz carriers due to a noise precursor are shown in Figs. 3(a) and 3(b), respectively. For FM, it was hard to gauge what constitutes poor performance when choosing the SNR because the worst performance in an FM-detection task is limited by $Δ f$ that is equal to the carrier frequency. Pilot data from three listeners for tones presented in quiet showed average FM-detection thresholds [in units of $10 log (Δ f)$ ] of 6.9 (SD = 1.2) dB for the 1-kHz carrier and 14.2 (SD = 1.1) dB for the 4-kHz carrier. These thresholds translate to geometric-mean frequency deviations of $Δ f$ = 4.9 Hz, and $Δ f$ = 26.1 Hz for the 1- and 4-kHz carriers, respectively. It was decided that the SNR producing FM-detection thresholds that are substantially increased by the simultaneous noise masker would provide room for FM unmasking. For the tones presented in a noise masker without a precursor, FM-detection thresholds averaged across listeners were 14.4 (SD = 1.7) dB for the 1-kHz carrier, and 19.5 (SD = 1.8) dB for the 4-kHz carrier. When converted to frequency deviations from the carrier, the geometric-mean thresholds were 27.6 Hz and 89.2 Hz for the 1- and 4-kHz carriers, respectively. In both cases, the thresholds in noise were also higher than those observed in quiet for comparable carrier and modulation frequencies in previous studies. Moore and Sek (1992) showed FM-detection thresholds around $Δ f$ of ∼5 Hz for a 1-kHz carrier, and Byrne et al. (2013) showed the thresholds to be around 20 Hz for a 4-kHz carrier, in agreement with our limited pilot data. Higher FM-detection thresholds result in a greater $Δ f / f_{mod}$ and, consequently, in a long-term spectrum of the FM tone with multiple relatively intense sidebands. The sidebands occur at frequencies of $f_{c} \pm n * f_{mod}$ , where n is a positive integer number, and $f_{c}$ and $f_{mod}$ denote the carrier frequency and the modulation rate, respectively. To investigate the possibility that listeners detected FM in the tones in noise by detecting the sidebands in the long-term spectrum, we calculated the spectra for the FM tones corresponding to the average thresholds and the equivalent rectangular bandwidths (ERBs; Glasberg and Moore, 1990) of auditory filters at the two carrier frequencies. The ERBs were 133 and 456 Hz, for the 1- and 4-kHz tones, respectively. The first sidebands in the spectra of the FM tones that fell outside of the ERB were −36 dB and −84 dB, relative to the level of the 1- and 4-kHz carriers, respectively. Sidebands that were further away from the carriers decayed rapidly in level. Because the FM tones were presented at 15 dB SNR, the sidebands outside the auditory filters tuned to the carrier frequencies that fell within the band of the two-octave noise masker were completely masked by the noise. The more remote sidebands, which fell outside of the noise bandwidth, had levels below hearing thresholds. Thus, it is unlikely that the FM was detected using differences between the long-term spectra of the modulated and unmodulated carriers. Most listeners showed FM unmasking due to a precursor for both carrier frequencies. The mean shifts in threshold in the log-transformed tracking units were −1.19 (SD = 1.31) dB and −2.04 (SD = 1.51) dB for the 1- and 4-kHz carriers, respectively. A two-way repeated-measures ANOVA performed on the log-transformed shifts in frequency deviation at threshold with the main factors of condition (precursor vs no-precursor) and carrier frequency showed a significant effect of the precursor [F(1,29) = 58.9, p < 0.001]. There was also a significant effect of the carrier frequency [F(1,29) = 230.0, p < 0.001], indicating a significantly larger $Δ f$ value at FM-detection thresholds for the 4-kHz than for the 1-kHz carrier. Finally, there was a significant interaction between the carrier frequency and noise precursor [F(1,29) = 8.1, p = 0.008]. A post hoc t-test revealed that the magnitude of unmasking was greater for the 4–kHz carrier than for the 1-kHz carrier [t(29) = −2.8, p = 0.008].

FIG. 3. — (Color online) Individual shifts in FM-detection threshold for a 1-kHz (a) and a 4-kHz (b) carrier presented in noise due to a noise precursor. The horizontal dashed lines and the shaded areas between dotted lines represent the mean and ±1 SE of the mean, respectively.

Unmasking, expressed as a change in $Δ f$ in Hz between the no-precursor and precursor conditions, was statistically greater for the 4-kHz than for the 1-kHz carrier. However, this increase reflects increased absolute bandwidths of auditory filters with an increasing center frequency (Glasberg and Moore, 1990). Although the relative bandwidth decreases somewhat with an increasing center frequency (Shera et al., 2002; Oxenham and Shera, 2003), the tuning of cochlear filters estimated based on psychophysical simultaneous-masking data is characterized by constant relative bandwidths (i.e., constant $Q_{ERB} = ERB / CF$ ) for CFs above ∼1 kHz (Glasberg and Moore, 1990). Because of that, we compared the magnitudes of FM unmasking expressed as a fraction of the corresponding carrier frequencies. For this relative unmasking, we no longer found a reliable difference in FM unmasking between the two carrier frequencies [t(29) = −1.7, p = 0.11].

To investigate whether the size of FM unmasking depends on the threshold in the no-precursor condition, we plotted the relationships between FM-detection thresholds without the precursor and the unmasking magnitude, which is shown in Fig. 4. The MAD metric identified no outliers and, therefore, all data were included in the correlations for both carrier frequencies. Unlike for AM unmasking, no significant correlation with performance in the no-precursor condition was found for the 1-kHz carrier (r = −0.06, p = 0.74), but there was a significant correlation between the two variables for the 4-kHz carrier (r = −0.45, p = 0.014).

FIG. 4. — (Color online) The relationship between FM-detection thresholds without a noise precursor and threshold shifts with a precursor for the 1-kHz (a) and 4-kHz (b) carriers. The dashed lines denote the best fitting linear function relating the two measures.

Across the two types of modulation, we found that a noise precursor provides behavioral benefits in detection of both 20-Hz AM and FM for both the 1- and 4-kHz carriers. For AM, the results are in line with prior studies that demonstrated AM unmasking for higher modulation rates of 40 and 50 Hz (Jennings et al., 2018; Marrufo-Pérez et al., 2018a; Wojtczak et al., 2019) and replicate the effect for a 20-Hz modulation rate (Almishaal et al., 2017). Our results also extend these previous observations of AM unmasking to FM, likely due to FM being detected via AM at the output of the cochlear filters swept by the fluctuating frequency.

A direct comparison between the magnitudes of AM and FM unmasking would require an estimation of cochlear filter bandwidths for each listener and making some assumptions about how the fluctuations in the filter outputs combine over the FM cycle (Henry et al., 2017). Since auditory filters were not measured in this study, using an auditory model to make such predictions for individual listeners would not be informative without using reasonable constraints. It has been suggested that when detecting FM, listeners may weigh changes on the low-frequency side of the excitation pattern more heavily because they are larger due to a steeper slope on that side (Zwicker, 1956; Moore and Sek, 1992). The fact that the AM unmasking effect was larger at 1 kHz than at 4 kHz while the opposite was true for FM does not indicate that the results are inconsistent across the two modulation types. Cochlear filters increase in absolute bandwidth (in Hz) between 1 and 4 kHz while their relative bandwidths (related to the center frequency) decrease with increasing frequency (Shera et al., 2002; Oxenham and Shera, 2003). The dependence of cochlear filter bandwidths on frequency could produce the apparently inconsistent findings. However, if FM and AM unmasking are mediated by the same mechanism, the shifts in thresholds for both types of modulation would be expected to be positively correlated at both carrier frequencies. Figure 5 shows the relationship between AM and FM unmasking for the subset of listeners (n = 21) who provided data for both types of modulation. As in the other correlation analyses, we identified outlier data points and excluded them from analysis to prevent outliers from driving correlations or lack thereof. This led to the exclusion of no data points for the 1-kHz carrier and two data points for the 4-kHz carrier.

FIG. 5. — (Color online) The relationship between AM and FM unmasking magnitudes for the 1-kHz (a) and 4-kHz (b) carriers. The dashed lines denote the best fitting linear function relating the two measures. Faint red circles indicate outlier data points. Note that different tracking variables were used in the two experiments and, thus, the unmasking dB values cannot be directly compared.

The correlations between AM and FM unmasking magnitudes were significant for both carrier frequencies (1 kHz, r = 0.41, p = 0.033, right-tailed; 4 kHz, r = 0.58, p = 0.004, right-tailed). This is consistent with the notion that the same mechanism underlies AM and FM unmasking. The fact that the correspondence in AM and FM unmaking was found at both carrier frequencies supports the notion that for the 20-Hz modulation rate, FM was detected via FM-to-AM conversion despite robust phase locking of auditory-nerve responses at 1 kHz (Joris and Verschooten, 2013). This result is consistent with conclusions from the studies by Moore and Sek (1995, 1996) and Moore et al. (2019) that detection of FM for higher modulation rates (≳10 Hz) does not utilize fine-structure cues even when the carrier frequency is below the limit of phase locking.

In summary, our results replicate previous findings of AM unmasking and demonstrate that a similar phenomenon also affects FM detection at least at modulation rates for which FM is encoded via FM-to-AM conversion. Indeed, in our data, the two effects were correlated in their amplitude, which is consistent with a shared underlying mechanism.