The detection of variations in the amplitude of sounds (amplitude modulation, AM) is fundamental for robust auditory processing and is particularly important for speech perception. Indeed, comprehension of speech submitted to severe reduction of spectral cues is maintained as long as AM information is preserved (Remez, 1981; Shannon et al., 1995; Van Tasell et al., 1987) and, conversely, degradation of AM information impedes speech comprehension (Drullman, 1995; Dubbelboer and Houtgast, 2007; Houtgast and Steeneken, 1985).

The ability to perceive AM cues and the reliance on them in performing linguistic tasks have been observed since birth. Specifically, newborns’ brains have been shown to detect changes in speech sounds (plosive consonants) when the signal is degraded so as to preserve only the slowest AM cues (< 8 Hz) in each frequency band (Cabrera and Gervain, 2020). These results were shown using electroencephalography, with an oddball design measuring mismatch responses to a change from a frequent to an infrequent consonant stimulus in which the original speech stimuli were degraded to contain only < 8 Hz modulations in amplitude.

Coherently with newborn studies, efficient exploitation of AM cues has been observed in older infants completing behavioral consonant discrimination tasks (Bertoncini et al., 2011; Cabrera et al., 2013), even though some investigations have highlighted greater dependence on faster AM cues, for this kind of task, in 3-month-olds and 6-month-olds as compared with adults (Cabrera, Lorenzi and Bertoncini, 2015; Cabrera and Werner, 2017).

Using non-speech stimuli (amplitude-modulated noises or pure tones), Walker et al. (2019) revealed that 3-month-old infants exhibit sensitivity to AM as a function of modulation rate, similarly to adult listeners (i.e., with a low-pass shape when using broadband carriers). Such result strongly suggests that auditory temporal acuity, the limit of the auditory system's ability to follow AM fluctuations as they become faster, is mature early on. However, this study also indicated that infants show poorer AM sensitivity (i.e., higher AM detection thresholds) than adult listeners. Furthermore, investigations conducted with older children have confirmed that auditory sensitivity to AM continues to develop up to 11 years of age (Banai et al., 2011; Buss et al., 2019; Cabrera et al., 2019; Hall and Grose, 1994; Peter et al., 2014).

Two hypotheses have been put forward to explain this slow developmental trajectory of AM detection thresholds: (i) first, it might stem from the maturation of the sensory mechanisms underlying AM extraction: a bank of modulation filters which are centrally implemented and organized in neural sites selectively tuned to specific AM rates (Bacon and Grantham, 1989; Biberger and Ewert, 2016; Dau et al., 1997; Giraud et al., 2000; Houtgast, 1989; Liégeois-Chauvel et al., 2004); (ii) second, this late development might also depend on immaturity in ‘processing efficiency’: the ability to make efficient use of the sensory information that has been extracted by the modulation filters when this is available for further central processing. In support of this second hypothesis, computational models have shown that AM perception can be limited by factors such as short-term memory capacities, suboptimal decision making, and internal noise (e.g. Cabrera et al., 2019; 2022). Internal noise, here, is a general concept referring to all forms of neural variability altering both accuracy and consistency. Behaviorally, this is manifested by the fact that, in contrast with ideal observers, human listeners do not provide the same response when presented with the same stimulus multiple times (Green, 1964).

In contradiction with the first hypothesis, that late AM development is linked to late sensory development, previous investigations with both infants and children have shown early maturation of the sensory-processing mechanisms involved in AM processing. Such results have been found when measuring AM detection thresholds at rates from 4 to 128 Hz, using broadband or narrowband noise carriers (Cabrera et al., 2019; Hall and Grose 1994; Walker et al., 2019). To the best of our knowledge, only one study has reported temporal acuity to be worse in children than adults (Buss et al., 2019). In this study, greater differences in AM detection between adults and children (5-to-11-year-olds) were found when AM detection thresholds were measured at higher (e.g. 256 Hz) as opposed to lower rates (e.g. 16, 64 Hz). To further assess the sensory maturity of AM processing, AM maskers have also been employed. Such ‘maskers’ are competing patterns of AM that can be introduced either in the same frequency region as the carrier (‘on-frequency masking’) or in a different frequency region (‘off-frequency masking’). An ‘AM masking effect’ is observed when AM detection thresholds are degraded (i.e., elevated) by the introduction of the AM masker compared to a non-masked stimulus condition. Masking effects are thus meaningful, as they are supposed to reflect the selectivity of the human modulations filters tuned to specific AM rates (Bacon and Grantham, 1989; Dau et al., 1997; Houtgast, 1989). In line with this, previous studies have shown differences in AM masking effects between young children and adults. Specifically, Buss et al. (2019) have observed higher susceptibility to AM masking in 5-year-olds than in adults for off-frequency conditions but not for on-frequency conditions, interpreted as the sign of ongoing maturation of selective listening. Cabrera et al. (2019), in turn, found increasing susceptibility to AM masking between 5 and 7 years of age when comparing AM detection thresholds for deterministic vs non-deterministic carriers (pure tones vs narrowband noises respectively). These results were explained by higher (worse) AM detection thresholds for the younger participants in the deterministic (pure tones) condition, thus reducing AM masking effect in this age group: at 5-6 years of age, children behave as if the stimulus (the pure tone) contains more noise than it really does. In a subsequent modeling study, the authors found that worse AM detection thresholds in 5-to-6-year-olds were best simulated by implementing adult-like sensory processing (i.e., adult-like modulation frequency selectivity) but with increased levels of internal noise as compared to older children and adults. Acting at the output of the modulation filters, internal noise, here, represents a form of randomness in the auditory system which affects the efficient use of AM information at more central stages. Cabrera et al. (2022) obtained similar results in a modeling study on temporal integration for AM in childhood.

In sum, both experimental investigations and computational modeling of the development of AM detection support the idea that the extraction of AM information is mature from an early age, but that the ability to make an efficient use of this information is sub-optimal in young listeners. Two additional findings can be cited in support of such hypothesis. Firstly, reduced efficiency for AM processing has also been observed in developmental animal studies. For example, juvenile gerbils display higher variability in auditory cortical neuron activity when detecting AM compared with adults, and lower neural firing rates for AM sounds following training for AM detection (Caras and Sanes, 2019). Secondly, improvement of processing efficiency with age has also been shown in humans in other auditory domains. In this regard, Buss, Hall and Grose (2009) found shallower psychometric functions in school-aged children compared with adults for intensity discrimination, suggesting higher internal noise; Hill et al. (2004) showed that auditory backward masking thresholds are best simulated in 9-to-10-year-olds when using the same temporal window as adults (simulating similar temporal resolution), but higher internal signal-to-masker ratios at the decision stage (simulating poorer processing efficiency).

Despite the converging evidence outlined above, poor processing efficiency in young listeners must be further investigated. Fundamentally, the underlying explanations of this phenomenon remain to be discovered, and studying the cognitive impact of processing efficiency can help to enrich our understanding of the development of core auditory capacities (Sanes and Wooley, 2011). Critically, to date, modeling studies have supported the hypothesis of internal noise impacting the development of AM detection but there is a considerable lack of support of experimental nature, as previous experimental studies only measured detection thresholds.

To fill this gap, we present an experimental and modeling investigation of the hypothesis that reduced AM perception in children might be due to poorer processing efficiency and, specifically, to higher levels of internal noise. In order to address this issue, we first evaluated AM detection and AM masking in a large cohort of 86 children between 6 and 9 years of age as compared to 15 young adults. Specifically, AM detection thresholds were measured in two conditions using (i) a pure tone as carrier (that is, a deterministic carrier with no competing AM fluctuations) or (ii) a narrowband noise as carrier (a stochastic carrier presenting interfering intrinsic random AM fluctuations, cf. Fig. 1 in Varnet and Lorenzi, 2022). This allows for estimation of susceptibility to AM masking as the difference in AM detection thresholds between the two conditions. Then, we assessed processing efficiency for AM detection, a proxy of internal noise in the AM domain, using the ‘double-pass psychophysical paradigm’. Introduced by Green (1964) and recently applied by Attia et al. (2021) for AM and FM detection, this paradigm targets variability in perceptual decisions. Precisely, the double-pass consistency task consists in presenting the same set of stimuli two times (i.e., in two ‘passes’) to a same participant, who takes part in a signal detection task. The participant's responses are expected to vary to a certain extent from the first to the second presentation, and the amount of variation observed, i.e., intersession consistency (estimated as ‘Percentage of agreement’ in our experimental procedure, see the section ‘Procedure’ of Task 2) that is the proportion of consistent responses between the two passes on a trial to trial basis, is assumed to relate to the level of internal noise constraining the perceptual decision (Sanes and Wooley, 2011).

Note that we only used noise carriers in this task, as they allow to study the relation between external and internal noise on perceptual performance, as listeners tend to show more consistent responses across multiple passes when internal noise is lower than external noise and, conversely, less consistent responses across multiple passes when internal noise is higher than external noise (Attia et al., 2021; Green, 1964).

Based on previous evidence (Cabrera et al., 2019; 2022), we expected to observe in children as compared with adults overall poorer AM sensitivity, but comparable susceptibility to AM masking, and poorer response consistency in the double-pass task.

We then simulated the experimental data using a computational model of the human auditory system based on the modulation filterbank concept, in order to explore whether making vary the variance of internal noise implemented at the output of perceptual AM filters could explain the double-pass results both at the group level and at the individual level. In Cabrera et al. (2019), using a similar modeling procedure, the variance of internal noise was the only model parameter requiring modification to account for differences in AM detection and masking between young (mean age 5 years) and older listeners (6 to 11 years of age). Here, we expected analogous tendencies for the simulation of the double-pass results at the group level.