This paper presents a quantitative model for describing data from modulation-detection and modulation-masking experiments, which extends the model of the “effective” signal processing of the auditory system described in Dau et al. [J. Acoust. Soc. Am. 99, 3615–3622 (1996)]. The new element in the present model is a modulation filterbank, which exhibits two domains with different scaling. In the range 0–10 Hz, the modulation filters have a constant bandwidth of 5 Hz. Between 10 Hz and 1000 Hz a logarithmic scaling with a constant $Q$ value of 2 was assumed. To preclude spectral effects in temporal processing, measurements and corresponding simulations were performed with stochastic narrow-band noise carriers at a high center frequency (5 kHz). For conditions in which the modulation rate ${\mathrm{(f}}_{\mathrm{mod}})$ was smaller than half the bandwidth of the carrier $\mathrm{(\Delta f),}$ the model accounts for the low-pass characteristic in the threshold functions [e.g., Viemeister, J. Acoust. Soc. Am. 66, 1364–1380 (1979)]. In conditions with $f_{\mathrm{mod}}\text{>Δf/2,}$ the model can account for the high-pass characteristic in the threshold function. In a further experiment, a classical masking paradigm for investigating frequency selectivity was adopted and translated to the modulation-frequency domain. Masked thresholds for sinusoidal test modulation in the presence of a competing modulation masker were measured and simulated as a function of the test modulation rate. In all cases, the model describes the experimental data to within a few dB. It is proposed that the typical low-pass characteristic of the temporal modulation transfer function observed with wide-band noise carriers is not due to “sluggishness” in the auditory system, but can instead be understood in terms of the interaction between modulation filters and the inherent fluctuations in the carrier.

This paper describes a quantitative model for signal processing in the auditory system. The model combines a series of preprocessing stages with an optimal detector as the decision device. The present paper gives a description of the various preprocessing stages and of the implementation of the optimal detector. The output of the preprocessing stages is a time-varying activity pattern to which ‘‘internal noise’’ is added. In the decision process, a stored temporal representation of the signal to be detected (template) is compared with the actual activity pattern. The comparison amounts to calculating the correlation between the two temporal patterns and is comparable to a ‘‘matched filtering’’ process. The detector itself derives the template at the beginning of each simulated threshold measurement from a suprathreshold value of the stimulus. The model allows one to estimate thresholds with the same signals and psychophysical procedures as those used in actual experiments. In the accompanying paper [Dau et al., J. Acoust. Soc. Am. 99, •••–••• (1996)] data obtained for human observers are compared with the optimal-detector model for various masking conditions.

This study examines auditory brainstem responses (ABR) elicited by rising frequency chirps. The time course of frequency change for the chirp theoretically produces simultaneous displacement maxima by compensating for travel-time differences along the cochlear partition. This broadband chirp was derived on the basis of a linear cochlea model [de Boer, “Auditory physics. Physical principles in hearing theory I,” Phys. Rep. 62, 87–174 (1980)]. Responses elicited by the broadband chirp show a larger wave-V amplitude than do click-evoked responses for most stimulation levels tested. This result is in contrast to the general hypothesis that the ABR is an electrophysiological event most effectively evoked by the onset or offset of an acoustic stimulus, and unaffected by further stimulation. The use of this rising frequency chirp enables the inclusion of activity from lower frequency regions, whereas with a click, synchrony is decreased in accordance with decreasing traveling velocity in the apical region. The use of a temporally reversed (falling) chirp leads to a further decrease in synchrony as reflected in ABR responses that are smaller than those from a click. These results are compatible with earlier experimental results from recordings of compound action potentials (CAP) [Shore and Nuttall, “High synchrony compound action potentials evoked by rising frequency-swept tonebursts,” J. Acoust. Soc. Am. 78, 1286–1295 (1985)] reflecting activity at the level of the auditory nerve. Since the ABR components considered here presumably reflect neural response from the brainstem, the effect of an optimized synchronization at the peripheral level can also be observed at the brainstem level. The rising chirp may therefore be of clinical use in assessing the integrity of the entire peripheral organ and not just its basal end.

A multi-channel model, describing the effects of spectral and temporal integration in amplitude-modulation detection for a stochastic noise carrier, is proposed and validated. The model is based on the modulation filterbank concept which was established in the accompanying paper [Dau et al., J. Acoust. Soc. Am. 102, 2892–2905 (1997)] for modulation perception in narrow-band conditions (single-channel model). To integrate information across frequency, the detection process of the model linearly combines the channel outputs. To integrate information across time, a kind of “multiple-look” strategy, is realized within the detection stage of the model. Both data from the literature and new data are used to validate the model. The model predictions agree with the results of Eddins [J. Acoust. Soc. Am. 93, 470–479 (1993)] that the “time constants” associated with the temporal modulation transfer functions (TMTF) derived for narrow-band stimuli do not vary with carrier frequency region and that they decrease monotonically with increasing stimulus bandwidth. The model is able to predict masking patterns in the modulation-frequency domain, as observed experimentally by Houtgast [J. Acoust. Soc. Am. 85, 1676–1680 (1989)]. The model also accounts for the finding by Sheft and Yost [J. Acoust. Soc. Am. 88, 796–805 (1990)] that the long “effective” integration time constants derived from the data are two orders of magnitude larger than the time constants derived from the cutoff frequency of the TMTF. Finally, the temporal-summation properties of the model allow the prediction of data in a specific temporal paradigm used earlier by Viemeister and Wakefield [J. Acoust. Soc. Am. 90, 858–865 (1991)]. The combination of the modulation filterbank concept and the optimal decision algorithm proposed here appears to present a powerful strategy for describing modulation-detection phenomena in narrow-band and broadband conditions.

Three experimental paradigms were used to specify the auditory system’s frequency selectivity for amplitude modulation (AM). In the first experiment, masked-threshold patterns were obtained for signal-modulation frequencies of 4, 16, 64, and 256 Hz in the presence of a half-octave-wide modulation masker, both applied to the same noise carrier with a bandwidth ranging from 1 to 4 kHz. In the second experiment, psychophysical tuning curves (PTCs) were obtained for signal-modulation frequencies of 16 and 64 Hz imposed on a noise carrier as in the first experiment. In the third experiment, masked thresholds for signal-modulation frequencies of 8, 16, 32, and 64 Hz were obtained according to the “classical” band-widening paradigm, where the bandwidth of the modulation masker ranged from $\frac{1}{8}$ to 4 octaves, geometrically centered on the signal frequency. The first two experiments allowed a direct derivation of the shape of the modulation filters while the latter paradigm only provided an indirect estimate of the filter bandwidth. Thresholds from the experiments were predicted on the basis of an envelope power-spectrum model (EPSM) which integrates the envelope power of the modulation masker in the passband of a modulation filter tuned to the signal-modulation frequency. The Q-value of second-order bandpass modulation filters was fitted to the masking patterns from the first experiment using a least-squares algorithm. Q-values of about 1 for frequencies up to 64 Hz suggest an even weaker selectivity for modulation than assumed in earlier studies. The same model also accounted reasonably well for the shape of the temporal modulation transfer function (TMTF) obtained for carrier bandwidths in the range from 1 to 6000 Hz. Peripheral filtering and effects of peripheral compression were also investigated using a multi-channel version of the model. Waveform compression did not influence the simulated results. Peripheral bandpass filtering only influenced thresholds for high modulation frequencies when signal information was strongly attenuated by the transfer function of the peripheral filters.