Second-order temporal modulation transfer functions.

Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181-1196 (2000)].