Second-order modulation detection thresholds for pure-tone and narrow-band noise carriers

Modulation perception has typically been characterized by measuring detection thresholds for sinusoidally amplitude-modulated (SAM) signals. This study uses multicomponent modulations. "Second-order" temporal modulation transfer functions (TMTFs) measure detection thresholds for a sinusoidal modulation of the modulation waveform of a SAM signal [Lorenzi et al., J. Acoust. Soc. Am. 110, 1030-2038 (2001)]. The SAM signal therefore acts as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM signal's modulation depth (at rate f'm) generates two additional components in the modulation spectrum at fm - f'm and fm + f'm. There is no spectral energy at the envelope beat frequency f'm in the modulation spectrum of the "physical" stimulus. In the present study, second-order TMTFs were measured for three listeners when fm was 16, 64, and 256 Hz. The carrier was either a 5-kHz pure tone or a narrow-band noise with center frequency and bandwidth of 5 kHz and 2 Hz, respectively. The narrow-band noise carrier was used to prevent listeners from detecting spectral energy at the beat frequency f'm in the "internal" stimuli's modulation spectrum. The results show that, for the 5-kHz pure-tone carrier, second-order TMTFs are nearly low pass in shape; the overall sensitivity and cutoff frequency measured on these second-order TMTFs increase when fm increases from 16 to 256 Hz. For the 2-Hz-wide narrow-band noise carrier, second-order TMTFs are nearly flat in shape for fm = 16 and 64 Hz, and they show a high-pass segment for fm = 256 Hz. These results suggest that detection of spectral energy at the envelope beat frequency contributes in part to the detection of second-order modulation. This is consistent with the idea that nonlinear mechanisms in the auditory pathway produce an audible distortion component at the envelope beat frequency in the internal modulation spectrum of the sounds.