Monaural and interaural temporal modulation transfer functions measured with 5-kHz carriers
The pressure wave forms presented to the left and right ears (left column) and instantaneous interaural level difference (ILD, right column) of stimulus envelopes in signal and nonsignal intervals of an interaural modulation detection task. In the upper set of panels, the carrier is a pure tone while in the lower panels the carrier is a 30-Hz-wide interaurally uncorrelated band of noise. The depth of the sinusoidal amplitude modulation of each stimulus is the same in the upper and lower panels . The instantaneous ILD functions in the lower panels were computed from the Hilbert envelopes of the noise wave forms using Eq. (1).
One cycle of ILD (as in Fig. 1) computed using Eq. (1) for several SAM pure tones with various monaural modulation depths. The solid black line is ILD for a stimulus with , the largest threshold measured in this experiment. The dashed black line is a sinusoid with the same peak amplitude as the solid black line. The largest instantaneous difference between the solid and dashed black lines is 0.71 dB. The gray lines represent ILD for the values of indicated in the figure. It can be seen that ILD is nearly sinusoidal for the range of threshold measured in this experiment.
Monaural and interaural TMTFs showing threshold modulation depth (in dB) as a function of modulation frequency averaged across three listeners. In the left column, TMTFs for different carriers are represented in each panel: top panel, 5-kHz pure-tone carrier; middle panel, 30-Hz-wide band of noise; bottom panel, 300-Hz-wide band of noise. The two bands of noise were centered at 5 kHz. The different symbol types represent monaural and interaural TMTFs, as indicated in the legend. Error bars represent standard errors of the mean computed across three listeners and are in many cases smaller than the symbols. In the top panel, the monaural, no-masker TMTF is almost completely obscured by the monaural TMTF (with masker). The open diamonds in the top panel represent the monaural TMTF for a 5-kHz pure-tone carrier reported by Kohlrausch et al. (2000). The open circles in the middle and bottom panels represent monaural TMTFs for 31- and 314-Hz-wide bands of noise, both centered at 5 kHz, reported by Dau et al. (1997). In the right column, in separate panels, the monaural and interaural TMTFs are replotted from the left column. The same symbol type represents the same data in each column.
The monaural tonal TMTF and the interaural TMTFs measured with a pure tone and diotic noise carriers fitted with functions consisting of two straight lines. The data are replotted from Fig. 3. The data points have been grayed out to improve the clarity of the fitted functions. The fitted functions correspond to the parameters shown for Fit 1 in Table I and are plotted over only those data points that were included in the fitting procedure. The breakpoint of each fitted function (point of intersection of the two straight lines) is shown in parentheses after each entry in the figure legend.
The interaural TMTFs measured for the individual listeners for a diotic 300-Hz-wide band noise carrier. Error bars represent standard errors of the mean computed across four threshold estimates for each listener.
Top panel: Difference between monaural modulation-detection thresholds measured with a narrowband-noise carrier (diamonds, 30-Hz wide; triangles, 300-Hz wide) and those measured with a tonal carrier. Bottom panel: Difference between interaural modulation-detection thresholds measured with interaurally uncorrelated noise carriers and interaurally correlated noise carriers (diamonds, 30-Hz wide; triangles 300-Hz wide). All differences were computed on the mean data shown in Fig. 3.
Top panel: Monaural envelope power spectra averaged over 1000 random noise samples for 30-Hz-wide noise (solid line) and 300-Hz-wide noise (dashed line), where the total power was equal at the two bandwidths. Bottom panel: Spectra of instantaneous ILD functions averaged over 1000 samples of interaurally uncorrelated noise with bandwidths of 30 Hz (solid line) and 300 Hz (dashed line). Instantaneous ILD functions were computed from the Hilbert envelopes of the left- and right-ear wave forms using Eq. (1). In all cases, the stimuli were 1 s in duration and were windowed with 150-ms raised-cosine on-off ramps. Spectra were obtained by computing FFTs on digital waveforms sampled at 44.1 kHz.
For each set of data listed in the first column, the 3-dB-down cutoff frequency is shown for the best-fitting, low-pass Butterworth filter of first order (second column) and second order (third column). Fits were performed on all data of each TMTF up to the modulation frequency at which the slope changed from positive to negative. Parameters of the best-fitting functions consisting of two line segments are shown in the remaining columns. Fit 1 was performed on all data of each TMTF up to the modulation frequency at which the slope changed from positive to negative. Fit 2 was performed on one less data point than Fit 1 (the data point for the highest modulation frequency was excluded). The breakpoint for each fit is the frequency at the point of intersection of the two line segments, the 3-dB cutoff is the frequency at which the function is 3 dB down from its maximum, and the roll-off is the slope of the line above the breakpoint. The percentage in parentheses beneath each and breakpoint is the percentage of variance accounted for by each fitted function [computed as shown in Eq. (2)].
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