Examples of STDFs estimated from speech for frequencies of 250, 1000, 3000, and 6000 Hz. Red denotes high dependency, yellow medium, and dark blue low dependency between the given frequencies at the given lag.
SDFs computed from speech using Eq. (8) . Each peaked curve represents the overall statistical dependency SDF(f 1, f 2) between frequency pairs f 1 and f 2 for a fixed f 1, with the maximum dependency occurring at f 1 = f 2. For a given center frequency f c, the function SDF(fc , f2 ) can be interpreted as a bandpass filter with the maximum gain at f c. Only the SDFs corresponding to every fifth f 1 are shown for visual clarity. Note that the dependencies when f 1 = f 2 are not fixed (deterministic) since the SDF is not a measure of the instantaneous correlation between frequencies but is computed across all temporal delays k where cross-channel dependencies do exist [see Eq. (5) ].
Interpolated SDFs for center frequencies 750, 2833, and 6167 Hz. The upper horizontal lines denote the threshold δERB = −0.12 that provides the best fit to ERBs and lower vertical dashed lines denote the optimal δBark = −0.17 that provides the best fit to Bark bandwidths.
Bandwidths of SDFs as a function of center frequency with the attenuation parameter δ separately fitted to ERB and Bark data. Bandwidths of ERB (straight solid line) and Bark critical bands (dashed curved line) are shown as a reference.
Relative error (in hertz) between SDF bandwidths and the bandwidths of the ERB (solid line) and Bark critical bands (dashed-dotted line).
Examples of TDFs measured for frequencies of 250, 1000, 2000, and 6000 Hz up to a maximum delay of 600 ms. The TDF is shown without the logarithm in Eq. (6) on the left in order to visualize the decay of structure to zero at long delays and with the logarithm on the right.
Left: RMSE between the 3166-Hz integrated TDF and the power law function with different exponentials m. Right: Integrated TDF as a function of integral length and the corresponding threshold according to the power law with best fitting m = 0.77 (see Heil and Neubauer, 2003 ).
Left: Weighting functions of the 1-kHz TDF (solid line), weights of Eq. (12) from Viemeister and Wakefield (1991) fitted to the data of Plomp and Bouman (1959 ; dashed line), and the weights of Eq. (12) with parameters fitted to the detection thresholds of TDF in Eq. (10) (dashed-dotted line). Right: Detection thresholds for the TDF (solid line), weights of Viemeister and Wakefield (1991 ; dashed line), and weights with parameters fitted to the TDF (dashed-dotted line) as a function of stimulus duration.
Time-constants τ of the TDFs as a function of frequency and length d of the TDF interval included in the analysis. Unexplained variances (1 − r 2) of the exponential fits to the TDF data are also shown.
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