Oscillations, Waves, and Interactions - GWDG

44 A. Kohlrausch and S. van de Par
Figure 4. Simultaneous masked thresholds of a 260-ms, 1100-Hz signal as a function of
the fundamental frequency f0 of the harmonic complex masker. Thresholds are expressed
relative to the level of a single masker component. The maskers were presented at a level of
75 dB SPL. Squares: zero-phase complex; right-pointing triangles: negative Schroeder-phase
complex; left-pointing triangles: positive Schroeder-phase complex. Reused with permission
from Ref. [9]. Copyright 1995, Acoustical Society of America.
results obtained at 1100 Hz would allow a direct prediction for the phase characteristic
in the range of three octaves around 1100 Hz. The comparison with the results at
550 Hz indeed revealed the expected relation, while towards higher frequencies, the
curvature changed somewhat less with center frequency than expected for a system,
in which the amplitude and phase characteristics of the filters remain constant on a
logarithmic frequency scale.
One final important observation from these initial Schroeder-phase studies needs
to be mentioned. The view on the shape of the auditory filters was in the 1980’s
strongly influenced by the work of Patterson, Moore and colleagues, who had used
the notched-noise technique to estimate the amplitude characteristic of the auditory
filter. The best characterization was possible with a so-called rounded exponential
filter shape [17]. A time-domain implementation of a filter with such an amplitude
characteric was possible based on so-called gamma-tone filters [18,19]. Due to the
large amount of studies supporting this concept of auditory filters, we were interested
to analyze the Schroeder-phase stimuli with such a filter.
Figure 5 presents, in a similar format as Figs. 1 and 3, four periods of the waveform
for harmonic complexes with fundamental frequency 100 Hz. The analysis shows the
output of the gamma-tone filter tuned to 1100 Hz, and the three subpanels are for the
three different phase choices. It is apparant that this filter does not lead to differences
in the modulation depth between the three stimuli, and based on this simulation
one would expect quite similar masking behaviour of all three complex tones, in
contrast to the experimental data. The major reason for the similar treatment of the
two Schroeder-phase maskers by the gamma-tone filter is its antisymmetric phase