Oscillations, Waves, and Interactions - GWDG

56 A. Kohlrausch and S. van de Par
Figure 12. Idealized
envelope spectra (dashed
curves) and averaged spectra
of Hilbert envelopes
(solid curves) of Gaussian
noise (upper panel), multiplied
noise (middle panel),
and low-noise noise (lower
panel). Each averaged
curve results from 1000 1-slong
realizations which were
randomly selected from a
10-s-long noise buffer and
then windowed with 50ms
Hanning ramps. Note
that the power density is
plotted on a logarithmic
scale. Reused with permission
from Ref. [41]. Copyright
1999, Acoustical Society
of America.
has a phase difference of 90 degrees relative to the masker, the noise zero crossings
appear when the sinusoidal waveform has its maxima (or minima). Therefore, in
the resulting signal the low envelope values disappear. The dashed line in Fig. 11
shows this strong effect on the envelope distribution of a multiplied noise by adding
a sinusoid with 90 degree phase difference.
Besides the distribution of the envelope values, also the envelope spectrum of
multiplied noise differs from that of Gaussian noise. Due to its symmetric power
spectrum, the envelope of ideal multiplied noise only has modulation frequencies
up to half its bandwidth, while for Gaussian noise, intrinsic modulation frequencies
range up to the whole bandwidth. Figure 12 shows envelope spectra, computed
from 1-s long realizations, for 50-Hz wide narrowband noises with three different
statistics: Gaussian noise (top panel), multiplied noise (middle panel) and low-noise
noise (bottom panel). These different envelope spectra have been of great use in
modelling amplitude modulation detection [41].
3.2.3 Role in hearing research and perceptual insights
Due to the many properties in which multiplied noise differs from Gaussian noise,
it allows to investigate a great number of different psychoacoustic concepts. In the
following, we want to give three examples: