Oscillations, Waves, and Interactions - GWDG

Specific signal types in hearing research 47
Noise signals have been extensively used to study auditory masking where they
often serve as masker signals. For example, in the early experiments related to critical
bandwidth by Hawkins and Stevens [27], white Gaussian noise maskers were used
to measure the dependence of masked thresholds of a tonal signal as a function of
frequency. Probably the preference for using noise signals as a masker is related to its
uniform energy distribution across time and frequency and the fact that it is a well
defined signal. The inherently stochastic nature of noise, however, has implications
for its masking behavior as was demonstrated in studies that employed reproducible
noise for which the stochastic uncertainties in the noise are effectively removed. Generally,
reproducible noise produces lower masked thresholds than running noise [28].
3.1 Low-noise noise
3.1.1 Definition
In the previous section we discussed that a filtering operation on white Gaussian
noise causes the autocorrelation function to change from a delta function at lag zero,
to a pattern that reflects predictability of successive time samples of such noise. This
predictability is reflected in a smooth development of the envelope of the time domain
noise waveform 1 . The rate of fluctuation in the temporal envelope is proportional to
the bandwidth of the filtered noise signal. The spectrum of the envelope has a large
DC component and a downward tilting slope that leaves very little spectral power
beyond frequencies equal to the bandwidth of the bandpass noise. Interestingly, the
degree of fluctuation is independent of the bandwidth, which is reflected in the probability
density function of the temporal envelope values which is Rayleigh distributed.
Thus, there is an inherently high degree of fluctuation in Gaussian noise.
The inherent fluctuations that are present in Gaussian noise have prompted the
development of so-called low-noise noise [29]. This special type of noise has the same
spectral envelope as Gaussian noise, but a much lower degree of inherent fluctuations
in its temporal envelope, hence the name low-noise noise. This allowed the study of
the contribution of envelope fluctuations to auditory masking phenomena by comparing
the masking effect of Gaussian and low-noise noise. The first to pursue this
idea where Pumplin and Hartmann [30].
3.1.2 Stimulus generation
The original manner to generate low-noise, such as promoted by Ref. [29] was via a
special optimization algorithm. First a band-pass noise was digitally generated in
the frequency domain by setting amplitudes in a restricted spectral range to some
specific values, e. g., one constant value, and randomizing the phases. Such a noise
will approximate all the properties of a bandpass Gaussian noise when the product of
time and frequency is sufficiently large. Via a steepest descent algorithm, the phase
spectrum was modified step-by-step in the direction which made the temporal enve-
1 There are alternative manners to determine the envelope of a signal which lead to
somewhat different envelopes. We will consider here the Hilbert envelope.