Oscillations, Waves, and Interactions - GWDG

Specific signal types in hearing research 55
frequency with a sinusoid of higher frequency. This operation is an example of
modulation with suppressed carrier. The resulting signal is a bandpass noise with
a center frequency equal to the frequency of the sinusoid. The bandwidth is given
by twice the cut-off frequency of the lowpass noise. By tuning the frequency of the
sinusoid, the center frequency of the multiplied noise is easily tunable, and such an
operation does not require the use of digital computers.
3.2.2 Acoustic properties and perceptual insights
Multiplied noise has regular zero crossings with a rate equal to its center frequency.
Its spectrum is symmetric around its center or carrier frequency: Above the carrier
frequency, the spectrum is identical to the spectrum of the original lowpass noise,
while the spectrum below the carrier is a mirrored version of this spectrum. Furthermore,
the envelope distribution of multiplied noise is also different from that of
Gaussian noise. While the envelope of Gaussian noise has a Rayleigh distribution,
the distribution of the envelope of multiplied noise correponds to the positive half of
a Gaussian distribution. This latter fact follows from the process of generation: the
envelope of multiplied noise corresponds to the absolute value of the original lowpass
noise time function. As a consequence, the envelope distribution of multiplied noise
has its highest value at zero. In contrast, for Gaussian noise, the probability of zero
envelope values is zero.
Due to the regular zero crossings, it is possible to add a sinusoid to multiplied noise
with a fixed finestructure phase relation to the masker, if the sinusoidal frequency
corresponds to the noise carrier frequency. If the sinusoid is added in phase, the
resulting signal has still the same zero crossings as the noise alone, and overall, the
envelope distribution is not much affected (see Fig. 11). When the sinusoidal signal
Figure 11. The envelope probability distribution is shown for a multiplied noise masker
alone (solid line) and for a multiplied noise masker plus signal added in phase (long-dashed
line), and with a fine-structure phase difference of π/2 (short-dashed line). The signal-tomasker
ratio is 25 dB. Reused with permission from Ref. [40]. Copyright 1998, Acoustical
Society of America.