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Effect of Changing the Average Duration
In this section we will examine random pitch signals. The values have been
chosen from a logarithmic scale of frequencies with various quantization
levels. Later we will use the same method for analyzing some pieces
according to their MIDI encryptions. The pitch signals are stored as
sound files. The frequency of the middle C, or the
MIDI note number 60, is used as a reference point. We can have up to 273
quantization levels per semitone. The value of the pitches are restricted
to 20 to 2100 Hz.
Unless noted, in all the signals
the pitches are quantized to frequency values of the welltempered scale.
Once the random signal is generated the average value of the signal in
time is subtracted from all the samples.
Figure 43 shows the power spectrum and the first 30
seconds of a random signal with average note duration of 0.1 second.
We can see that the power spectrum for this random signal is flat, which
means that there are as many fast oscillations (structures) as there
are slow oscillations.
The power spectrum is shown on a loglog scale and for having a
reference, the line which represents the spectrum is plotted on
top of all the plots in this section.
Figure 44 shows the power
spectrum and the first 10 seconds of random signals with average note
durations of 0.5, 2, and 200 seconds (for all the signals 1000 seconds of
the random signal was generated.) Notice how these signals start to
show a ``slope'' on the high frequency spectrum. This slope indicates
some temporal correlation in that region. Obviously a
constant value is more correlated than a random signal; therefore with
a higher value of average note duration, the signal becomes more correlated.
In fact we can characterize these functions as a
spectrum, while in the case of the flat spectrum
for all the regions and for the other cases
in the region of correlation and in other regions.
Figure 43:
The time domain and power spectrum of white noise with average
duration of 0.1 seconds. (a) illustrates the first 30 seconds of the signal
and (b) is the power spectrum of such a signal in loglog scale.
The line representing the is also drawn for reference. Notice that
the power spectrum for this signal is flat for the area of our inspection
which is between 0.001 and 5 Hz.

Figure 44:
The time domain and (loglog scale) power spectrum of random signals
with average duration of 0.5, 2, and 200 are illustrated.
The line representing the line is also drawn for reference.
Notice that the power spectrums show a slope steeper than the line
in the area of correlation while the rest of the spectrum stays flat.

Next: Longterm correlation
Up: What Is Noise
Previous: Power Spectrum
Contents
Shahrokh Yadegari
20010301