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An important requirement of digital additive synthesis is the accurate
and independent mapping of the control parameters, amplitude,
frequency, and phase into sinusoids as described earlier in
equation 1.1:
The amplitude represents the maximum displacement of the
varying quantity from its average value. The frequency
gives the mumber of peaks per second in a sine wave whereas the
reciprocal of , the period , is the time between
amplitude peaks. Finally, the phase , describes the
displacement in time from its origin [15]. The required
resolutions for frequency and phase can
be estimated from the just noticeable difference (JND) curve
derived for the human ear [16]. The curve shows that the
human ear is capable for noticing pitch differences of percent at
Hz which corresponds to a resolution of Hz. With a sampling
rate of 48kHz the resolution needs to be 16 bit for frequency
and phase . Amplitude resolution is dictated
largely by what is considered acceptible in audio terms, and the
resources that are available. With this in mind, 16 bits was chosen for
the amplitude parameter.
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Norbert Lindlbauer
2000-01-19