[sDIY](early) wavetable synthesis

[mbartkow at ET.PUT.Poznan.PL]

> Is there a way to predict the frequencies of partials which originate
> from aliasing in a non-interpolated wavetable?

When you sample any waveform, its spectrum is being replicated
at each multiple of the sampling frequency. For example, if you
sample a 1kHz sine using 8kHz sampling rate, the spectrum of the
sampled signal contains the original 1kHz partial (and a comple-
mentary -1kHz one) as well as all partials resulting from the
n*8kHz-1kHz, n*8kHz+1kHz formula, e.g. 7kHz, 9kHz, 15kHz, 17kHz 
and so on.
When you sample a complex signal, its whole spectrum is replicated 
in the same way as in the example. Aliasing occurs, when the sampling
rate is too low and the reflected spectrum overlaps with the high end
of the base band. Aliasing is unrecoverable and sounds like nasty
inharmonic distortion. I understand that in some cases a little bit
of aliasing is desired as it adds the digital grittiness to an
intentionally aggressive sound.

> If yes, what happens with these partials when the pitch of the
> wavetabele is changed (by different methods used)?

All partials scale appropriatelly. 
If you read out the samples from the wavetable faster than
originally sampled, the whole spectrum scales upwards, and
more partials fall outside of the "hearing range".
Conversely, after downscalling more and more original spectrum
replicas are hearable in the 20-20kHz band. Even if there is
no aliasing in the sampled wave, the scaled down "images" (that's
the proper name for the replicas) can be heard as inharmonic 
distortions. Therefore they are often confused with real aliasing.
Good samplers employ lowpass filters to eliminate the undesired
images. The filter cutoff frequency is scaled appropriatelly
to the sample readout rate. Interpolation is a form of digital
lowpass filtering.

regards,

m.b.