[sdiy] PPG/Prophet VS question

[ASSI]

On Freitag, 24. April 2009, Tom Wiltshire wrote:
> I've got a question; something that I've only just realised I don't
> understand.

Good question.

> I know (or think I do - I've read) that the digital oscillators on
> the PPG (and the similar oscillators on the Prophet VS) produce
> aliasing as the frequency becomes higher. The manual for the DSI
> Evolver notes the same thing about the digital oscillators in that
> instrument, which is what you'd expect, since they were based on
> the Prophet VS.
>
> The question is this: Why should they produce aliasing?

They always produce aliasing because they produce a discrete-time 
signal which has by definition an infinite number of aliases.  The 
question is whether you can hear the aliasing products in the 
reconstructed signal band.

> It was my understanding that all of these instruments use a
> variable sample rate, and just play back the same small wavetable
> of samples at higher speed to raise the pitch. If this is true, the
> relationship between the sample rate and the output frequency would
> remain constant. To put it another way, one wave cycle always takes
> 128 samples (or 256 or whatever it is) so why does a higher
> frequency cause problems?

The NCO in question does not quite work like that, it is phase 
accumulator based and uses truncation to produce the sample address.  
The DAC output is produced at a different frequency (I'm pretty 
certain it is fixed), so you have in effect another re-sampling 
operation from NCO to DAC that produces additional aliases since the 
wavetables themselves do in the most general case not produce a 
properly bandlimited signal either; be it due to insufficient 
filtering of the source material, source noise that survives the 
filtering and the quantization noise.  Quantization noise can be 
modeled with good success as a sawtooth wave at a fraction of the DAC 
nyquist frequency at -6*ENOB (effective number of bits) for the 
oscillators in question as long as the phase accumulator does not skip 
codes.  However it will just do that if the frequency of playback 
becomes higher, which happens at around the middle octave IIRC.  Then 
the signal from the wavetable becomes undersampled at the DAC and the 
assumption you made is no longer valid.


Achim.
-- 
+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk]>+

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