digital synthesis

[Bjorn Wesen]

>   If you trivially generate waveforms with discontinuities digitally, like
>   sawtooth or triangle waves, you end up with aliasing, that is correct.
You
>   need to make sure the signal is appropriately band limited. You can
>   manufacture alias-free basic "analog" waveforms like triangle, square
and
>   sawtooth by integration of bandlimited impulse trains (the result remain
>   bandlimited).
>
>The manufactured alias-free waveforms, like a sawtooth, would need
>several versions, say, one for each octave you wanted to play.


Why? They are realtime calculated.

>But how about a PWM output (a very common VCO feature)?  There the
>high frequency content changes depending on the symmetry *and* the
>frequency.  How would you handle something like that?

PWM (rectangular wave with duty cycle control) is one of the things possible
using the integration method I mentioned above.

>And audio FM modulation creates wild frequencies for a living, so
>that's going to alias fiercely.  Audio PWM modulation?  Yikes!

In what way does frequency modulation create new frequencies? And in what
way would it introduce aliasing, provided your underlying generation is
aliasfree?

>It's a very difficult problem.  Some things that are trivially easy to
>do in the analog domain are (maybe) impossible in the digital domain.

Solving problems is what engineering is all about. It might not be trivial
to implement these things in a good way but it's possible.

Check out "Alias-Free Digital Synthesis of Classic Analog Waveforms" by
Stilson-Smith (CCRMA/Stanford) in case you haven't done so already, it
describes exactly these things.

/Bjorn