Hi,

while reading this paper about band limited impulse train synthesis I stumbled across sinc interpolation, which apparently can generate resampled versions of a discrete signal without aliasing.

This might be a really handy tool for wavetable oscillators. The obvious problem here is that it contains a sum from minus infinity to infinity which we right now cannot calculate in a finite timeframe. Given that the influence of higher/lower parts of this sum decreases rapidly, one could only calculate a window of that sum and still get a good approximation which would be pratically aliasing free.

However, that still is a lot of computation and I wonder if something like this has ever been used in a sythesizer.

Then I had a second thought: Apparently you can record any sample from any source, extract one oscillator cycle of a low frequency note and use that as a wavetable. The you can use the sinc interpolation to pre-compute more waves with less harmonics. Lets say we have a base wavetable that is aliasing free up to C0, and then we sinc-interpolate a new wavetable thats aliasing free up to C1, then one for C2, etc. etc.

In the final oscillator algorithm, its just a matter of picking the right wavetable (so for E0 you would use the wavetable for C1) and playing it back at the right speed (which will basically be less or equal that one wavetable-step per sample => aliasing free). Obviously that means that when going from C1 to C#1 there will be a change in the underlying wavetable (because C1 can use the wave thats valid up to C1 and C#1 has to use the next wave which is valid up to C2). An interpolation could make this change less rapid and less audible.