[PD] Anti-aliasing filter

[julien.breval at tremplin-utc.net]

Hello

> I've got an additive synth which generates some very
> high frequency partials and hence aliasing distortion
> occurs when the fundamental is high enough.
> 
> I tried to fix this by using a low pass (lop~) filter
> before the dac. This didn't fix the problem and I
> suspect that lop~ only filters up to about 22kHz. Is
> there a way of implementing a 'brick wall' filter
> which will stop ALL frequencies past a cutoff? (i.e.
> not just frequencies in the audible range)

You can make a 'brick' filter using an FFT transform, but the sound will be 
more or less altered (depending on the window size and the overlap you use for 
the FFT). I programmed a dual similar filter for adding the low partials of a 
sound to the high partials of another sound (the limit is as vertical as 
possible). As there was nothing else running in the patch, I could set the 
window size to 4096 (for accurate frequency resolution) and the overlap to 16 
(for accurate "time" resolution). The problem of this method is that it takes 
lots of CPU.

Another solution is to calculate the highest partial that won't produce 
aliasing, in function of the fundamental.
If we call F the fundamental, the k-th partial will have a frequency of F + k*F 
(if you chose another harmonicity system, you may adapt this formula). 
Therefore the maximum number of computable partials of the F fundamental is the 
integer part of (22050-F)/F. 
For F = 10 Hz, you can compute 2204 partials
For F = 1000 Hz, you can only compute 21 partials 
The idea, here, is to limit the number of partials to the maximum (you can 
evaluate this maximum in realtime, in function of the fundamental). You can 
either mute the partials that outpass the limit (the most simple solution) or 
not even calculate them.


I hope it will help

j