[music-dsp] Gibbs effect removal

[Joe Wright]

I got distracted and am now just about to implement this.

For the range of wavetables (e.g. 0 - 127 corresponding ot the midi notes),
should k be fixed?

e.g.  k = (pi/2) / number of partials for midi note 0.

Or should it be calculated for each wavetable?

e.g.  k = (pi/2) / number of partials for midi note x.


If its fixed then the partials remain the same volume throughout the set
(and calculation is easier).  If not, then they don't.

Thanks

Joe
joe at nyrsound.com

> In order to reduce the gibbs effect you have to tweak the ideal
> coefficients (like, for a saw wave, 1, 1/2, 1/3, ...) so that the higher
> ones are brought towards zero. You have to use a "windowing" function
> that goes from 1 to 0, the raised cosine one is a cosine function raised
> to power 2 - it's the one I used in Rainbow, for no particular reason
> actually (you could use other ones)...
>
> Maybe you'll want an example now, for a 4 harmonics wavetable, instead
> of
> 1, 1/2, 1/3, 1/4 serie, you'd use:
> 1, 1/2*cos(k)^2, 1/3*cos(2k)^2, 1/4*cos(3k)^2
> where k = (pi/2/4)

> Patrice



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