[PD] fractional delay for PD

[Charles Henry]

On Sat, Feb 28, 2009 at 8:25 PM, David Doukhan <david.doukhan at gmail.com> wrote:

> I don't even know what method have been used in vd~ ...
> The only thing I've read in the corresponding help patch, is that the
> interpolation method used by that component does an interpolation over
> 4 values.
> Does anyone know the name of the method used by that component? It
> would allow me get better clues on its theoretical efficiency, and to
> know if spending some time to program/test some alternative method
> would be usefull...


vd~ appears to use the same 4-point interpolation method as tabread4~,
which is just a cubic polynomial fit through 4 points.  Other methods
of finding interpolation polynomials for improved response were
discussed a few months ago in the thread on different tabread4's.  Let
me know if you need anything.

Chuck

http://lists.puredata.info/pipermail/pd-list/2008-06/062878.html
http://lists.puredata.info/pipermail/pd-list/2008-06/063256.html
http://lists.puredata.info/pipermail/pd-list/2008-06/063303.html

I did a lot of analysis on the functions, involved.
big math lecture is here:
http://lists.puredata.info/pipermail/pd-list/2008-07/063601.html
tables and transforms:
http://lists.puredata.info/pipermail/pd-list/2008-07/063489.html

Algorithm is here in d_delay.c:

  262   while (n--)
  263     {
  264         t_sample delsamps = x->x_sr * *in++ - zerodel, frac;
  265         int idelsamps;
  266         t_sample a, b, c, d, cminusb;
  267         if (delsamps < 1.00001f) delsamps = 1.00001f;
  268         if (delsamps > limit) delsamps = limit;
  269         delsamps += fn;
  270         fn = fn - 1.0f;
  271         idelsamps = delsamps;
  272         frac = delsamps - (t_sample)idelsamps;
  273         bp = wp - idelsamps;
  274         if (bp < vp + 4) bp += nsamps;
  275         d = bp[-3];
  276         c = bp[-2];
  277         b = bp[-1];
  278         a = bp[0];
  279         cminusb = c-b;
  280         *out++ = b + frac * (
  281             cminusb - 0.1666667f * (1.-frac) * (
  282                 (d - a - 3.0f * cminusb) * frac + (d + 2.0f*a - 3.0f*b)
  283             )
  284         );
  285     }