[PD] better tabread4~

[Miller Puckette]

O can see how that could happen.  I think the error in Lagrange is spread
out over all frequencies whereas I can imagine other interpolation methods
in which the error would be at frequencies closer to the original sound
(and so much harder to perceive in a situation like the one you're 
working in).

cheers
Miller

On Wed, Jun 11, 2008 at 12:05:34AM +0200, cyrille henry wrote:
> ok, thanks for the answer.
> i understand what's in your book, but i found other references where cubic 
> interpolation is used for a function that offer continuity of the 1st 
> derivative.
> 
> i can understand that tabread4~ minimise the error when the table is large 
> (when you play it faster than the original speed).
> but with a small table, or when you play it slower, the first derivative 
> discontinuity create lot's of high frequency.
> 
> So, in this condition, the function i use offer a better quality.
> see in the svn externals/nusmuk/tab/tabosc4c~-help.pd for more.
> 
> cyrille
> 
> 
> Miller Puckette a ?crit :
> >I believe "lagrange interpolation" just means polynomail.  tabread4~ uses
> >cubic interpolation... details are in
> >   http://crca.ucsd.edu/~msp/techniques/latest/book-html/node31.html
> >
> >It may be that there's a better way to do 4-point interpoation than 
> >Lagrange
> >but the way to find out would be by doing careful distortion measurements.
> >In particular, I know there are ways do do 4-point interpolation that don't
> >give discontinuous first derivatives, but I think most measures of 
> >distortion
> >would indicate using the Lagrance one instead.
> >
> >cheers
> >Miller
> >
> >On Tue, Jun 10, 2008 at 05:29:49PM +0200, cyrille henry wrote:
> >>
> >>Charles Henry a ?crit :
> >>>On Tue, Jun 10, 2008 at 4:43 AM, cyrille henry
> >>><cyrille.henry at la-kitchen.fr> wrote:
> >>>
> >>>>i realized that the 4 points interpolation in tabread4~ (and tabosc4~) 
> >>>>are not optimal.
> >>>Please describe.  I've analyze the interpolation formula too, and I
> >>>think that it is a true cubic interpolation.  Is the numerical
> >>>accuracy bad?
> >>well, i think the tabread4~ interpolation is a lagrange interpolator (but 
> >>i'm may be wrong).
> >>at least with tabread4~, the 1st derivative is not continuous, while it 
> >>should be with a cubic interpolation.
> >>
> >>i program a cubic interpolation, and the shape of the waveform is really 
> >>different.
> >>
> >>please compile the object and look at the help patch to see the 
> >>difference.
> >>
> >>i can also send waveforme picture if needed.
> >>
> >>
> >>cyrille
> >>
> >>
> >>>Chuck
> >>>
> >>>_______________________________________________
> >>>Pd-list at iem.at mailing list
> >>>UNSUBSCRIBE and account-management -> 
> >>>http://lists.puredata.info/listinfo/pd-list
> >>>
> >>>
> >>_______________________________________________
> >>Pd-list at iem.at mailing list
> >>UNSUBSCRIBE and account-management -> 
> >>http://lists.puredata.info/listinfo/pd-list
> >
> >_______________________________________________
> >Pd-list at iem.at mailing list
> >UNSUBSCRIBE and account-management -> 
> >http://lists.puredata.info/listinfo/pd-list
> >
> >