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 > >>><[EMAIL PROTECTED]> 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 > >>> > >>>_______________________________________________ > >>>[email protected] mailing list > >>>UNSUBSCRIBE and account-management -> > >>>http://lists.puredata.info/listinfo/pd-list > >>> > >>> > >>_______________________________________________ > >>[email protected] mailing list > >>UNSUBSCRIBE and account-management -> > >>http://lists.puredata.info/listinfo/pd-list > > > >_______________________________________________ > >[email protected] mailing list > >UNSUBSCRIBE and account-management -> > >http://lists.puredata.info/listinfo/pd-list > > > > _______________________________________________ [email protected] mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
