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@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
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