[PD] tabread4~ "broken" interpolation algorithm - was Re:, Max Smoother Audio than Pd?

[Matteo Sisti Sette]

 > It occurs to me that there exists one very obvious function for which
 > the squared error is minimized for a 4-point interpolator.  4-point
 > interpolator impulse functions have to be 0 outside the interval
 > [-2,2].
 >
 > So,
 > E=|f(x)-sinc(x)|^2 is minimized when
 >
 > f(x)={sinc(x) -2<x<2  ,    0 elsewhere

I may be missing something but I'm afraid the E in your formula is not 
the error that is supposed to be minimized.

The ideally interpolated signal (which is the one in reference to which 
the error has to be minimized) is not just a sinc: it is the sum of an 
infinite series of sinc's centered at the sampled points and scaled with 
the sampled values.

(I won't try to write it in a latex-like fashon, I would certainly get 
it wrong - not because of latex syntax, I mean I would get it wrong even 
if I tried to write it down manually)

Please correct me if I am wrong


-- 
Matteo Sisti Sette
matteosistisette at gmail.com
http://www.matteosistisette.com