> 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
matteosistise...@gmail.com
http://www.matteosistisette.com
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