Charles Henry escribió:
The error depends on x the signal. Here, I want to make the
*convenient* assumption that the spectrum of x is flat, since we want
some kind of generality and we want to minimize average error across
frequencies. This would make the problem equivalent to using just
*one* dirac-delta in place of x and we would get the problem to reduce
back to just the difference of the impulse responses
|sinc(t)-f(t)|^2
Ah ok.
This *convenient* assumption is equivalent to (or at least implies)
assuming that the only sample that matters for interpolating the signal
between -2 and 2 is the one semple at 0.
This seems to me a too much strong assumption.
I'm not saying that your conclusion is wrong (though I suspect it is).
Let's take a step back:
> Here, I want to make the
> *convenient* assumption that the spectrum of x is flat
Stated this way, it sounds reasonable, doesn't it. If it does, then it
means that by "flat spectrum" you mean the _power spectrum_ of x
considered as a _stochastic process_ rather than a deterministic signal.
Brought to the domain of time, assuming x has a flat power spectrum
means assuming x is white noise. (btw a closer-to-reality assumption
would be that it is pink noise - but that's not the point here) Not a
dirac delta.
So minimizing the error would be to minimize the power, or probably
energy, of the error meant as a stochastic process.
Though I should have the notions to go a bit further in at least
_formulating_ (not solving) the problem, those notions are a bit
oxidated, if not completely gone from my head :(
But I'm sure it is not equivalent to minimizing the integral of the
difference between the operators applied to a delta function.
--
Matteo Sisti Sette
matteosistise...@gmail.com
http://www.matteosistisette.com
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