Re: [Phys-l] some questions related to sampling

[Stefan Jeglinski <jeglin@4pi.com>]

> I don't see it that way.  We got something extra in the
> frequency domain, but only because we provided something
> in the time domain.  Specifically, we padded the input
> with a huge number of zeros.

OK, to be precise, I assume you are saying we essentially padded the 
time domain with an infinite number of zeros. This increase in Nt 
allows the f-domain representation to be infinitely finely divided 
(df -> 0), hence the continuous representation.


> Bottom line:  "Sampling theorem" and "practical
> interpolation" are not the same thing.

In your strict sense, I agree. But it seems easy enough to find an 
example of practical interpolation. Consider the function x(t) = t^2 
* Exp[-at], which is easy enough to analyze in closed form from the 
Fourier standpoint, and happens to be a good representation for the 
impulse response of a [real] matched filter I am modelling. One can 
sample this function above the Nyquist rate and use the sampling 
theorem to interpolate very nicely between sample points, for all 
intents and purposes indistinguishable from the original function.


Stefan Jeglinski