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

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

More to discuss, but I have these comments after 
a number of G&Ts for the evening:

> In the limit as ɢx gets small and Nɢx gets big, the output
> becomes nearly continuous and spans a huge frequency range,
> in which case the discrete Fourier transform looks a whole
> lot like the old fashioned non-discrete Fourier transform.

Hmmm. Not sure I would use this wording, but 
correct me if I'm wrong. As NÉ¢x gets big, the 
output does indeed span a huge frequency range, 
but does not become "more" continuous, it seems 
to me. Refer to your own fourier-refined link, 
section 3 (in particular the move from Fig 2 to 
Fig 3 via eq 23), where you discuss increasing 
the resolution - this is what I would have 
interpreted as creating a transform that is 
nearly continuous, "via using the existing data 
in more-informative ways."


>  > I have been applying the DFT to sampled data (specifically a
> >  single-pulse, hence non-periodic, waveform)
>
> There is no such thing.  All DFT methods are tantamount to
> *assuming* that your input signal is periodically continued.

I have seen discussions in which the comment is 
made: sampling "causes" the periodic extension. I 
have felt this is either a very deep statement, 
or a very poorly-worded statement. Your use of 
the word "tantamount" doesn't help me decide :-)


Stefan Jeglinski