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

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