I'm ultimately going somewhere with this, but feel I need to get some
things clear in my head first. While it may not be the ideal starting
place, I want to begin with this article:
You will have to read/skim the article for context. I'm not sure
whether some of my confusion is from being dense, or just reading an
article that is not well-written/organized. In particular, I am
interested in this quote from the article:
=========
The DFT and the DTFT can be viewed as the logical result of applying
the standard continuous Fourier transform to discrete data. From that
perspective, we have the satisfying result that it's not the
transform that varies, it's just the form of the input:
If it is discrete, the Fourier transform becomes a DTFT.
If it is periodic, the Fourier transform becomes a Fourier series.
If it is both, the Fourier transform becomes a DFT.
=========
I'm not getting the *significance* of the difference between the DTFT
and the DFT. There seems to be a lot of mathematical effort to
distinguish the two. The statement above implies that the DFT is a
particular case of the DTFT.
I have been applying the DFT to sampled data (specifically a
single-pulse, hence non-periodic, waveform) without any issues
AFAICT, but then I ran across this article and out of curiosity am
trying to understand if it has any true significance. To put it
another way, if I am fourier-transforming discrete data, who cares if
it merely discrete, or discrete and periodic? Who cares about the
semantics of DFT or DTFT?
Like I said, I'm going somewhere with this (other questions), but
just want to get some other thoughts before I try to explain further.