I was looking into the fundamental frequency in DFT and I noticed many sources mention that the fundamental frequency is $1/N$, where $N$ is the number of samples. (When doing the DFT, we have $k/N$, so all frequencies end up multiple of $1/N$)

It is also mentioned that the frequency resolution is $Fs/N$, where $Fs$ is the sampling frequency of the discrete signal. However $Fs$ is nowhere to be seen in the DFT. Why is that? I’m sure there’s a simple explanation behind this that correlates $1/N$ to $Fs/N$, but I couldn’t find it anywhere. What confused me is that in the DFT we are calculating amplitude and phase at frequencies multiples of $1/N$, but they end up being multiples of $Fs/N$ in the signal frequency spectrum.

  • $\begingroup$ dsp.stackexchange.com/questions/69186/… and dsp.stackexchange.com/questions/69430/… You just helped demonstrate the point I make in the first reference. $\endgroup$ – Cedron Dawg Jul 29 '20 at 1:42
  • $\begingroup$ @yggdrasil: I'm happy to reopen this if you can let us know what in the indicated duplicate doesn't make sense. Please edit your question to update it with this information. $\endgroup$ – Peter K. Jul 29 '20 at 1:47
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    $\begingroup$ @PeterK. Actually, the question in the first reference isn't that similar, but I don't mind you closing this. But hey, "I told you so." and I hope the OP gives me an upvote, because that answer should be written on the walls around here. IMnsHO Come to think of it, so should the second. They are probably the most valuable answers I have given here. $\endgroup$ – Cedron Dawg Jul 29 '20 at 1:50
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    $\begingroup$ @PeterK. I have no problem that. I agree. $\endgroup$ – Cedron Dawg Jul 29 '20 at 1:53
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    $\begingroup$ @CedronDawg Thanks! I’ll take a look at the blog when I’ve time. I found that an easy and intuitive way to explain this are digital images. They are just a bunch of 2D samples and in most cases we don’t really know what the sampling rate is (if there’s one at all). Yet we can do DFT and IDFT without problems. $\endgroup$ – yggdrasil Jul 30 '20 at 3:03

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