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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.

yggdrasil
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  • https://dsp.stackexchange.com/questions/69186/dft-exercise-in-the-book-understanding-digital-signal-processing-3-ed/69233#69233 and https://dsp.stackexchange.com/questions/69430/amplitude-after-fourier-transform/69432#69432 You just helped demonstrate the point I make in the first reference. – Cedron Dawg Jul 29 '20 at 01:42
  • @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. – Peter K. Jul 29 '20 at 01:47
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    @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. – Cedron Dawg Jul 29 '20 at 01:50
  • @CedronDawg Fair enough! I thought the information in your answer was enough to answer this question... and I thought duplicate was the best way to close this. – Peter K. Jul 29 '20 at 01:52
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    @PeterK. I have no problem that. I agree. – Cedron Dawg Jul 29 '20 at 01:53
  • @CedronDawg That “k=Cycles per Frame” really explained why the DFT doesn’t have a Fs in it. Thanks! You have my upvote, and that answer may be hard to google due to the question being a bit different. I hope my question here will help other people find it as this can be a very confusing topic. – yggdrasil Jul 29 '20 at 12:20
  • To me, the "cycle per frame" is the critical fact about understanding the DFT and what the bins mean. It should be the first thing mentioned when introducing it as far as I am concerned. I'm delighted it helped you out, but defer to Peter's adhering to policy. In case you didn't notice, it has been closed, so you see, I see it, other people with big vote numbers see it. Don't worry, if somebody else asks again, if I see it, I'll put the ref in another comment. You can too, as can anybody. It can be confusing, so questions of this nature arise a lot. – Cedron Dawg Jul 29 '20 at 13:42
  • I would also encourage you to read my blog articles. The DFT is the central topic, though I've strayed some in a few. This is a link to the first one, which explains another topic that is also found confusing: Euler's equation.$$ e^{i\theta} = \cos(\theta) + i \sin(\theta) $$ Some of the material you find in my articles, you won't find anywhere else (yet). https://www.dsprelated.com/showarticle/754.php – Cedron Dawg Jul 29 '20 at 13:45
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    @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. – yggdrasil Jul 30 '20 at 03:03
  • DPI is one. ;-) You are welcome, the blog articles aren't going anywhere and the early ones are meant to be introductory, so eazy peazy. I actually haven't done too much with 2D DFTs. – Cedron Dawg Jul 30 '20 at 03:19

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