Timeline for Inverse DFT: Is there a valid / intuitive interpretation of results for non-integral timestamps?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 26, 2020 at 19:09 | history | edited | Andy Walls | CC BY-SA 4.0 |
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| Sep 26, 2020 at 19:03 | history | edited | Andy Walls | CC BY-SA 4.0 |
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| Sep 26, 2020 at 9:38 | vote | accept | Eddie C | ||
| Sep 25, 2020 at 20:53 | comment | added | Eddie C | @AndyWalls I added my C++ code above. I don't care for optimization, just want to understand DFT / IDFT. I could use another tool in order to look at the 3D plot if no one stops me ;) Still hope to see a corkscrew, that would fit my understanding so far | |
| Sep 25, 2020 at 20:07 | comment | added | Andy Walls | @EddieC I'd recommend prototyping whatever you want to do in MatLab/Octave or Python. It's a lot faster to create it there than in C/C++, plus you have plotting and analysis tools that are ready to use. | |
| Sep 25, 2020 at 20:04 | comment | added | Andy Walls | @EddieC A real signal in the time domain transforms to a real-even + imaginary-odd function in the frequency domain. If you do something in the frequency domain to perturb that real-even + imaginary-odd configuration of the values, then you will end up with complex values in the time domain when performing the inverse transform. I'd really have to see your exact implementation to see what is going on. | |
| Sep 25, 2020 at 19:25 | comment | added | Fat32 | Nice and correct answer for what is being asked. However, there's another possible interpretation of a slightly different inverse DFT with non-integer $n$, depending on how you construct your inverse DFT. That will yield a much better interpolation. Let me put an answer for that too. | |
| Sep 25, 2020 at 19:09 | comment | added | Eddie C | @AndyWalls Thank you! I understand that interpolation can yield "horrible" results if (n+d) is not an integer. I am still not sure why IDFT is “hallucinating” these complex values between my real-valued input data. I am now guessing that if I plotted $f(n)$ from IDFT in 3D with continous time (like here), I would see some kind of "corkscrew" and in order to intersect the plane $Im=0$ when $n$ is an integer, it has to wiggle through the whole space. Is this right? | |
| Sep 25, 2020 at 17:49 | comment | added | Andy Walls | @robertbristow-johnson Thanks. That looks more precise than my hand-waving at the end. I was drawing on experience from the DTFT/IDTFT. | |
| Sep 25, 2020 at 17:46 | comment | added | robert bristow-johnson | This is about the Dirichlet kernel, but I don't like the Wikipedia page on it. I will look for another, better, refefence. | |
| Sep 25, 2020 at 17:37 | history | answered | Andy Walls | CC BY-SA 4.0 |