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So I know that applying FFT on a time-domain signal, shows which frequency components exists and what amplitudes each frequency signal has.

My question is, suppose the signal contains same frequency rate and amplitude, but different phases. Can we realize it from the results of FFT?

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    $\begingroup$ Unless taking FFTs of the different phase signals separately, no. Not just by FFT, simply impossible, like telling whether 5 is from 3 + 2 or 1 + 4. $\endgroup$
    – OverLordGoldDragon
    Commented Jul 16, 2021 at 4:23
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    $\begingroup$ hay @OverLordGoldDragon , i just now see that you made the same point an hour before me. i hadn't noticed before. sorry. those reps should go to you. $\endgroup$
    – robert bristow-johnson
    Commented Jul 16, 2021 at 18:26
  • $\begingroup$ @robertbristow-johnson At that point maybe I'd delete my answer for the absurd vote-to-effort ratio (not saying you should)... regardless remark appreciated. $\endgroup$
    – OverLordGoldDragon
    Commented Jul 17, 2021 at 5:12
  • $\begingroup$ @OverLordGoldDragon , i'll make it up for you in the future (with some bounty). i owe you. $\endgroup$
    – robert bristow-johnson
    Commented Jul 17, 2021 at 14:28
  • $\begingroup$ @robertbristow-johnson That's kind of you, though, upvoting some of my posts should suffice. Alternatively I have a high-effort post planned I could notify of, in a month or so. $\endgroup$
    – OverLordGoldDragon
    Commented Jul 17, 2021 at 14:52

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I am thinking of two numbers. They add to the number 15.

Tell me what the two numbers are.

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