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In training examples we always do a transformation on signals which have t-scale in labeled in radians. I understand that Pi is just a number, but I still have some troubles to understanding how to relate real-life continuous signal with t-labeled in seconds.

In my head when we have real-life signal (Amplitude on time) we have full information about that signal and can determine all of it frequency components. And I know how to do it converting this signal to discrete time, but how to do it with continuous time FT?

So my question is:

could you please explain to me, ho to apply fourier transform and get frequency compnonents out of continuous signal which lengthis for example 3 seconds or something and it's aperiodic.

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    $\begingroup$ Could you post an example waveform where you see the time axis given in radians? I assume it is cycles of a sine wave but would be clearer to refer to the example you are using. (For example one cycle of a sine wave is 2 \pi radians —- if the frequency was 1/3 cycles/second then that would be 3 second duration. $\endgroup$ – Dan Boschen May 6 '20 at 13:43
  • $\begingroup$ @DanBoschen Yes, this is the exact reason of my confusion. When your signal is given as you describe it you have to know the frequency of the signal to use it. But if you just have an oscillogram of a signal how do you apply FT to it? For example, you have a Cos(2/3*pi*t) -- t is in seconds. This cosine will have a full revolution in 3 seconds. How I apply FT to this signal? $\endgroup$ – qqffx May 6 '20 at 13:53
  • $\begingroup$ That waveform is in units of seconds, so that is x(t) and you use the Fourier Transform equation. If that isn’t clear then I suggest that you add that specific example to your question above as x(t) then show the Fourier Transform equation and proceed from there showing how you would compute the transform as that would where exactly you are getting stuck. $\endgroup$ – Dan Boschen May 6 '20 at 14:04
  • $\begingroup$ "Pi is just a number"???!!! Okay then, we're past that. So, you have a continuous signal. What kind of a bucket are you holding it in? $\endgroup$ – Cedron Dawg May 6 '20 at 15:24

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