6
$\begingroup$

Consider a signal, f(t), with impulse samples taken N times, i.e f[0],f[1],f[2],...f[N-1] Let us perform FFT on it. Now, we have the amplitude on the y-axis and the frequency on the x-axis. I want to know if the unit of the quantity on the y-axis remains the same. If yes, why? If no, what happens to it?

Example: If we consider a voltage signal. What will be the unit of the quantity on y-axis after FFT of f(t)?

  • 0
    Thank you Sir. Is that particular edit okay?2012-07-25

2 Answers 2

6

It's still a voltage. If you do a continuous Fourier transform, you go from signal to signal integrated over time, which is signal per frequency, but in a discrete Fourier transform you're just summing discrete voltages with coefficients, and the result is still a voltage. Of course if you want you can multiply it by the time interval between sample points to get a voltage per frequency unit.

  • 0
    So, the coefficients are dimensionless? I guess that convention works. Though it seems more appropriate to choose units consistent with the continuous Fourier transform on modulated Dirac combs, which has a direct correspondence with the DFT.2017-08-03
0

The unit stays the same. More concretely, a Fourier transform changes a function $f: X \to Y$ to a function $\hat f: Z \to Y$ (in physics, $X$ is usually the set of time points and $Z$ the set of frequencies), so the codomain of the function and hence its unit stays the same.

  • 0
    More precisely, a discrete Fourier transform. A continuous Fourier transform does change the dimensions of the function values.2012-07-25