What are the units of FFT output?
The FFT sums samples xk in the original units (U) multiplied by unitless complex values (due to discretization) e−2πj⋅. Thus the units after FFT remain the same as for the original signal, i.e. U.
What is the unit of power spectrum?
Power spectral density is commonly expressed in watts per hertz (W/Hz).
Does Fourier transform change units?
If you compute a Fourier transform, it changes the unit. A “forward” Fourier transform (t->f) adds /Hz to your unit, a “backward” (f->t) adds /s. The reason is that a Fourier transform shows how your original unit (“amplitude”) distributes over frequency. So the unit is naturally amplitude per frequency.
How do you calculate FFT of a signal?
Fourier transform
- N = number of samples.
- n = current sample.
- xn = value of the signal at time n.
- k = current frequency (0 Hz to N-1 Hz)
- Xk = Result of the DFT (amplitude and phase)
What is the unit of Fourier transform?
What are units of a Fourier transform ( FFT )?
My question has to do with the physical meaning of the results of doing a spectral analysis of a signal, or of throwing the signal into an FFT and interpreting what comes out using a suitable numerical package, now take the modulus (abs) and square the result, i.e. |fft (v)|^2.
Do you get a by the continuous Fourier transform?
You get a ( ω) by the continuous Fourier transform. Note, however, that delta-functions are not dimensionless! indeed, a i δ ( ω − ω i) has units of voltage-per-frequency, just as a ( ω) — which in fact it is! a ( ω) = ∑ i a i δ ( ω − ω i) in this case. Thanks for contributing an answer to Physics Stack Exchange!
What is the voltage at a specific frequency?
Asking what is the voltage at a specific frequency assumes a discrete set of frequencies. You get a ( ω) by the continuous Fourier transform. Note, however, that delta-functions are not dimensionless! indeed, a i δ ( ω − ω i) has units of voltage-per-frequency, just as a ( ω) — which in fact it is! a ( ω) = ∑ i a i δ ( ω − ω i) in this case.
Are there any units that remain the same after FFT?
The units after FFT remain the same as for the original signal, i.e. U. If you take the absolute value, the same again. For instance, the -frequency index gives you the DC, or average value of your signal (or at least it is proportional, with a factor of the number of samples, or its square root depending on the normalization).