# What are the units of my data after an FFT?

Magnetometer measures the derivative of the magnetic field, or dB/dt, with an output in microvolts (mV). The Sampling rate is 128 Hz, so if we collect data for 2 minutes, $2 \times 60 \times 128=15360$ points (discrete case). When I perform an FFT on these time series, what will the units of amplitude density be after the transform?

• Your raw data is in mv vs 1/time thus after FFT the ordinate still has units of mv and the abscissa units of time. – porphyrin Dec 6 '16 at 8:45

If you look at a power density spectrum (squared), then the units above should be squared as well (mV$$^2$$ or T$$^2$$/s$$^2$$).
If you take the absolute value, the same again. For instance, the $$0$$-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).
The continuous Fourier transform, in contrast, "sums" the samples times complex cisoids times a time differential (the $$\mathrm{d}t$$). Its units would be U.s (s for seconds). Unless you normalize it by something with a unit.