Units for fourier transform of measured voltage
If your signal was originally volts before being acquired, you can use dBV as unit (or dBµV or any other variants).

You need to know the load impedance to determine power though. So if you know your load impedance is for example 50 ohms, then you can calculate the power and label it in dBW or dBm. If you don't know the impedance, then it doesn't make sense to display watts, only volts.

If the FFT is scaled properly, its y axis should be in the same unit as the input signal (Volts here) and thus, the 20log10 conversion in dB gives dBV, however there are several gotchas:


  I'd like to present the data as dBV or something similar but this seems to require RMS measurements.


Be really careful about how it is scaled. If you write the code yourself using matlab or a relative, it is always a good idea to use a signal like "sin(wt)" which has a known amplitude and frequency, and check that the FFT really gives a spike with the proper amplitude and frequency... you never know.

About "RMS": The FFT will give you the amplitude of each sine component of your waveform. If you want that to be displayed as RMS, then you can remove 3dB (and use "dBV RMS" as a label), if you want peak amplitude then don't remove 3dB (and display it as dBV). It's the same information.

Also be aware that unless the signal frequency is an integer divider of the sampling frequency, then the signal peak on the FFT will be split between two bins. You need to sum both bins to know the amplitude of the original signal.