What is the unit for power spectrum of acceleration signals in log scale I have a signal recorded by an accelerometer in m/s^2. It is basically accelerations over a period of time. I have calculated the power spectrum of the signal over in a certain frequency band and then transferred into a 20log(x) scale for plotting. I am wondering what should be unit for it?

Since it has been transferred into a log scale, I could use dB, but the standard formula for dB calculation is something like 20log(x/x0), where x0 is the reference and cancels out the unit leaving us with just dB. I am not sure if I can the same thing in the above case since I don't have any reference power? Can I just assume something like x0=1 and report the numbers in dB?

If not, then I am not sure what should accompany dB. In one paper, I have seen for accelerations reported in gravities 1g = 9.8m/s^2,dB g^2/2 was used as the unit for the power spectrum? This makes me guess maybe I should use dB m/2s^2 or weirdly dB m^2/2s^4? Any ideas are greatly appreciated.
The typical practice with decibels is to append the unit.  Unfortunately, it's informal, so you'll see things like "dBm" in RF circuits which refers to "dB with a reference of 1mW", not "dB with a reference of 1 meter".

you could:


Put a note in your graph that $0\mathrm{dB} = \mathrm{1 m/s^2}$
Use "dBg" (and use 1g as your reference)
Just keep the y-axis as the log of acceleration squared (and yes, $\mathrm{m^2/s^4}$ is awkward, but it's the correct unit).