My question has to do with the physical meaning of the results of doing the spectral analysis of a signal, or, put another way, of interpreting what comes out of throwing a signal into an FFT of a math package.
(i) take a signal, a time-varying voltage v(t)
(ii) throw it into an FFT -- you get back a sequence of real numbers (Laurance: ok, not quite the FFT, but the abs(fft)^2 )
(iii) throw it onto a plot. You now have a frequency spectrum g(w) with frequency on the x axis, and
(?iv?) ... WHAT PHYSICAL UNITS on the y axis? (and what meaning?)
My understanding is that this frequency spectrum shows how much of the various frequencies are present in the voltage signal -- they are spectral coefficients in the sense that they are the coefficients of the sines and cosines of the various frequencies required to reconstitute the original signal.
But to relate them to something with meaning in the real world, it would be helpful to know the UNITS of these spectral coefficients.
The other problem is that without knowing the UNITS, I can't make the right choice for how to move to a dB scale for graphing them. (I want to use a dB scale because I have some tiny measurements and some huge measurements so dB scale is the best way to show the extreme range on a single plot.)
So I have to make a choice: do I use the 20log10 dB conversion (corresponding to a field measurement, like voltage)? Or do I use the 10log10 dB conversion (corresponding to an energy measurement, like power)? Which one to use depends on what the units are?
Any light shed on this would be greatly appreciated!