Physical Key Extraction Attacks on PCs

I was surprised that the researchers were able to obtain keys quickly with most of these methods and, apparently, with other processes running on the machine (though, in the case of the acoustic, "coil whine", attack, they acknowledge that a non-idle machine results in reduced signal fidelity).

Does anyone know how they are able to take spectral analyses of, e.g., em signals, and turn them into data? I imagine the software is fairly complex. I'm not sure how I'd even approach this kind of problem!