Paul, I'd be interested in your thoughts about proper means to do spectrum analysis on real data. I've found using outright Fourier transforms to be tricky and have, with some, preferred to use _multitaper methods_ which clearly have Fourier mathematics built into them, but focus upon managing spectral leakage and aliasing. Barbour, Parker, "Normalization of Power Spectral Density estimates". Barbour, Parker, "psd: Adaptive, sine multitaper power spectral density estimation for *R*", Computers & Geosciences 63 (2014) 1–8.