When using the Fourier transform, or correlations, I was always disturbed by various elements of it that just didn’t sit well with me.  Well, when you perform a DFT on a time series sooner or later the correlation waves will not be pinned to zero at each end, which becomes a nuisance when you want to recreate the signal with a reverse DFT.  For example, if you take a 12 sample time series, you get one wavelength with 12 samples, 2 wavelengths with 6 samples each, 3 wavelengths with 4 samples each, 4 wavelengths with 3 samples each, but 5 wavelengths will have 2.4 samples each... Clearly it is impossible to have a fraction of a sample, and this is the problem, 12 does not divide equally by 5 or to put it another way, 5 is co-prime with 12.  It turns out that there is no ideal window size for a DFT, the problem simply exists.  What appears apparent now is that a separate DFT is required for each prime frequency, and that may in fact be one of the things prime numbers are useful for!