Just wondering if you came across the DPlot issue on the FFT giving the incorrect phase angle (180 out in the example) with the last DPlot FFT data point?
Seriously, it creates an error that may be significantly reduced in an inverse FFT (if the SW had a switch).
At present my best answer is this is a consequence of the way the complex numbers are packed into reals by the FFT routines used, and that last phase angle shouldn't be used. Using REALFT (when N is a power of 2) that last phase angle isn't even calculated - it's always 0.