# How to interpret the imaginary part of an inverse fourier transform

The fourier transform of arbitrary real data can (usually will) result in complex data. If the real data represents samples in time, then the complex FT data represent frequencies with the magnitudes representing the amplitude and the phase angles representing the phase.

If I perform some arbitrary manipulation on the complex FT data prior to applying an inverse fourier transform, the result of the IFT can also be complex. My question is, how do I interpret the imaginary part of the IFT result? My guess is that a complex IFT result is non-physical, and that this must imply that my original arbitrary manipulation was also therefore non-physical.

Is this correct? If so, are there equations which describe whether such a manipulation would be non-physical.

$$X_k=X^*_{N-k}$$
where $X_k$ is the DFT of a real-valued sequence $x_n$, and $N$ is the length of the DFT.