On 6/24/19, Marten van Kerkwijk <m.h.vankerkwijk@gmail.com> wrote:
Hi Eric,
The easiest definitely is for the mask to just propagate, which that even if just one point is masked, all points in the fft will be masked.
On the direct point I made, I think it is correct that since one can think of the Fourier transform of a sine/cosine fit, then there is a solution even in the presence of some masked data, and this solution is distinct from that for a specific choice of fill value. But of course it is also true that the solution will be at least partially degenerate in its result and possibly indeterminate (e.g., for the extreme example of a real transform for which all but the first point are masked, all cosine term amplitudes are equal to the value of the first term, and are completely degenerate with each other, and all sine term amplitudes are indeterminate; one has only one piece of information, after all). Yet the inverse of any of those choices reproduces the input. That said, clearly there is a choice to be made whether this solution is at all interesting, which means that you are right that it needs an explicit user decision.
FWIW: The discrete Fourier transform is equivalent to a matrix multiplication (https://en.wikipedia.org/wiki/DFT_matrix, https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.dft.html), so whatever behavior you define for a nonmasked array times a masked vector also applies to the FFT of a masked vector. Warren
All the best,
Marten