Re #7266. First a round of cleanup before doing actual work.
Re #7266. Reworked the entirety of the algorithm.

Now starts the cleanup effort.
Re #7266. Cleaned up code and documentation before closing ticket.

Crazy things like updating the help and removing debug printing.
Re #7266. Removing boilerplate comment.
Re #7266. Added error propagation for PDF transforms.
Merge remote-tracking branch 'origin/feature/7266_PDFFourierTransform'