A defect became a coordinate system.
BFFT began by refusing the accepted diagnosis of a forgotten Fourier transform. The transform was not repaired by tuning it harder. Its coordinates were changed until the hidden rotation geometry became ordinary, stable machinery. That repair produced a library with an inverse and understandable data order; it also opened routes toward transforms made from junctions and delays rather than a familiar processor recipe.
- Everyone assumed
- An abandoned real Fourier transform was inaccurate because its factor tree was intrinsically ill-behaved.
- I asked
- What if the tree was sound and its local coordinates were the actual defect?
- I changed
- Re-coordinate every quadratic leaf as the same normalized complex plane, then rebuild the inverse, the memory order, and the dataflow around that geometry.
- Now there is
- A working C and C++ transform library, alternate DIF, DIT, and diagonal traversals, and executable designs that describe Fourier computation as routed flow and phase delay.