[nicwilson]

It is, because wavenumber and position are distinct variables and are orthogonal to each other. FT turn position into wavenumber (positional frequency) and wavenumber into negative position:

[ 0 1] [x] [ ω]

          = 

[-1 0] [ω] [-x]

see also https://en.wikipedia.org/wiki/Linear_canonical_transformatio...

the rotation matrix [[ 0 1], [-1 0]] is a 90 degree rotation.

[meindnoch]

Ok, now I see it!