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

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_transformation#Fourier_transform https://en.wikipedia.org/wiki/Linear_canonical_transformatio... the rotation matrix [[ 0 1], [-1 0]] is a 90 degree rotation.