The FFT is crucial for an efficient implementation of cDFT, because it reduces the complexity of the convolution integrals from O(n 2 ) to O(n log n). However, the frequency values k at which the transformation is evaluated can not be chosen arbitrarily. If an FFT is evaluated in the skewed coordinate system s, the resulting k s values are also skewed. To calculate a convolution with an analytic weight function, the axes in frequency space must be transformed into a Cartesian coordinate system. This transformation is done by aligning the phases k r • r = r ⊺ k r and k s • s = s ⊺ k s of the Fourier transform. Using the coordinate transform in real space r = Hs or r ⊺ = s ⊺ H ⊺ , the following relation is obtained: ) and ( ) as: