Fast Fourier Transform - Other Generalizations

Other Generalizations

An O(N5/2 log N) generalization to spherical harmonics on the sphere S2 with N2 nodes was described by Mohlenkamp (1999), along with an algorithm conjectured (but not proven) to have O(N2 log2 N) complexity; Mohlenkamp also provides an implementation in the libftsh library. A spherical-harmonic algorithm with O(N2 log N) complexity is described by Rokhlin and Tygert (2006).

Various groups have also published "FFT" algorithms for non-equispaced data, as reviewed in Potts et al. (2001). Such algorithms do not strictly compute the DFT (which is only defined for equispaced data), but rather some approximation thereof (a non-uniform discrete Fourier transform, or NDFT, which itself is often computed only approximately).