Fast Fourier Transform on FCC and BCC Lattices with Outputs on FCC and BCC Lattices Respectively

Abstract

In this paper, we show fast Fourier transform (FFT) algorithms for efficient, non-redundant evaluations of discrete Fourier transforms (DFTs) on face-centered cubic (FCC) and body-centered cubic (BCC) lattices such that the corresponding DFT outputs are on FCC and BCC lattices, respectively. Furthermore, for each of those FFTs, we deduce the structures of its spatial (frequency respectively) domains that are contained in the Voronoi cell centered at 0 with respect to the DFT (inverse DFT respectively) associated sublattice.