Journal of Applied Crystallography

Volume 35, Part 4 (August 2002)

short communications

J. Appl. Cryst. (2002). 35, 505 [ doi:10.1107/S0021889802008312 ]

Elimination of minimal FFT grid-size limitations

D. A. Langs

Abstract: The fast Fourier transform (FFT) algorithm as normally formulated allows one to compute the Fourier transform of up to N complex structure factors, F(h), N/2 [greater-than or equal to] h > -N/2, if the transform [rho] (r) is computed on an N-point grid. Most crystallographic FFT programs test the ranges of the Miller indices of the input data to ensure that the total number of grid divisions in the x, y and z directions of the cell is sufficiently large enough to perform the FFT. This note calls attention to a simple remedy whereby an FFT can be used to compute the transform on as coarse a grid as one desires without loss of precision.

Keywords: fast Fourier transform; electron density.