Elimination of minimal FFT grid-size limitations

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.