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research papers
The Cooley-Tukey fast Fourier algorithm and the factored trigonometric Fourier algorithm are compared for four typical crystallographic problems. With general PL/1 programs the execution speed of the fast Fourier algorithm ranged from 4.7 to 19 times faster than the trigonometric algorithm. In addition the PL/1 fast Fourier program was 1.8 times faster than a space group specific, fixed axial length trigonometric Fourier FORTRAN program. Our results indicate that the fast Fourier is the most efficient algorithm available for crystallographic Fourier series calculations, with efficiency increasing as one goes to larger problems.