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A comparison of the fast Fourier and trigonometric Fourier algorithms
Author(s) -
Hubbard C. R.,
Quicksall C. O.,
Jacobson R. A.
Publication year - 1972
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889872009264
Subject(s) - algorithm , fourier transform , trigonometry , fourier series , fast fourier transform , discrete time fourier transform , fourier analysis , trigonometric functions , cooley–tukey fft algorithm , sine and cosine transforms , fortran , mathematics , computer science , mathematical analysis , geometry , short time fourier transform , operating system
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.