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  • 1
    Electronic Resource
    Electronic Resource
    Fast Fourier transforms for space groups containing rotation axes of order three and higher (1992)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 346-349 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Methods are described for exploiting the symmetry of uniaxial space groups containing rotation axes of order three and higher to improve the efficiency of computation of Fourier transforms. Mapping a symmetrical two-dimensional section into four dimensions enables the selection of non-contiguous asymmetric units over which fast Fourier transforms can be performed that reduce the computation time by a factor of approximately the order of the rotation axis. The application of the procedure to plane group p3 and its extension to p4 and p6 are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767391015027
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fast Fourier transform algorithms for real and symmetric data (1992)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 48 (1992), S. 415-418 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Procedures are described for computing the Fourier trans forms of one-dimensional periodic sequences of real numbers and sequences that contain Hermitian and translational symmetry. Transforms from real sequences to Hermitian sequences and back are particularly efficient if the number of grid points in a period is two or four times an odd number. If the relation between points that are separated by half of a period is a change of sign or complex conjugate, periods that are a power of two times an odd number are also favorable for constructing algorithms that minimize redundant computations and complex multiplications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767391015039
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures (1990)
    Springer
    Circuits, systems and signal processing 9 (1990), S. 449-500 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Fourier transform algorithms are described using tensor (Kronecker) products and an associated class of permutations. Algebraic properties of tensor products and the related permutations are used to derive variants of the Cooley-Tukey fast Fourier transform algorithm. These algorithms can be implemented by translating tensor products and permutations to programming constructs. An implementation can be matched to a specific computer architecture by selecting the appropriate variant. This methodology is carried out for the Cray X-MP and the AT&T DSP32.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189337
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    Paper (German National Licenses)
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