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Fast Fourier transform calculation of electron density maps.

L F Ten Eyck

    Methods in Enzymology
    |January 1, 1985
    PubMed
    Summary

    This study details the mathematical foundation of the fast Fourier transform (FFT) for crystallographic Fourier syntheses. It also presents computer program designs for implementing these transforms across various systems.

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    Area of Science:

    • Crystallography
    • Computational Chemistry
    • Applied Mathematics

    Background:

    • Crystallographic data analysis relies on Fourier transforms to model electron density.
    • Efficient computation of these transforms is crucial for large datasets and complex structures.

    Purpose of the Study:

    • To elucidate the mathematical underpinnings of the fast Fourier transform (FFT) in crystallographic contexts.
    • To describe the connection between symmetry operations in real and reciprocal space.
    • To present adaptable computer program architectures for crystallographic Fourier transforms.

    Main Methods:

    • Detailed mathematical explanation of the fast Fourier transform algorithm.
    • Analysis of symmetry operator relationships between real and reciprocal space.
    • Development of modular program designs for Fourier transform calculations.

    Main Results:

    • A comprehensive description of the mathematical basis for applying FFT to crystallographic Fourier syntheses.
    • Clarification of the interplay between real and reciprocal space symmetry.
    • Availability of FORTRAN IV and Ratfor programs for building Fourier transform functionalities.

    Conclusions:

    • The presented mathematical framework and program designs facilitate efficient crystallographic Fourier transform calculations.
    • The provided software components are suitable for integration into diverse computational crystallographic workflows.
    • This work enhances the computational tools available for crystallographic data analysis.

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