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Fourier transformation by smooth interpolation
Author(s) -
Shankland D. G.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560050857
Subject(s) - interpolation (computer graphics) , fourier transform , computation , transformation (genetics) , fourier analysis , grid , fourier series , fast fourier transform , function (biology) , mathematical analysis , pseudo spectral method , mathematics , discrete fourier transform (general) , algorithm , geometry , physics , chemistry , classical mechanics , fractional fourier transform , motion (physics) , evolutionary biology , biology , gene , biochemistry
A method is presented for efficiently computing the Fourier transform of a function, such as (charge density) 1/3 , known numerically at a number of points in the unit cell of a crystal. The method utilizes an implicit interpolant which would be maximally smooth, consistent with the data. However, the interpolant is not computed, but the Fourier coefficients are obtained directly. Specialization of the formulas to a uniform grid is made and results in an enormous saving of computation.