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Automatic Three‐Dimensional Fourier Synthesis
Author(s) -
Zlokazov V. B.
Publication year - 1997
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/s0021889897005037
Subject(s) - fourier transform , fourier analysis , discrete time fourier transform , intuition , computer science , algorithm , discrete fourier transform (general) , fourier series , inverse , short time fourier transform , mathematical analysis , mathematics , geometry , philosophy , epistemology
Formally, Fourier synthesis is performed by visual analysis of two‐dimensional Fourier maps. The advantage of this is the use of the analyst's experience and intuition, but this procedure is rather tiresome and time consuming. More attractive is the idea of an automatic analysis of three‐dimensional Fourier maps, as these maps provide the fastest access to the physical information. An automatic procedure for finding peaks (positions of atoms in a crystal) of a three‐dimensional function F ( x , y , z ), which is the inverse Fourier transform of the experimental structure factors, is a very convenient, and in computer‐based crystallographic data analysis, a quite indispensable tool. This paper describes a method for three‐dimensional peak search. Also, interpretation of the practical aspects of Fourier synthesis in terms of discrete Fourier transform is given, which is more appropriate than the continuous approach.