Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

The Fourier transform General features

Fourier demonstrated that for any function/(x), there exists another function F(h) such that [Pg.90]

The Fourier transform operation is reversible. That is, the same mathematical operation that gives F(h) from f(x) can be carried out in the opposite direction, to givef(x) from F(h) specifically, [Pg.91]

Returning to the visual transforms of Figs. 2.7-2.10 each object (the sphere in Fig. 2.7, for instance) is the Fourier transform (the back-transform, if you wish) of its diffraction pattern. If we build a model that looks like the diffraction pattern on the right, and then obtain its diffraction pattern, we get an image of the object on the left. [Pg.91]

There is one added complication. The preceeding functionsf(x) and F(h)are one-dimensional. Fortunately, the Fourier transform applies to periodic functions in any number of dimensions. To restate Fourier s conclusion in three dimensions, for any function f(x,y,z) there exists the function F(h,k,l) such that [Pg.91]

Thinking again about the potential usefulness of computing IT s in crystallography, you will see that we can use the Fourier transform to obtain information about real space, f(x,y,z), from information about reciprocal space, F(h,k, 1)- Specifically, the diffraction pattern contains information whose Fourier transform is information about the contents of the unit cell. [Pg.91]


See other pages where The Fourier transform General features is mentioned: [Pg.90]   


SEARCH



Fourier transform , generally

General Transformations

Generalized Fourier transform

© 2024 chempedia.info