🚀 go-pugleaf

In <1993Jan19.145159.19327@gserv1.dl.ac.uk> g.coulter@daresbury.ac.uk (G. Coulter) writes:

>I wounder if someone could help explain to  me Fourier Transforms
>(FFT's) I don't  want  the formulae involved just an  overview of
>the  technique. ie  How it works?  what is it used for?  What are
>the results of using the transform & how do you get back  to your
>initial say 2d data, any other  general information would also be
>very welcome.

After there was a response about what a FFT looks like I just want
to give an example what it is used for.
If you are collecting images -in my case these are astronomical 
ones- you often have a convolution between the object you are 
looking at and a so called point-spread-function.
The convolution is defined by a very nasty mathematical operation.
It looks like this:

    i(x) = \int( o(y) p(x-y) dy )

where i(x) is the image, o(x) the object and p(x) the psf.
\int stands for an integral sign.
If you do a FT, the convolution results in a multiplication:

    I(u) = O(u) P(u)

where the uppercase letters are the FT's corresponding to the
lowercase letters (letter==function).
Of course everybody can get O(u) from this formula, if P(u) doesn't 
equal 0 on the whole field. A simple devision yields:

    O(u) = I(u) / P(u)

An inverse transformation yields the object o(x).
Unfortunately you don't know the psf in every case. But that's a much
more complicated topic.

Hope that helps and everything was in an understandable English.

Markus