Name
       fft - fft 2d on an image

Synopsis
       fft [options] <in> <out>

Description
       fft  computes  a Fast Fourier Transform on an input image.
       fft can also compute an  inverse  FFT.  Results  can  have
       swapped quadrants, and can be expressed in polar or carte-
       sian coordinates.

       Take  care  about  the  formats  :   polar/cartesian   and
       swapped/unswapped.  The default procedure is:

       In  input  of  a  forward FFT, an image is required. It is
       taken as the real part (in  cartesian  coordinates)  of  a
       complex  2d  signal  which imaginary part is set to zeros.
       The output of a forward FFT is a complex 2d signal, i.e. 2
       image planes. By default, the output is converted to polar
       coordinates  (modulus,  phase),  and  then  quadrants  are
       swapped  in  both modulus and phase to put low frequencies
       at the center of the  images.   To  prevent  this  default
       behaviour, use the -n and -c options described below.

       In  input of an inverse FFT, a cube containing 2 images is
       required. It is taken as a complex 2d signal  which  first
       plane  contains  the modulus and second plane contains the
       phase. Before the inverse FFT is computed, a  swapping  of
       quadrants  occurs,  and  then  a  conversion  to cartesian
       (real, imaginary) coordinates  is  performed.  To  prevent
       quadrant  swapping or cartesian conversion, use the -n and
       -c options described below.

       The output of an inverse FFT is a cube containing 2 images
       in  cartesian  unswapped  format, first one being the real
       part, second one being  the  imaginary  part  (meaningless
       imagewise).

Algorithm
       fft  uses  the Danielson-Lanczos lemma, in a code based on
       one originally written by  N.  M.  Brenner,  described  in
       Numerical Recipes in C.

Options
       -c     Switches to cartesian mode the following data:
              output  for  a  forward  FFT (default is polar), or
              input for an inverse FFT.

       -i     Inverse FFT. The input is  a  cube  containing  two
              planes  only. Default I/O format for these 2 planes
              is polar coordinates (modulus, phase). It will out-
              put  a cube containing 1 plane only (imaginary part
              is  meaningless  imagewise).   The  input  will  be
              swapped before FFT, unless the -n option is used.

       -n     This  option  prevents fft from swapping the output
              of a forward FFT and the input of an inverse FFT.

       Swapping is done according to the following rule :
       1 2
       4 3
       becomes then
       3 4
       2 1
       which puts then the lowest frequencies at  the  center  of
       the image.

Files
       Input files shall all comply with FITS format.