% @(#)fft_freq.hlq	17.1.1.1 (ESO-IPG) 01/25/02 17:43:35 
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%.COPYRIGHT  (c)  1990 European Southern Observatory
%.IDENT      fft_freq.hlq
%.AUTHOR     KB, IPG/ESO
%.KEYWORDS   MIDAS, help files, FFT/FREQUENCY
%.PURPOSE    On-line help file for the command: FFT/FREQUENCY
%.VERSION    1.0  04-APR-1990 : Creation, KB
%.VERSION    1.1  26-OCT-1992 : Upgrade, KB
%----------------------------------------------------------------
\se
SECTION./FREQ
\es\co
FFT/FREQUENCY						26-OCT-1992  KB
\oc\su
FFT/FREQUENCY inr ini outr outi
        make discrete Fourier transform with frequency scaling
\us\pu
Purpose:
           Compute the discrete Fourier transform of real or complex frame
           and shift origin of frequency domain to center.
\up\sub
Subject:
           Transformation, filter.
\bus\sy
Syntax:       
           FFT/FREQUENCY inr ini outr outi
\ys\pa
           inr = frame containing the real part of input frame
\ap\pa
           ini = frame containing the imaginary part of input frame;
\\
                if input frame is real, omit parameter `ini' or set it to `?'
                if you enter values for any of the following parameters.
\ap\pa
           outr = frame for real part of result transform,
                defaulted to `fftr.bdf'
\ap\pa
           outi = frame for imaginary part of result transform,
                defaulted to `ffti.bdf'
\ap\sa
See also:
           FFT/FINVERSE, FFT/FPOWER, FFT/IMAGE, CREATE/FILTER
\as\no
Note:
           All internal calculations are done in double precision and
           only the final result frames are truncated to single precision.
\\
           To calculate the inverse Fourier transformation use FFT/FINVERSE,
           not FFT/INVERSE which only works for frames obtained with the
           FFT/IMAGE command!
\\
           If the number of pixels in an axis of the input frame is not a power
           of 2, the input frame is expanded to the next higher power of 2.
           The result frames will have the original no. of pixels but the
           result frames with expanded size are also kept with names
           `exp_fftr.bdf' and `exp_ffti.bdf'. These frames should be used later
           when calculating the inverse Fourier transform via FFT/FINVERSE!
\\
           The FFT command does NOT work for 3-dim frames.
\on\exs
Examples:
\ex
           FFT/FREQU rr ri
             Do FFT for image where real part is contained in frame `rr.bdf'
             and imaginary part in frame `ri.bdf'. The real and imaginary parts
             of the FFT are stored in `fftr.bdf' and `ffti.bdf'.
\xe\ex
           FFT/FREQU lola ? zr zi
             Do FFT for real frame `lola.bdf' (no imaginary part) and store
             results in `zr.bdf' and `zi.bdf'.
\xe\sxe