function [F,u] = rdftI(f,x)
%
%  RDFT
%    Roger's slow 1-D DFT function.
%  [F,u] = RFFT2(f,x) returns in F the 1-D Discrete
% Fourier transform of the data in f defined over the
% vector in x.  The matrix u is a spatial
% frequency variable and may be omitted.
%
%  Note that this command is written for academic purposes
%  and is much slower than the FFT and FFT2 commands 
%  which use a fast radix-2 type transform.
%                                                  RJM  3/22/95

n = length(x);

i=sqrt(-1);
pi=3.141592653589793284626433;

dx=(x(n)-x(1))/n;

p=[0:n-1]';

for k= 1:n,
    
  Fmat=f.*exp(-i*2*pi*((k-1)/n*ones(n,1).*p));    
    % Above line performs all multiplications
  F(k) = 6.25*sum(Fmat)/n;
    % Above line adds up all the multiplications
end


% Now F contains the 1-D DFT.

a1=ceil(n/2);
a2=ceil(n/2+1);

F = [ F(a2:n)    F(1:a1)];

u=linspace(x(1)/dx,x(n)/dx,n);