dsft.m

linear time－frequency toolbox

function F=dsft(F);
%DSFT  Discrete Symplectic Fourier Transform
%   Usage:  C=dsft(F);
%
%   DSFT(F) computes the discrete symplectic Fourier transform of F.
%   F must be a matrix or a 3D array. If F is a 3D array, the 
%   transformation is applied along the first two dimensions.
%
%   Let F be a K x L matrix. Then the DSFT of F is given by
% 
%                               L-1 K-1
%    C(m+1,n+1) = 1/sqrt(K*L) * sum sum F(k+1,l+1)*exp(2*pi*i(k*n/K-l*m/L))
%                               l=0 k=0
% 
%   for m=0,...,L-1 and n=0,...,K-1.
%
%   The DSFT is its own inverse.

error(nargchk(1,1,nargin));

D=ndims(F);

if (D<2) || (D>3)
  error('Input must be two/three dimensional.');
end;

W=size(F,3);

if W==1
  F=dft(idft(F).');
else
  % Apply to set of planes.
  
  R1=size(F,1);
  R2=size(F,2);
  Fo=zeros(R2,R1,W);
  for w=1:W
    Fo(:,:,w)=dft(idft(F(:,:,w).'));
  end;
  F=Fo;
end;