function [coef]=comp_dwilt(f,g,M)
%COMP_DWILT  Compute Discrete Wilson transform.
%   
%
%   Url: http://ltfat.github.io/doc/comp/comp_dwilt.html

% Copyright (C) 2005-2015 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.1.1
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program.  If not, see <http://www.gnu.org/licenses/>.

L = size(f,1);
a=M;
N=L/a;
W=size(f,2);


coef=zeros(2*M,N/2,W,assert_classname(f,g));

coef2=comp_sepdgt(f,g,a,2*M,0);

if (isreal(f) && isreal(g))

    % If the input coefficients are real, the calculations can be
  % be simplified. The complex case code also works for the real case.

  % Unmodulated case.
  coef(1,:,:)=coef2(1,1:2:N,:);

  % cosine, first column.
  coef(3:2:M,:,:)=sqrt(2)*real(coef2(3:2:M,1:2:N,:));
  
  % sine, second column
  coef(M+3:2:2*M,:,:)=-sqrt(2)*imag(coef2(3:2:M,2:2:N,:));
  
  % sine, first column.
  coef(2:2:M,:,:)=-sqrt(2)*imag(coef2(2:2:M,1:2:N,:));
  
  % cosine, second column
  coef(M+2:2:2*M,:,:)=sqrt(2)*real(coef2(2:2:M,2:2:N,:));

  % Nyquest case
  if mod(M,2)==0
    coef(M+1,:,:) = coef2(M+1,1:2:N,:);
  else
    coef(M+1,:,:) = coef2(M+1,2:2:N,:);
  end;


else
  % Complex valued case
  

  % Unmodulated case.
  coef(1,:,:)=coef2(1,1:2:N,:);

  % odd value of m
  coef(2:2:M,:,:)=1/sqrt(2)*i*(coef2(2:2:M,1:2:N,:)-coef2(2*M:-2:M+2,1:2:N,:));
  coef(M+2:2:2*M,:,:)=1/sqrt(2)*(coef2(2:2:M,2:2:N,:)+coef2(2*M:-2:M+2,2:2:N,:));

  % even value of m
  coef(3:2:M,:,:)=1/sqrt(2)*(coef2(3:2:M,1:2:N,:)+coef2(2*M-1:-2:M+2,1:2:N,:));
  coef(M+3:2:2*M,:,:)=1/sqrt(2)*i*(coef2(3:2:M,2:2:N,:)-coef2(2*M-1:-2:M+2,2:2:N,:));

  % Nyquest case
  if mod(M,2)==0
    coef(M+1,:,:) = coef2(M+1,1:2:N,:);
  else
    coef(M+1,:,:) = coef2(M+1,2:2:N,:);
  end;

end;



