function f=ref_idwiltiii(c,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_idwiltiii
%@verbatim
%REF_IDWILTIII   Reference Inverse DWILT type III
%   Usage:  f=ref_idwiltiii(c,g,a,M);
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_idwiltiii.html}
%@end deftypefn

% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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(g,1);
W=size(c,2);

N=L/a;

F=zeros(L,M*N);

l=(0:L-1)';

pif=pi/4;
for n=0:floor(N/2)-1
  for m=0:2:M-1
    F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos((m+.5)*pi*l/M+pif);
    F(:,1+m+(2*n+1)*M)=sqrt(2)*circshift(g,(2*n+1)*a).*sin((m+.5)*pi*l/M+pif);
  end;
  for m=1:2:M-1
    F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*sin((m+.5)*pi*l/M+pif);
    F(:,1+m+(2*n+1)*M)=sqrt(2)*circshift(g,(2*n+1)*a).*cos((m+.5)*pi*l/M+pif);
  end;
end;

f=F*c;

if 0
  pif=pi/4;
  for n=0:floor(N/2)-1
    for m=0:2:M-1
      %F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos((m+.5)*(pi/M.*l-pi/2));
      %F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos( ...
						      %       m*pi*l/M -m*pi/2+pi*l/(2*M)-pi/4);
      F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos((m+.5)*pi*l/M+pif);
      
    end;
    for m=1:2:M-1
      %F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos((m+.5)*(pi/M.*l-pi/2));
      %F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*cos( ...
						      %       m*pi*l/M -m*pi/2+pi*l/(2*M)-pi/4);
      F(:,1+m+2*n*M)=sqrt(2)*circshift(g,2*n*a).*sin((m+.5)*pi*l/M+pif);
      
    end;
    %for m=0:M-1
      %  F(:,1+m+(2*n+1)*M)=sqrt(2)*circshift(g,(2*n+1)*a).*sin((m+.5)*(pi/M.*l-pi/2));
      %end;
    for m=0:2:M-1
      F(:,1+m+(2*n+1)*M)=sqrt(2)*circshift(g,(2*n+1)*a).*sin((m+.5)*pi*l/M+pif);
      
    end;
    for m=1:2:M-1
      F(:,1+m+(2*n+1)*M)=sqrt(2)*circshift(g,(2*n+1)*a).*cos((m+.5)*pi*l/M+pif);
      
    end;
    
  end;
end;



