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function c=ref_dwiltiii(f,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_dwiltiii
%@verbatim
%REF_DWILTIII Reference DWILT type III
% Usage: c=ref_dwiltiii(f,g,a,M);
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_dwiltiii.html}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.2.0
%
% 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);
W=size(f,2);
% Possibly zero-extend the window if necessary.
g=fir2long(g,L);
N=L/a;
F=zeros(L,M*N);
l=(0:L-1)';
pif=pi/4;
if 0
% This is the definition where the odd and even indices are split
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;
else
% Combined definition
% This is the definition where the odd and even indices are split
for n=0:N-1
for m=0:M-1
if rem(m+n,2)==0
F(:,1+m+n*M)=sqrt(2)*circshift(g,n*a).*cos((m+.5)*pi*l/M+1/4*pi+(m+n)*pi);
else
F(:,1+m+n*M)=sqrt(2)*circshift(g,n*a).*cos((m+.5)*pi*l/M+3/4*pi+(m+n)*pi);
end;
end;
end;
end;
c=F.'*f;
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