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function f=ref_irdgt(c,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_irdgt
%@verbatim
%REF_IRDGT Reference Inverse Real DGT
% Usage: c=ref_rdgt(f,g,a,M);
%
% Linear algebra version of the algorithm. Create big matrix
% containing all the basis functions and multiply with the transpose.
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_irdgt.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(g,1);
b=L/M;
N=L/a;
Mhalf=ceil(M/2);
F=zeros(L,M*N);
l=(0:L-1).';
for n=0:N-1
% Do the unmodulated coefficient.
F(:,M*n+1)=circshift(g,n*a);
for m=1:Mhalf-1
F(:,M*n+2*m)=sqrt(2)*cos(2*pi*m*l/M).*circshift(g,n*a);;
F(:,M*n+2*m+1)=sqrt(2)*sin(2*pi*m*l/M).*circshift(g,n*a);;
end;
if mod(M,2)==0
F(:,M*(n+1))=cos(pi*l).*circshift(g,n*a);;
end;
end;
% dot-transpose will work because F is real.
f=F*c;
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