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function f=ref_iedgt_1(c,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_iedgt_1
%@verbatim
%REF_IEDGT_1 Reference Inverse Even DGT by IDGTII
% Usage c=ref_edgt(f,g,a,M);
%
% The input window must be odd-centered of length 2L.
%
% a must be divisable by 2.
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_iedgt_1.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)/2;
W=size(c,2);
N=L/a;
M=L/b;
clong=zeros(M,2*N,W);
% Copy the first M/2 coefficients of the first/last time shift.
clong(1:M/2,1,:)=c(1:M/2,:);
clong(1:M/2,N+1,:)=c(1+(N-1)*M+M/2:N*M,:);
% Scale the first coefficients correctly
clong(1,1,:)=clong(1,1,:)*sqrt(2);
clong(1,N+1,:)=clong(1,N+1,:)*sqrt(2);
% Copy the remaining coefficients to the first/last time shift, such
% that we get an odd symmetry.
clong(M:-1:M/2+2,1,:) = -clong(2:M/2,1,:);
clong(M:-1:M/2+2,N+1,:) = -clong(2:M/2,N+1,:);
% Copy the body of the coefficients
clong(:,2:N,:)=c(M/2+1:M/2+M*(N-1),:);
% Copy the unmodulated coefficients for the second half
clong(1,N+2:2*N,:)=clong(1,N:-1:2,:);
% Copy the modulated coefficients for the second half
clong(2:M,N+2:2*N,:)=-clong(M:-1:2,N:-1:2,:);
clong=reshape(clong,2*M*N,W);
fdouble=ref_idgtii(clong,g,a,2*b);
f=fdouble(1:L,:);
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