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function c=ref_dctiii_1(f)
%-*- texinfo -*-
%@deftypefn {Function} ref_dctiii_1
%@verbatim
%REF_DCTII Reference Discrete Consine Transform type III
% Usage: c=ref_dctiii(f);
%
% The transform is computed by an FFT of 4 times the length of f.
% See the Wikipedia article on "Discrete Cosine Transform"
%
% This is the inverse of REF_DCTII
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_dctiii_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(f,1);
W=size(f,2);
if ~isreal(f)
c=ref_dctiii_1(real(f))+i*ref_dctiii_1(imag(f));
else
% Scale coefficients to obtain orthonormal transform.
f(1,:)=sqrt(2)*f(1,:);
f=f*sqrt(2*L);
% Make 4x long vector
lf=[f;...
zeros(1,W);...
-flipud(f);...
-f(2:end,:);...
zeros(1,W);...
flipud(f(2:end,:))];
fflong=real(ifft(lf));
c=fflong(2:2:2*L,:);
end
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