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function c=ref_rdft_1(f)
%-*- texinfo -*-
%@deftypefn {Function} ref_rdft_1
%@verbatim
%REF_RDFT_1 Reference RDFT by FFT
% Usage: c=ref_rdft_1(f);
%
% Compute RDFT by doing a DFT and returning half the coefficients.
%
% The transform is orthonormal
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_rdft_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);
Lhalf=ceil(L/2);
Lend=Lhalf*2-1;
if ~isreal(f)
c=ref_rdft_1(real(f))+i*ref_rdft_1(imag(f));
else
cc=fft(f);
c=zeros(size(f));
% Copy the first coefficient, it is real
c(1,:)=1/sqrt(2)*real(cc(1,:));
% Copy the cosine-part of the coefficients.
c(2:2:Lend,:)=real(cc(2:Lhalf,:));
% Copy the sine-part of the coefficients.
c(3:2:Lend,:)=-imag(cc(2:Lhalf,:));
% If f has an even length, we must also copy the Niquest-wave
% (it is real)
if mod(L,2)==0
c(end,:)=1/sqrt(2)*real(cc(L/2+1,:));
end;
% Make it an ortonomal transform
c=c/sqrt(L/2);
end;
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