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function f=comp_inonsepdgtreal_quinqux(coef,g,a,M,do_timeinv)
%-*- texinfo -*-
%@deftypefn {Function} comp_inonsepdgtreal_quinqux
%@verbatim
%COMP_INONSEPDGTREAL_QUINQUX Compute Inverse discrete Gabor transform
% Usage: f=inonsepdgt(c,g,a,M);
%
% Input parameters:
% c : Array of coefficients.
% g : Window function.
% a : Length of time shift.
% M : Number of channels
% do_timeinv : Do a time invariant phase ?
% Output parameters:
% f : Signal.
%
%
% This is a computational subroutine, do not call it directly.
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/comp/comp_inonsepdgtreal_quinqux.html}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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/>.
% AUTHOR : Nicki Holighaus and Peter L. Soendergaard
% TESTING: TEST_NONSEPDGT
% REFERENCE: OK
% Check input paramameters.
M2=size(coef,1);
N=size(coef,2);
W=size(coef,3);
L=N*a;
coef2=zeros(M,N,W,assert_classname(coef,g));
coef2(1:M2,:,:)=coef;
if rem(M,2)==0
coef2(M2+1:M,1:2:N-1,:)=conj(coef(M2-1:-1:2,1:2:N-1,:));
coef2(M2:M,2:2:N ,:) =conj(coef(M2-1:-1:1,2:2:N,:));
else
coef2(M2+1:M,1:2:N-1,:)=conj(coef(M2:-1:2,1:2:N-1,:));
coef2(M2+1:M,2:2:N ,:)=conj(coef(M2-1:-1:1,2:2:N,:));
end;
coef=coef2;
lt=[1 2];
mwin=comp_nonsepwin2multi(g,a,M,lt,L);
% phase factor correction (backwards), for more information see
% analysis routine
E = exp(2*pi*i*a*kron(0:N/2-1,ones(1,2)).*...
rem(kron(ones(1,N/2), 0:2-1),2)/M);
coef = bsxfun(@times,coef,E);
% simple algorithm: split into sublattices and add the result from eacg
% sublattice.
f=zeros(L,W,assert_classname(coef,g));
for ii=0:2-1
% Extract sublattice
sub=coef(:,ii+1:2:end,:);
f=f+comp_idgt(sub,mwin(:,ii+1),2*a,[0 1],0,0);
end;
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