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function gf=comp_wfac(g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} comp_wfac
%@verbatim
%COMP_WFAC Compute window factorization
% Usage: gf=comp_wfac(g,a,M);
%
% References:
% T. Strohmer. Numerical algorithms for discrete Gabor expansions. In
% H. G. Feichtinger and T. Strohmer, editors, Gabor Analysis and
% Algorithms, chapter 8, pages 267--294. Birkhauser, Boston, 1998.
%
% P. L. Soendergaard. An efficient algorithm for the discrete Gabor
% transform using full length windows. IEEE Signal Process. Letters,
% submitted for publication, 2007.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/comp/comp_wfac.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 : Peter L. Soendergaard.
% TESTING: OK
% REFERENCE: OK
L=size(g,1);
R=size(g,2);
N=L/a;
b=L/M;
c=gcd(a,M);
p=a/c;
q=M/c;
d=N/q;
gf=zeros(p,q*R,c,d,assert_classname(g));
% Set up the small matrices
% The w loop is only used for multiwindows, which should be a rare occurence.
% Therefore, we make it the outermost
if p==1
% Integer oversampling
if (c==1) && (d==1) && (R==1)
% --- Short time Fourier transform of single signal ---
% This is used for spectrograms of short signals.
for l=0:q-1
gf(1,l+1,1,1)=g(mod(-l,L)+1);
end;
else
for w=0:R-1
for s=0:d-1
for l=0:q-1
gf(1,l+1+q*w,:,s+1)=g((1:c)+mod(-l*a+s*p*M,L),w+1);
end;
end;
end;
end;
else
% Rational oversampling
for w=0:R-1
for s=0:d-1
for l=0:q-1
for k=0:p-1
gf(k+1,l+1+q*w,:,s+1)=g((1:c)+c*mod(k*q-l*p+s*p*q,d*p*q),w+1);
end;
end;
end;
end;
end;
% dft them
if d>1
gf=fft(gf,[],4);
end;
% Scale by the sqrt(M) comming from Walnuts representation
gf=gf*sqrt(M);
gf=reshape(gf,p*q*R,c*d);
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