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function f=comp_idgt_fac(coef,gf,L,a,M)
%-*- texinfo -*-
%@deftypefn {Function} comp_idgt_fac
%@verbatim
%COMP_IDGT_FAC Full-window factorization of a Gabor matrix.
% Usage: f=comp_idgt_fac(c,g,a,M)
%
% Input parameters:
% c : M x N array of coefficients.
% gf : Factorization of window (from facgabm).
% a : Length of time shift.
% M : Number of frequency shifts.
% Output parameters:
% f : Reconstructed signal.
%
% Do not call this function directly, use IDGT.
% This function does not check input parameters!
%
% If input is a matrix, the transformation is applied to
% each column.
%
% This function does not handle multidimensional data, take care before
% you call it.
%
% 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_idgt_fac.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
% Calculate the parameters that was not specified.
N=L/a;
b=L/M;
R=prod(size(gf))/L;
W=prod(size(coef))/(M*N*R);
N=L/a;
b=L/M;
[c,h_a,h_m]=gcd(a,M);
h_a=-h_a;
p=a/c;
q=M/c;
d=N/q;
ff=zeros(p,q*W,c,d,assert_classname(coef,gf));
C=zeros(q*R,q*W,c,d,assert_classname(coef,gf));
f=zeros(L,W,assert_classname(coef,gf));
% Apply ifft to the coefficients.
%coef=ifft(reshape(coef,M,N*W))*sqrt(M);
coef=ifft(coef)*sqrt(M);
% Set up the small matrices
coef=reshape(coef,M,N,R,W);
if p==1
for rw=0:R-1
for w=0:W-1
for s=0:d-1
for l=0:q-1
for u=0:q-1
C(u+1+rw*q,l+1+w*q,:,s+1)=coef((1:c)+l*c,mod(u+s*q+l,N)+1,rw+1,w+1);
end;
end;
end;
end;
end;
else
% Rational oversampling
for rw=0:R-1
for w=0:W-1
for s=0:d-1
for l=0:q-1
for u=0:q-1
C(u+1+rw*q,l+1+w*q,:,s+1)=coef((1:c)+l*c,mod(u+s*q-l*h_a,N)+1,rw+1,w+1);
end;
end;
end;
end;
end;
end;
% FFT them
if d>1
C=fft(C,[],4);
end;
% Multiply them
for r=0:c-1
for s=0:d-1
CM=reshape(C(:,:,r+1,s+1),q*R,q*W);
GM=reshape(gf(:,r+s*c+1),p,q*R);
ff(:,:,r+1,s+1)=GM*CM;
end;
end;
% Inverse FFT
if d>1
ff=ifft(ff,[],4);
end;
% Place the result
if p==1
for s=0:d-1
for w=0:W-1
for l=0:q-1
f((1:c)+mod(s*M+l*a,L),w+1)=reshape(ff(1,l+1+w*q,:,s+1),c,1);
end;
end;
end;
else
% Rational oversampling
for w=0:W-1
for s=0:d-1
for l=0:q-1
for k=0:p-1
f((1:c)+mod(k*M+s*p*M-l*h_a*a,L),w+1)=reshape(ff(k+1,l+1+w*q,:,s+1),c,1);
end;
end;
end;
end;
end;
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