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function cout=comp_dgt_walnut(f,gf,a,M)
%-*- texinfo -*-
%@deftypefn {Function} comp_dgt_walnut
%@verbatim
%COMP_DGT_WALNUT First step of full-window factorization of a Gabor matrix.
% Usage: c=comp_dgt_walnut(f,gf,a,M);
%
% Input parameters:
% f : Factored input data
% gf : Factorization of window (from facgabm).
% a : Length of time shift.
% M : Number of channels.
% Output parameters:
% c : M x N*W*R array of coefficients, where N=L/a
%
% Do not call this function directly, use DGT instead.
% This function does not check input parameters!
%
% The length of f and gamma must match.
%
% If input is a matrix, the transformation is applied to
% each column.
%
% This function does not handle the multidim case. Take care before
% calling this.
%
% 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_dgt_walnut.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(f,1);
W=size(f,2);
LR=numel(gf);
R=LR/L;
N=L/a;
[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(f,gf));
if p==1
% --- integer oversampling ---
if (c==1) && (d==1) && (W==1) && (R==1)
% --- Short time Fourier transform of single signal ---
% This is used for spectrograms of short signals.
ff(1,:,1,1)=f(:);
else
for s=0:d-1
for r=0:c-1
for l=0:q-1
ff(1,l+1:q:W*q,r+1,s+1)=f(r+s*M+l*c+1,:);
end;
end;
end;
end;
else
% --- rational oversampling ---
% Set up the small matrices
% The r-loop (runs up to c) has been vectorized
for w=0:W-1
for s=0:d-1
for l=0:q-1
for k=0:p-1
ff(k+1,l+1+w*q,:,s+1)=f((1:c)+mod(k*M+s*p*M-l*h_a*a,L),w+1);
end;
end;
end;
end;
end;
% This version uses matrix-vector products and ffts
% fft them
if d>1
ff=fft(ff,[],4);
end;
C=zeros(q*R,q*W,c,d,assert_classname(f,gf));
for r=0:c-1
for s=0:d-1
GM=reshape(gf(:,r+s*c+1),p,q*R);
FM=reshape(ff(:,:,r+1,s+1),p,q*W);
C(:,:,r+1,s+1)=GM'*FM;
end;
end;
% Inverse fft
if d>1
C=ifft(C,[],4);
end;
% Place the result
cout=zeros(M,N,R,W,assert_classname(f,gf));
if p==1
% --- integer oversampling ---
if (c==1) && (d==1) && (W==1) && (R==1)
% --- Short time Fourier transform of single signal ---
% This is used for spectrograms of short signals.
for l=0:q-1
cout(l+1,mod((0:q-1)+l,N)+1,1,1)=C(:,l+1,1,1);
end;
else
% The r-loop (runs up to c) has been vectorized
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
cout((1:c)+l*c,mod(u+s*q+l,N)+1,rw+1,w+1)=C(u+1+rw*q,l+1+w*q,:,s+1);
end;
end;
end;
end;
end;
end;
else
% Rational oversampling
% The r-loop (runs up to c) has been vectorized
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
cout((1:c)+l*c,mod(u+s*q-l*h_a,N)+1,rw+1,w+1)=C(u+1+rw*q,l+1+w*q,:,s+1);
end;
end;
end;
end;
end;
end;
cout=reshape(cout,M,N*W*R);
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