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function fr = comp_insdgfb(c,g,shift,Ls,dual)
%-*- texinfo -*-
%@deftypefn {Function} comp_insdgfb
%@verbatim
%COMP_INSDGFB Non-stationary Gabor filterbank synthesis
% Usage: fr = comp_insdgfb(c,g,shift,Ls,dual)
% fr = comp_insdgfb(c,g,shift,Ls)
% fr = comp_insdgfb(c,g,shift)
%
% Input parameters:
% c : Transform coefficients (matrix or cell array)
% g : Cell array of Fourier transforms of the analysis
% windows
% shift : Vector of frequency shifts
% Ls : Original signal length (in samples)
% dual : Synthesize with the dual frame
% Output parameters:
% fr : Synthesized signal (Channels are stored in the
% columns)
%
% Given the cell array c of non-stationary Gabor coefficients, and a
% set of filters g and frequency shifts shift this function computes
% the corresponding non-stationary Gabor filterbank synthesis.
%
% If dual is set to 1 (default), an attempt is made to compute the
% canonical dual frame for the system given by g, shift and the size
% of the vectors in c. This provides perfect reconstruction in the
% painless case, see the references for more information.
%
%
% References:
% P. Balazs, M. Doerfler, F. Jaillet, N. Holighaus, and G. A. Velasco.
% Theory, implementation and applications of nonstationary Gabor frames.
% J. Comput. Appl. Math., 236(6):1481--1496, 2011.
%
% N. Holighaus, M. Doerfler, G. A. Velasco, and T. Grill. A framework for
% invertible, real-time constant-Q transforms. IEEE Transactions on
% Audio, Speech and Language Processing, 21(4):775 --785, 2013.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/comp/comp_insdgfb.html}
%@seealso{cqt, icqt, erblett, ierblett}
%@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
% Date: 10.04.13
%% Check input arguments
if nargin < 5
dual = 1;
if nargin < 3
error('Not enough input arguments');
end
end
if iscell(c) == 0 % If matrix format coefficients were used, convert to
% cell
[M,N,CH] = size(c);
c = reshape(c,N*M,CH);
c = mat2cell(c,M*ones(N,1),CH);
else
N = length(c);
CH = size(c{1},2);
M = cellfun(@(x) size(x,1),c);
end
timepos = cumsum(shift); % Calculate positions from shift vector
NN = timepos(end); % Reconstruction length before truncation
timepos = timepos-shift(1); % Adjust positions
fr = zeros(NN,CH,assert_classname(c{1},g{1})); % Initialize output
if nargin < 4
Ls = NN; % If original signal length is not given do not truncate
end
if dual == 1 % Attempt to compute canonical dual frame
g = nsgabdual(g,shift,M,Ls);
end
%% The overlap-add procedure including multiplication with the synthesis
% windows
if numel(M) == 1
M = M*ones(N,1);
end
for ii = 1:N
Lg = length(g{ii});
win_range = mod(timepos(ii)+(-floor(Lg/2):ceil(Lg/2)-1),NN)+1;
temp = fft(c{ii})*M(ii);
temp = temp(mod([end-floor(Lg/2)+1:end,1:ceil(Lg/2)]-1,M(ii))+1,:);
fr(win_range,:) = fr(win_range,:) + ...
bsxfun(@times,temp,g{ii}([Lg-floor(Lg/2)+1:Lg,1:ceil(Lg/2)]));
end
fr = ifft(fr);
fr = fr(1:Ls,:); % Truncate the signal to original length (if given)
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