function f=insdgtreal(c,g,a,M,varargin)
%INSDGTREAL Inverse NSDGT for real-valued signals
% Usage: f=insdgt(c,g,a,M,Ls);
%
% Input parameters:
% c : Cell array of coefficients.
% g : Cell array of window functions.
% a : Vector of time positions of windows.
% M : Vector of numbers of frequency channels.
% Ls : Length of input signal.
% Output parameters:
% f : Signal.
%
% insdgt(c,g,a,Ls) computes the inverse non-stationary Gabor transform
% of the input coefficients c.
%
% insdgt is used to invert the functions NSDGT and UNSDGT. Please
% read the help of these functions for details of variables format and
% usage.
%
% For perfect reconstruction, the windows used must be dual windows of the
% ones used to generate the coefficients. The windows can be generated
% using NSGABDUAL or NSGABTIGHT.
%
% See also: nsdgt, nsgabdual, nsgabtight
%
% Demos: demo_nsdgt
%
% References:
% P. Balazs, M. Dörfler, 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.
%
%
% Url: http://ltfat.github.io/doc/nonstatgab/insdgtreal.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% 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 : Florent Jaillet and Nicki Holighaus
% TESTING: TEST_NSDGT
% REFERENCE:
% Last changed 2009-05
if nargin<3
error('%s: Too few input parameters.',upper(mfilename));
end;
if ~isnumeric(a)
error('%s: a must be numeric.',upper(mfilename));
end;
definput.keyvals.Ls=[];
[flags,kv,Ls]=ltfatarghelper({'Ls'},definput,varargin);
timepos=cumsum(a)-a(1);
L=sum(a);
[g,info]=nsgabwin(g,a,M);
if iscell(c)
% ---- invert the non-uniform case ---------
N=length(c); % Number of time positions
W=size(c{1},2); % Number of signal channels
f=zeros(L,W,assert_classname(c{1})); % Initialisation of the result
else
% ---- invert the uniform case ----------------
[M2, N, W]=size(c);
f=zeros(L,W,assert_classname(c)); % Initialisation of the result
if ~info.isuniform
error('%s: M must be a scalar or a constant vector.',upper(mfilename));
end;
M=M(1);
end
for ii = 1:N
Lg = length(g{ii});
gt = g{ii};
% This is an explicit fftshift
idx=[Lg-floor(Lg/2)+1:Lg,1:ceil(Lg/2)];
gt = gt(idx);
win_range = mod(timepos(ii)+(-floor(Lg/2):ceil(Lg/2)-1),L)+1;
if iscell(c)
temp = ifftreal(c{ii},M(ii),1)*M(ii);
idx = mod([M(ii)-floor(Lg/2)+1:M(ii),1:ceil(Lg/2)]-1,M(ii))+1;
else
temp = ifftreal(c(:,ii,:),M,1)*M;
idx = mod([M-floor(Lg/2)+1:M,1:ceil(Lg/2)]-1,M)+1;
end
temp = temp(idx,:);
f(win_range,:) = f(win_range,:) + bsxfun(@times,temp,gt);
end
if ~isempty(Ls)
f = f(1:sum(a),:);
end;