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iCAPs_v2/packages/gspbox/operators/gsp_igft.m
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gsp_igft.m
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function [f] = gsp_igft(G,f_hat)
%GSP_IGFT Inverse graph Fourier transform
% Usage: f = gsp_igft(G,f_hat);
%
% Input parameters:
% G : Graph or Fourier basis
% f_hat : Signal
% Output parameters:
% f : Inverse graph Fourier transform of f_hat*
%
% 'gsp_igft(G,f_hat)' computes a graph Fourier transform of the signal
% f_hat with respect to the Fourier basis of the graph G: G.U.
% Alternatively, one can provide directly the Fourier basis instead of
% the graph G.
%
% f = U * f_hat
%
% To compute the Fourier basis of a graph G, you can use the function:
%
% G = gsp_compute_fourier_basis(G);
%
% Example:
%
% N = 30;
% G = gsp_sensor(N);
% G = gsp_compute_fourier_basis(G);
% f_hat = zeros(N,1);
% f_hat(5) = 1;
% f = gsp_igft(G,f_hat);
% gsp_plot_signal(G,f);
%
% See also: gsp_gft, gsp_gwft, gsp_compute_fourier_basis
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/operators/gsp_igft.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% 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/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% Author : Nathanael Perraudin, David I Shuma
% Date:
s = size(f_hat);
if ~isnumeric(G);
if ~gsp_check_fourier(G)
error(['GSP_IGFT: You need first to compute the Fourier basis\n',...
'You can do it with the function gsp_compute_fourier_basis']);
end
% U = G.U;
f=reshape(G.U * reshape(f_hat,G.N,[]),s);
else
% U = G;
f=reshape(G * reshape(f_hat,G.N,[]),s);
end
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