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iCAPs/packages/gspbox/filters/gsp_jtv_design_diffusion.m
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gsp_jtv_design_diffusion.m
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function [g,filtertype] = gsp_jtv_design_diffusion(G,tau,param)
%GSP_JTV_DESIGN_DIFFUSION Design a diffusion time-vertex filter
% Usage: [g,ft] = gsp_jtv_design_diffusion(G);
% [g,ft] = gsp_jtv_design_diffusion(G,tau);
% [g,ft] = gsp_jtv_design_diffusion(G,tau,param);
%
% Input parameters:
% G : Time-Vertex graph structure
% tau : Diffusivity parameter (default 1)
% param : Struct of optional paramenter
%
% Output parameters
% g : Cell array of time-vertex filters
% filtertype : Filter domain: ts
%
% Design a diffusion time-vertex filter
%
% Additional parameters
% ---------------------
%
% param.verbose*: verbosity level. 0 no log - 1 display warnings.
% (default 1)
% param.normalize : Normalize the kernel
%
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/filters/gsp_jtv_design_diffusion.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 : Francesco Grassi
% Date : July 2016
if nargin < 3
param = struct;
end
if nargin<2
tau=1;
end
if ~isfield(param,'verbose'), param.verbose = 1; end
if ~isfield(param,'normalize'), param.normalize = 0; end
if numel(tau)>1
Nf = numel(tau);
g = cell(Nf,1);
for ii = 1:Nf
[g{ii},filtertype] = gsp_jtv_design_diffusion(G,tau(ii),param);
end
return
end
if isstruct(G)
if ~isfield(G,'lmax')
if param.verbose
warning('GSP_JTV_DESIGN_DIFFUSION has to compute lmax')
end
G = gsp_estimate_lmax(G);
end
lmax = G.lmax;
if ~gsp_check_jtv(G)
error('GSP_JTV_DESIGN_DIFFUSION need the time dimension. Use GSP_JTV_GRAPH');
end
T = G.jtv.T;
fs = G.jtv.fs;
else
lmax = G;
end
if param.normalize
filter_norm = -psi(1) + log(2*tau*T/fs) + expint(2*tau*T/fs);
g = @(x,t) (t<(T/fs)).*(t>=0).*exp(-tau*abs(t).*x/(lmax*fs))/filter_norm;
else
g = @(x,t) (t<(T/fs)).*(t>=0).*exp(-tau*abs(t).*x/(lmax*fs));
end
filtertype = 'ts';
end
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