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iCAPs/packages/gspbox/filters/gsp_design_expwin.m
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gsp_design_expwin.m
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function [g]=gsp_design_expwin(G, bmax, a)
%GSP_DESIGN_EXPWIN create an expwin window of lenth N with parameter a
% Usage: g = gsp_design_expwin(G);
% g = gsp_design_expwin(G, bmax);
% g = gsp_design_expwin(G, bmax, a);
%
% Input parameters:
% G : Graph structure
% bmax : Maximum relative band (default 0.2)
% a : Slope parameter (default 1).
%
% Output parameters
% g : filter
%
% This function design the following filter:
%
% g(x) = s( (1-x) / bmax /lmax )
%
% where s(x) is the step function
%
% / 0 if x < -1
% s(x) = | exp(-a/x) / ( exp(-a/x) + exp(-a/(1-x)) ) if x in [-1, 1]
% \ 1 if x > 1
%
% It use a clever exponential construction to obtain a infinitely
% differentiable function that is band limited!
%
% This function will compute the maximum eigenvalue of the laplacian. To
% be more efficient, you can precompute it using:
%
% G = gsp_estimate_lmax(G);
%
% Example:
%
% Nf = 4;
% G = gsp_sensor(100);
% G = gsp_estimate_lmax(G);
% g = gsp_design_expwin(G);
% gsp_plot_filter(G,g);
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/filters/gsp_design_expwin.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
% Date : 18 December 2014
if nargin<3
a = 1;
end
if nargin<2
bmax = 0.2;
end
if numel(bmax)>1
g = cell(numel(bmax),1);
for ii = 1:numel(bmax);
g{ii} = gsp_design_expwin(G,bmax(ii),a);
end
return
end
if isstruct(G)
if ~isfield(G,'lmax')
% if param.verbose
fprintf('GSP_DESIGN_EXPWIN has to compute lmax \n')
% end
G = gsp_estimate_lmax(G);
end
lmax = G.lmax;
else
lmax = G;
end
g = @(x) gsp_smooth_downstep(x/bmax/lmax, a , 1);
end
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