gsp_design_smooth_indicator.m
2cb18aae5832master

gsp_design_smooth_indicator.m
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			function [g]=gsp_design_smooth_indicator(G, a1, a2)
			%GSP_DESIGN_SMOOTH_INDICATOR create a smooth indicator function
			% Usage: g = gsp_design_smooth_indicator(G, a1);
			% g = gsp_design_smooth_indicator(G, a1, a2);
			%
			% Input parameters:
			% G : Graph structure
			% a1 : Start of band cuttoff
			% a2 : End of band cuttoff (default 2*a1)
			%
			% Output parameters
			% g : filter
			%
			% This function design the following filter:
			%
			% / 1 if x < a1
			% g(x) = \| TBD
			% \ 0 if x > a2
			%
			% 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:
			%
			% G = gsp_sensor(100);
			% G = gsp_estimate_lmax(G);
			% g = gsp_design_smooth_indicator(G,0.3,0.4);
			% gsp_plot_filter(G,g);
			%
			%
			% Url: http://lts2research.epfl.ch/gsp/doc/filters/gsp_design_smooth_indicator.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<2
			a1 = 0.25;
			end

			if nargin<3
			a2 = 2*a1;
			end



			if numel(a1)>1
			g = cell(numel(a1),1);
			for ii = 1:numel(a1);
			g{ii} = gsp_design_expwin(G,a1(ii),a2(ii));
			end
			return
			end

			if isstruct(G)
			if ~isfield(G,'lmax')
			% if param.verbose
			fprintf('GSP_DESIGN_HEAT has to compute lmax \n')
			% end
			G = gsp_estimate_lmax(G);
			end
			lmax = G.lmax;
			else
			lmax = G;
			end

			if a1>=a2
			error('GSP_DESIGN_SMOOTH_INDICATOR: a2 has to be bigger than a1!')
			end

			g = @(x) ffin(x/lmax,a1,a2);



			end


			function y=fx(x,a)
			y = exp(-a./x);
			y(x<0)=0;
			end

			function y =gx(x,a)
			y=fx(x,a);
			y = y./(y+fx(1-x,a));
			end

			function y = ffin(x,a1,a2)
			y = gx(1-(x-a1)/(a2-a1),1);
			y(x<a1) = 1;
			end

iCAPs/packages/gspbox/filters/gsp_design_smooth_indicator.m2cb18aae5832master

gsp_design_smooth_indicator.mView Options

iCAPs/packages/gspbox/filters/gsp_design_smooth_indicator.m
2cb18aae5832master

gsp_design_smooth_indicator.m
View Options