Home > sgwt_toolbox > sgwt_cheby_coeff.m

sgwt_cheby_coeff

PURPOSE ^

sgwt_cheby_coeff : Compute Chebyshev coefficients of given function

SYNOPSIS ^

function c=sgwt_cheby_coeff(g,m,N,arange)

DESCRIPTION ^

 sgwt_cheby_coeff : Compute Chebyshev coefficients of given function

 function c=sgwt_cheby_coeff(g,m,N,arange)

 Inputs:
 g - function handle, should define function on arange
 m - maximum order Chebyshev coefficient to compute
 N - grid order used to compute quadrature (default is m+1)
 arange - interval of approximation (defaults to [-1,1] )
 
 Outputs:
 c - array of Chebyshev coefficients, ordered such that c(j+1) is 
 j'th Chebyshev coefficient

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % sgwt_cheby_coeff : Compute Chebyshev coefficients of given function
0002 %
0003 % function c=sgwt_cheby_coeff(g,m,N,arange)
0004 %
0005 % Inputs:
0006 % g - function handle, should define function on arange
0007 % m - maximum order Chebyshev coefficient to compute
0008 % N - grid order used to compute quadrature (default is m+1)
0009 % arange - interval of approximation (defaults to [-1,1] )
0010 %
0011 % Outputs:
0012 % c - array of Chebyshev coefficients, ordered such that c(j+1) is
0013 % j'th Chebyshev coefficient
0014 
0015 % This file is part of the SGWT toolbox (Spectral Graph Wavelet Transform toolbox)
0016 % Copyright (C) 2010, David K. Hammond.
0017 %
0018 % The SGWT toolbox is free software: you can redistribute it and/or modify
0019 % it under the terms of the GNU General Public License as published by
0020 % the Free Software Foundation, either version 3 of the License, or
0021 % (at your option) any later version.
0022 %
0023 % The SGWT toolbox is distributed in the hope that it will be useful,
0024 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0025 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0026 % GNU General Public License for more details.
0027 %
0028 % You should have received a copy of the GNU General Public License
0029 % along with the SGWT toolbox.  If not, see <http://www.gnu.org/licenses/>.
0030 
0031 function c=sgwt_cheby_coeff(g,m,N,arange)
0032   if ~exist('N','var')
0033     N=m+1;
0034   end
0035   if ~exist('arange','var')
0036       arange=[-1, 1];
0037   end
0038   a1=(arange(2)-arange(1))/2;
0039   a2=(arange(2)+arange(1))/2;
0040   for j=1:m+1
0041     c(j)=sum (g(a1* cos( (pi*((1:N)-0.5))/N) + a2).*cos(pi*(j-1)*((1:N)-.5)/N) )*2/N;
0042   end
0043

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