GSP_FILTER_ANALYSIS - Analysis operator of a gsp filterbank

Usage

coeffs = gsp_filter_analysis(G, fi, signal);
coeffs = gsp_filter_analysis(G, fi, signal, param);

Input parameters

Output parameters

Description

'gsp_filter_analysis(G,fi,signal)' computes the transform coefficients of a signal \(f\), where the atoms of the transform dictionary are generalized translations of each graph spectral filter to each vertex on the graph.

where the columns of \(D\) are \(g_{i,m}=T_i g_m\), and \(T_i\) is a generalized translation operator applied to each filter \(\hat{g}_m(\cdot)\).

Each column of c is the response of the signal to one filter.

Example:

Nf = 5;
param.distribute = 1;
G = gsp_sensor(256);
G = gsp_compute_fourier_basis(G);
paramf.log = 1;
g = gsp_design_warped_translates(G, Nf,paramf);
s = sign(G.U(:,2));
sf = gsp_vec2mat(gsp_filter_analysis(G,g,s),Nf);
paramplot.show_edges = 1;
figure()
subplot(221)
gsp_plot_signal(G,sf(:,2),paramplot);
subplot(222)
gsp_plot_signal(G,sf(:,3),paramplot);
subplot(223)
gsp_plot_signal(G,sf(:,4),paramplot);
subplot(224)
gsp_plot_signal(G,sf(:,5),paramplot);

This code produces the following output:

GSP_DESIGN_WARPED_TRANSLATES: has to compute the spectrum continuous density function approximation

Additional parameters

• param.method : Select the method to be used for the computation. * 'exact' : Exact method using the graph Fourier matrix * 'cheby' : Chebyshev polynomial approximation * 'lanczos' : Lanczos approximation Default: if the Fourier matrix is present: 'exact' otherwise 'cheby'
• param.order : Degree of the Chebyshev approximation Default: 30
• param.grid_order : grid order used to compute quadrature Default: param.order+1
• param.verbose : Verbosity level (0 no log - 1 display warnings) Default: 1