GSP_FILTER_SYNTHESIS - Synthesis operator of a gsp filterbank

Usage

s = gsp_filter_synthesis(G, filters, c);
s = gsp_filter_synthesis(G, filters, c, param);

Input parameters

Output parameters

Description

'gsp_filter_synthesis(G,filters,c)' computes the synthesis operator for coefficient \(c\), 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 = 4;
G = gsp_sensor(30);
G = gsp_estimate_lmax(G);
G = gsp_estimate_lmax(G);
g = gsp_design_mexican_hat(G, Nf);
f = zeros(G.N,1);
f(1) = 1;
f = G.L^2*f;
ff = gsp_filter_analysis(G,g,f);
f2 = gsp_filter_synthesis(G,g,ff);
paramplot.show_edges = 1;
figure()
subplot(211)
gsp_plot_filter(G,g)
subplot(223)
gsp_plot_signal(G,f,paramplot);
subplot(224)
gsp_plot_signal(G,f2,paramplot);

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.verbose : Verbosity level (0 no log - 1 display warnings) (default 1).