GSP_GFT - Graph Fourier transform

Usage

f_hat=gsp_gft(G,f);

Input parameters

`G`	Graph or Fourier basis
`f`	f (signal)

Output parameters

f_hat

Graph Fourier transform of f

Description

'gsp_gft(G,f)' computes a graph Fourier transform of the signal \(f\) with respect to the Fourier basis of the graph G: G.U. Alternatively, one can provide directly the Fourier basis instead of the graph G.

\begin{equation*} \hat{f}(\lambda_{\ell})=\langle f , u_{\ell} \rangle \end{equation*}

To compute the Fourier basis of a graph G, you can use the function:

G = gsp_compute_fourier_basis(G);

Example:

N = 30;
G = gsp_sensor(N);
G = gsp_compute_fourier_basis(G);
f = sin((1:N)'*2*pi/N);
fhat = gsp_gft(G,f);
gsp_plot_signal_spectral(G,fhat);