GSP_IGFT - Inverse graph Fourier transform

Usage

f = gsp_igft(G,f_hat);

Input parameters

`G`	Graph or Fourier basis
`f_hat`	Signal

Output parameters

`f`	Inverse graph Fourier transform of f_hat

Description

'gsp_igft(G,f_hat)' computes a graph Fourier transform of the signal f_hat 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_hat = zeros(N,1);
f_hat(5) = 1;
f = gsp_igft(G,f_hat);
gsp_plot_signal(G,f);