For a graph signal lying on an N-node directed ring graph, considering the weight matrix as the shift operator, answer the following:
(a) Write down the TV expression for the graph Fourier basis.
(b) Identify and order the graph frequencies.
(c) Compare your results with the conventional frequencies in the DFT.
(a) TV of the eigenvector vk (of the weight matrix) corresponding to the eigenvalue ?k is
and the eigenvectors can be normalized to have unit
`1 norm, we have
(b)
(c) The frequency ordering using the eigenvalues of the weight matrix of the graph is same
as the conventional frequencies in the DFT.
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