Consider a graph signal h defined on an N-node r-regular graph. Let the signal value at a node i be the degree of node i. Answer the following:
(a) Calculate the convolution product h?f, where f is an arbitrary signal defined on the
graph.
(b) Prove that the generalized translation operator has no effect on h.
(c) Prove that the resulting signal, when modulated to frequency ? j , is localized around
frequency
(a)
(b)
That is, the generalized translation operator has no effect on h.
(c)
That is, when the signal h is modulated to frequency
?j , is localized around frequency ?j
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