Consider a graph signal f = [3 , ? 2 , 0 , 1 , 6] T defined on the graph shown in Figure 10.1 . Compute the outputs f1 and f2 of LSI graph filters in cascade, as shown in Figure 10.5, for the following cases:
(a) H1 = 3I?2W+W2 andH2=I + 4W.
(b) H1 = 3I?2L+L2 andH2=I + 4L.
Use the vertex domain as well as the frequency domain methods to find the output graph
signals and verify your results. Also, draw frequency responses of the filters. Can you find an
equivalent filter H for the two filters H1 and H2 in cascade?
(a) The output graph signal is
(b) The output graph signal is
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