answer the question below:
(a)
(b) A signal
f = [3,0,2,4,0,1,2,3, 5] Tis defined on the graph
G as shown in Figure 10.10.
The edge weights a and b are unknown. Consider two polynomial filters
where
L is the directed Laplacian matrix (in-degree).
(i) What is the sum of the elements of each row of H1 and H2?
(ii) For filter H1, compute the filtered output at nodes 1 and 2. You should not compute
the full filter matrix for finding output at a single node. Find only the corresponding
row of the filter.
(iii) For filter H2, compute the filtered output at nodes 1 and 3. You should not compute
the full filter matrix for finding output at a single node. Find only the corresponding
row of the filter.
(iv) For filter H1, if the values of
(b)
(i) Since each row of the directed Laplacian sum to zero. Therefore, the the sum of the ele-
ments of each row of a filter is the coefficient of the identity term. For, filter H1, the sum is 3 and for filter H2, the sum is 1.
(ii) -21 and 8.
(iii) -47 and 5.
(iv) a = 4 and b = 6.
(v) Filter H1:
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