(a) Figure shows two periodic sequences, x 1 n and x 2 n , with period N 7 Find a sequence y 1 n whose DFS is equal to the product of the DFS of x 1 n and the DFS of x 2 n , i e , Y 1 k X 1 k X 2 k (b) Figure shows a periodic sequence x 3 n with period N 7 Find a sequence y 2 n whose DFS is equal to the product of the DFS of x 1 n and the DFS of x 3 n , i e , Y 2 k X 1 k X 3 k Part A In 6 7 5 3 i012 3 4 5 6 7 5 3 1 0 1 2 3 4 5 6 Part B LLI I ,L I 7 5 3 101 2 3 4 5 6 2

Question: (a) Figure shows two periodic sequences, x 1 [n] and x 2 [n], with period N = 7. Find a sequence y 1 [n] whose

(a) Figure shows two periodic sequences, x₁[n] and x₂[n], with period N = 7. Find a sequence y₁[n] whose DFS is equal to the product of the DFS of x₁[n] and the DFS of x₂[n], i.e.,?

Y₁[k] = X₁[k] X₂[k].

(b) Figure shows a periodic sequence x₃[n] with period N = 7. Find a sequence y₂[n] whose DFS is equal to the product of the DFS of x₁[n] and the DFS of x₃[n], i.e.,?

Y₂[k] = X₁[k] X₃[k].

Part A In] 6. -7 -5 -3 -i012 3 4 5 6

Part A In] 6. -7 -5 -3 -i012 3 4 5 6 ... -7 -5 -3 -1 0 1 2 3 4 5 6 Part B LLI...I.,L...I.. -7 -5 -3 -101 2 3 4 5 6 2.

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