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Discussion :: Exam Questions Papers - Exam Paper 1 (Q.No.28)

28. 

If x1[n] x1(z) with ROC = R1 and x2[n] x2(z) with ROC = R2 then ROC for x1[n] + x2[n] will be __________ (where Ri → Region of convergence and x1[n] and x2[n] are causal).
[A]. R1 ∩ R2
[B]. R1 ∪ R2
[C]. (R1 ∪ R2) ∩ (R1)
[D]. (R1 ∩ R2) ∪ (R1)

Answer: Option A

Explanation:

R1 ∩ R2, Suppose R1 for x1(n) be

Then ROC for x1(n) + x2(n)

R1 ∩ R2 (R1 < R2)

Then ROC for x1(n) + x2(n)

R1 ∩ R2(R1 < R2)

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