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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).
R1 ∩ R2
R1 ∪ R2
(R1 ∪ R2) ∩ (R1)
(R1 ∩ R2) ∪ (R1)
Correct Answer:
R1 ∩ R2
Explanation:
R
1
∩ R
2
, Suppose R
1
for
x
1
(
n
) be
Then ROC for
x
1
(
n
) +
x
2
(
n
)
R
1
∩ R
2
(R
1
< R
2
)
Then ROC for
x
1
(
n
) +
x
2
(
n
)
R
1
∩ R
2
(R
1
< R
2
)
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