If x1[n] x1(z) with ROC = R1 and x2[n] x2(z) with ROC = R2 then ROC for x1[n] +

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Home Aptitude

Question
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 R_i ? Region of convergence and x₁[n] and x₂[n] are causal).
Options
A. R₁ ? R₂
B. R₁ ? R₂
C. (R₁ ? R₂) ? (R₁)
D. (R₁ ? R₂) ? (R₁)

Correct Answer

R₁ ? R₂

Explanation

R₁ ? R₂, Suppose R₁ for x₁(n) be

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 ______

Then ROC for x₁(n) + x₂(n)

R₁ ? R₂ (R₁ < R₂)

Then ROC for x₁(n) + x₂(n)

R₁ ? R₂(R₁ < R₂)

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 ______