Multiple choice

If the region of convergence of x1 [n] + x2 [n] is $\dfrac{1}{3} \lt |z| \lt \dfrac{2}{3}$, then the region of convergence of xn [n] - x2 [n] includes

  1. $\dfrac{1}{3} \lt |z| \lt 3$
  2. $\dfrac{2}{3} \lt |z| \lt 3$
  3. $\dfrac{3}{2} \lt |z| \lt 3$
  4. $\dfrac{1}{3} \lt |z| \lt \dfrac{2}{3}$
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D Correct answer
Explanation

The ROC of addition or subtraction of two functions $x_1(n) \ and \ x_2(n)$ is $R_1 \cap R_2$. We have been given ROC of addition of two function and has been asked ROC of subtraction of two function. It will be same.

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