Multiple choice

If x[n]=(1/3)| n | - (1/2)n u[n], then the region of convergence (ROC) of its Z-transform in the z- Plane will be Z - plane will be

  1. $\dfrac{1}{3}$<$\left | z \right|$< 3
  2. $\dfrac{1}{3}$<$\left | z \right|$< $\dfrac{1}{2}$
  3. $\dfrac{1}{2}$<$\left | z \right|$< 3
  4. $\dfrac{1}{3}$<$\left | z \right|$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

x[n] = (1/3)^|n| - (1/2)^n u[n] has two components. For (1/3)^|n| (two-sided): ROC is 1/3 < |z| < 3. For (1/2)^n u[n](right-sided, causal): ROC is |z| > 1/2. The overall ROC is the INTERSECTION: (1/2, 3) since we need both components to converge. Therefore ROC is 1/2 < |z| < 3, which matches option C.

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