The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $x [n] = (2.0)^{| n |},$ $- \infty < n < + \infty$ then the ROC of its z-transform is represented by

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Solution

Given, $x [n] = (2.0)^{| n |} - \infty < n < n + \infty$

$= 2^{n} u [n] + {(\frac{1}{2})}^{n} u [- n - 1]$

$R O C : | Z | > 2 a n d | Z | < \frac{1}{2}$

$∴$ No ROC.

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