Find ROC of signal
$x (n) = 2^{n} s g n [n]$

\frac{1}{2} < | z | < 2

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|z| > 2

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No common ROC

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|z| < 2

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Solution

The correct option is C No common ROC
$x [n] = 2^{n} s g n (n)$
$s g n n = 2^{n} [u (n) - u (- n)]$
$= 2^{n} u [n] - 2^{n} u [- n]$
$↓$ $↓$
$| z | > 2 | z | < 2$
$∴ N o c o m m o n R O C f o r s i g n a l x [n]$

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