Consider the sequence $x [n] = a^{n} u [n] + b^{n} u [n]$ , where u[n] denotes the unit-step sequence and 0 < |a| < |b| < 1. The region of convergence (ROC) of the z-transform of x[n] is

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Solution

Given, $x [n] = a^{n} u [n] + b^{n} u [n]$

$Also given, 0 < |a| < |b| < 1$

$R O C = (| z | > | a |) a n d (| z | > | b |)$

$R O C = | z | > | b |$

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