The ROC of z-transform of the discrete time sequencexn - 13 nun- 12 n u-n-1 is

X(n) = (1/3)^n u(n) nbsp;(1/2)^n u( n 1) (1/3)^n u(n) is right sided signal so ROC will be |z| gt; 1/3 ...(i) (1/2)^n nbsp;u( n 1) is left sided si ...

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Basics of Z Transform

The ROC of z-...

Question

The ROC of z-transform of the discrete time sequence
$x (n) = {(\frac{1}{3})}^{n} u (n) - {(\frac{1}{2})}^{n} u (- n - 1)$ is

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Solution

$x (n) = (1 / 3)^{n} u (n) - (1 / 2)^{n} u (- n - 1)$

$(1/3)^{n} u(n) is right sided signal so ROC will be |z| > 1/3 ...(i)$

$- (1/2)^{n} u(-n-1) is left sided signal so ROC will be |z| < 1/2 ...(ii)$

$from (i) and (ii) we see that ROC of the function will be$

$1 / 3 < | z | < 1 / 2$

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The ROC of z-transform of the discrete time sequence x(n)=(13)nu(n)−(12)nu(−n−1) is

x(n)=(1/3)nu(n)−(1/2)nu(−n−1) (1/3)n u(n) is right sided signal so ROC will be |z| > 1/3 ...(i) - (1/2)n u(-n-1) is left sided signal so ROC will be |z| < 1/2 ...(ii) from (i) and (ii) we see that ROC of the function will be 1/3<|z|<1/2

The ROC of z-transform of the discrete time sequence
$x (n) = {(\frac{1}{3})}^{n} u (n) - {(\frac{1}{2})}^{n} u (- n - 1)$ is

$x (n) = (1 / 3)^{n} u (n) - (1 / 2)^{n} u (- n - 1)$

$(1/3)^{n} u(n) is right sided signal so ROC will be |z| > 1/3 ...(i)$

$- (1/2)^{n} u(-n-1) is left sided signal so ROC will be |z| < 1/2 ...(ii)$

$from (i) and (ii) we see that ROC of the function will be$

$1 / 3 < | z | < 1 / 2$