1
GATE ECE 2010
+1
-0.3
Consider the z-transform
X(z)=5$${z^2} + 4{z^{ - 1}} + 3;0 < \left| z \right| < \infty$$.

The inverse z - transform x$$\,\left[ n \right]$$ is

A
$$5\,\delta [n + 2] + 3\,\delta {\rm{\;}}[n]{\mkern 1mu} + 4\delta [n - 1]$$
B
$$5\,\delta [n - 2] + 3\,\delta [n] + 4\,\delta [n + 1]$$
C
$$5\,u[n + 2] + 3\,u[n]{\mkern 1mu} + 4\,u[n - 1]$$
D
$$5\,u[n - 2] + 3\,u[n]{\mkern 1mu} + 4\,u[n + 1]$$
2
GATE ECE 2009
+1
-0.3
The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is
A
$${1 \over 3} < \left| {z\,} \right| < {1 \over 2}$$
B
$$\left| {z\,} \right| > {1 \over 2}$$
C
$$\left| {z\,} \right| < {1 \over 2}$$
D
$$2 < \left| {z\,} \right| < 3$$
3
GATE ECE 2006
+1
-0.3
If the region of convergence of $${x_1}\left[ n \right]$$ + $${x_2}\left[ n \right]$$ is 1/3< $$\left| {z\,} \right|$$<2/3, then the region of convergence of $${x_1}\left[ n \right]$$ - $${x_2}\left[ n \right]$$ includes
A
$${1 \over 3} < \left| {z\,} \right| < 3$$
B
$${2 \over 3} < \left| {z\,} \right| < 3$$
C
$${3 \over 2} < \left| {z\,} \right| < 3$$
D
$${1 \over 3} < \left| {z\,} \right| < {2 \over 3}$$
4
GATE ECE 2005
+1
-0.3
The region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u(n) - {\left( {{6 \over 5}} \right)^n}u( - n - 1)$$ must be
A
$$\left| {z\,} \right| < {5 \over 6}$$
B
$$\left| {z\,} \right| > {6 \over 5}$$
C
$${5 \over 6} < \left| {z\,} \right| < {6 \over 5}$$
D
$${6 \over 5} < \left| {z\,} \right| < \infty$$
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