1
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
$${1 \over 3} < \left| {z\,} \right| < {2 \over 3}$$
2
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
$${6 \over 5} < \left| {z\,} \right| < \infty$$
3
GATE ECE 2004
+1
-0.3
The z transform of a system is
H(z) = $${z \over {z - 0.2}}$$ .
If the ROC is $$\left| {z\,} \right|$$ < 0.2, then the impulse response of the system is
A
$${(0.2)^n}\,u\left[ n \right]$$
B
$${(0.2)^n}\,u\left[ { - n - 1} \right]$$
C
$$- {(0.2)^n}\,u\left[ n \right]$$
D
$$- {(0.2)^n}\,u\left[ { - n - 1} \right]$$
4
GATE ECE 2001
+1
-0.3
The region of convergence of the z- transform of a unit step function is
A
$$\left| {z\,} \right| > 1$$
B
$$\left| {z\,} \right| < 1$$
C
(Real part of z )> 0
D
(Real part of z )< 0
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