1
GATE ECE 2009
MCQ (Single Correct Answer)
+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
$$2 < \left| {z\,} \right| < 3$$
2
GATE ECE 2006
MCQ (Single Correct Answer)
+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
$${1 \over 3} < \left| {z\,} \right| < {2 \over 3}$$
3
GATE ECE 2005
MCQ (Single Correct Answer)
+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
$${6 \over 5} < \left| {z\,} \right| < \infty $$
4
GATE ECE 2004
MCQ (Single Correct Answer)
+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
$$ - {(0.2)^n}\,u\left[ { - n - 1} \right]$$
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