1
GATE ECE 2008
+2
-0.6
In the following network (Fig .1), the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.
The expression and the region of convergence of the z-transform of the sampled signal are
A
$${{5z} \over {z - {e^{^{ - 5}}}}},\left| z \right| < {e^{ - 5}}$$
B
$${{5z} \over {z - {e^{^{ - 0.05}}}}},\left| z \right| < {e^{ - 0.05}}$$
C
$${{5z} \over {z - {e^{^{ - 0.05}}}}},\left| z \right| > {e^{ - 0.05}}$$
D
$${{5z} \over {z - {e^{^{ - 5}}}}},\left| z \right| < {e^{ - 5}}$$
2
GATE ECE 2008
+2
-0.6
In the following network (Fig.1), the switch is closed at t = 0 and the sampling starts from t=0. The sampling frequency is 10 Hz.

The samples x (n) (n=0, 1, 2,...........) are given by

A
5(1-$${e^{ - 0.05n}}$$)
B
$$5{e^{ - 0.05n}}$$
C
$$5(1 - {e^{ - 5n}})$$
D
$$5{e^{ - 5n}}$$
3
GATE ECE 2007
+2
-0.6
The z-transform X (z) f a sequence x$$\left[ n \right]$$ is given by = $${{0.5} \over {1 - 2{z^{ - 1}}}}$$ . It is given that the region of convergence of X$$\left[ z \right]$$ includes the unit circle. The value of x$$\left[ 0 \right]$$ is
A
-0.5
B
0
C
0.25
D
0.5
4
GATE ECE 1999
+2
-0.6
The z-transform of a signal is given by c(z)=$${1 \over 4}{{{z^{ - 1}}(1 - {z^{ - 4}})} \over {{{(1 - {z^{ - 1}})}^2}}}$$. Its final value is
A
1/4
B
zero
C
1.0
D
infinity
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