1
GATE ECE 2014 Set 3
Numerical
+1
-0
The input $$- 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the output is -2, then the value of the output at steady state is _____.
2
GATE ECE 2014 Set 3
+2
-0.6
Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements.

S1: The system is stable.
S2: $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$ is independent of t for t > 0.
S3: A non-casual system with the same transfer function is stable.

For the above system,

A
only S1 and S2 are true
B
only S2 and S3 are true
C
only S1 and S3 are true
D
S1, S2 and S3 are true
3
GATE ECE 2014 Set 3
+1
-0.3
For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})} \right| = \,1$$ , for all $$\omega$$. If Re (a) $$\ne$$ 0,$${\mathop{\rm Im}\nolimits} (a) \ne 0$$ then b equals
A
a
B
a*
C
1/a*
D
1/a
4
GATE ECE 2014 Set 3
Numerical
+2
-0
The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with the region of convergence $$\left| z \right| > 2$$. Then, $$x\left[ 2 \right]$$ is ____________________.
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