1
GATE ECE 2010
+2
-0.6
A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$.

Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = $${e^{ - 2t}}$$ u(t) is given by

A
$$({e^t} - {e^{3t}})\,u(t)$$
B
$$({e^{ - t}} - {e^{ - 3t}})\,u(t)$$
C
$$({e^{ - t}} + {e^{ - 3t}})\,u(t)$$
D
$$({e^t} + {e^{3t}})\,u(t)$$
2
GATE ECE 2010
+1
-0.3
Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}\left[ n \right]\, = \delta \left[ {n - 2} \right]$$ are connected in cascade. The overall impulse response of the cascaded system is
A
$$\delta \left[ {n - 1} \right] + \delta \left[ {n - 2} \right]$$
B
$$\delta \left[ {n - 4} \right]$$
C
$$\delta \left[ {n - 3} \right]$$
D
$$\delta \left[ {n - 1} \right]\delta \left[ {n - 2} \right]$$
3
GATE ECE 2010
+2
-0.6
The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$

Consider the following statements:
S1: The system is stable and causal for $$ROC:\,\,\,\left| z \right| > \,1/2$$
S2: The system is stable but not causal for $$ROC:\,\,\,\left| z \right| < \,1/4$$
S3: The system is neither stable nor causal for $$ROC:\,\,1/4\, < \,\left| z \right| < \,{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}$$

Which one of the following statements is valid?

A
Both S1 and S2 are true
B
Both S2 and S3 are true
C
Both S1 and S3 are true
D
S1, S2 and S3 are all true
4
GATE ECE 2010
+1
-0.3
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is
A
B
C
D
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