1
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
$$\delta \left[ {n - 1} \right]\delta \left[ {n - 2} \right]$$
2
GATE ECE 2004
+1
-0.3
The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$= u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {n - 7} \right],$$ where $$u\left[ n \right]$$ is the unit step sequence. The above system is
A
stable but not causal.
B
stable and causal.
C
causal but unstable.
D
unstable and not causal.
3
GATE ECE 2003
+1
-0.3
A sequence $$x\left( n \right)$$ with the $$z$$-transform $$X\left( z \right)$$ $$= {z^4} + {z^2} - 2z + 2 - 3{z^{ - 4}}$$ is applied as an input to a linear, time-invariant system with the impulse response $$h\left( n \right) = 2\delta \left( {n - 3} \right)$$
where $$\matrix{ {\delta \left( n \right) = 1,} & {n = 0} \cr {0,} & {otherwise} \cr }$$

The output at $$n = 4$$ is
A
-6
B
zero
C
2
D
-4
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