1
GATE ECE 2017 Set 1
+1
-0.3
Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as
$$y\left[ n \right]\, = \left\{ {\matrix{ {n\left| {x\left[ n \right]} \right|,} & {for\,\,0 \le n \le 10} \cr {x\left[ n \right] - x\left[ {n - 1} \right],} & {otherwise,} \cr } } \right.$$

Which one of the following statements is true about the system?

A
It is causal and stable
B
It is causal but not stable
C
It is not causal but stable
D
It is neither causal nor stable
2
GATE ECE 2011
+1
-0.3
A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is
A
stable and causal.
B
causal but not stable.
C
stable but not causal.
D
unstable and non causal.
3
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
$$\delta \left[ {n - 1} \right]\delta \left[ {n - 2} \right]$$
4
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.
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