1
GATE ECE 2003
+2
-0.6
Let P be linearity, Q be time-invariance, R be causality and S be stability.

A discrete time system has the input-output relationship,

$$y\left( n \right) = \left\{ {\matrix{ {x\left( n \right),} & {n \ge 1} \cr {0,} & {n = 0} \cr {x\left( {n + 1} \right),} & {n \le - 1} \cr } } \right.$$

Where $$x\left( n \right)\,$$ is the input and $$y\left( n \right)\,$$ is the output. The above system has the properties

A
P, S but not Q, R
B
P, Q, S but not R
C
P, Q, R, S
D
Q, R, S but not P
2
GATE ECE 2002
+2
-0.6
If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to
A
$${{ - z} \over {z - 5}}$$ and the system is stable.
B
$${z \over {z - 5}}$$ and the system is stable.
C
$${{ - z} \over {z - 5}}$$ and the system is unstable.
D
$${z \over {z - 5}}$$ and the system is unstable.
3
GATE ECE 1992
+2
-0.6
A linear discrete - time system has the characteristic equation, $${z^3} - 0.81\,\,z = 0.$$ The system
A
is stable.
B
is marginally stable.
C
is unstable.
D
stability cannot be assessed from the given information.
4
GATE ECE 1988
+2
-0.6
Consider the system shown in the Fig.1 below. The transfer function $$Y\left( z \right)/X\left( z \right)$$ of the system is
A
$${{1 + a\,{z^{ - 1}}} \over {1 + b\,{z^{ - 1}}}}$$
B
$${{1 + b\,{z^{ - 1}}} \over {1 + a\,{z^{ - 1}}}}$$
C
$${{1 + a\,{z^{ - 1}}} \over {1 - b\,{z^{ - 1}}}}$$
D
$${{1 - b\,{z^{ - 1}}} \over {1 + a\,{z^{ - 1}}}}$$
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