1
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n \right] + \beta x\left[ {n - 1} \right].$$ The system is stable only if
A
$$\left| \alpha \right| = 2,\,\left| \beta \right| < 2$$
B
$$\left| \alpha \right| > 2,\,\left| \beta \right| > 2$$
C
$$\left| \alpha \right| < 2$$, any value of $$\beta $$
D
$$\left| \beta \right| < 2,$$ any value of $$\alpha $$
2
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as
$$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} & {n = 1, - 1} \cr {4\sqrt 2 ,} & {n = 2, - 2} \cr {0,} & {otherwise} \cr } } \right.$$

If the input to the above system is the sequence $${e^{j\pi n/4}},$$ then the output is

A
$$4\sqrt 2 \,{\mkern 1mu} {e^{j\,\pi \,n\,\,/\,4}}$$
B
$$4\sqrt 2 \,{\mkern 1mu} {e^{ - j\,\pi \,n\,/4}}$$
C
$$4{\mkern 1mu} {e^{j\,\pi \,n\,/4}}$$
D
$$ - 4{\mkern 1mu} {e^{j\,\pi \,n\,/4}}$$
3
GATE ECE 2003
MCQ (Single Correct Answer)
+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
4
GATE ECE 2002
MCQ (Single Correct Answer)
+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.
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