1
GATE ECE 2008
+2
-0.6
A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ $$= 1,\,\,h\left[ 1 \right]\,\, = - 1,\,\,h\left[ 2 \right]\,\, = \,2$$, and zero otherwise. The system is given an input sequence $$x\left[ n \right]$$ with $$x\left[ 0 \right]$$ $$= \,x\left[ 2 \right]\, = \,1,$$ and zero otherwise. The number of nonzero samples in the output sequence $$y\left[ n \right]$$, and the value of $$y\left[ 2 \right]$$ are, respectively
A
5, 2
B
6, 2
C
6, 1
D
5, 3
2
GATE ECE 2006
+2
-0.6
A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$= \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The system is
A
linear, stable and invertible.
B
non-linear, stable and non-invertible.
C
linear, stable and non-invertible.
D
linear, unstable and invertible.
3
GATE ECE 2004
+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 $$\alpha$$
4
GATE ECE 2004
+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
$$- 4{\mkern 1mu} {e^{j\,\pi \,n\,/4}}$$
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