1
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
The $$z$$$$-$$ transform of a signal $$x\left[ n \right]$$ is given by $$4{z^{ - 3}} + 3{z^{ - 1}} + 2 - 6{z^2} + 2{z^3}.$$ It is applied to a system, with a transfer function $$H\left( z \right) = 3{z^{ - 1}} - 2.$$ Let the output be $$y(n)$$. Which of the following is true?
A
$$y\left( n \right)$$ is non causal with finite support
B
$$y\left( n \right)$$ is causal with infinite support
C
$$y\left( n \right)$$ $$ = 0;\,|n| > 3$$
D
$$\eqalign{ & {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}} = - {\mathop{\rm Re}\nolimits} {\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}; \cr & {\rm I}m{\left[ {Y\left( z \right)} \right]_{z = {e^{j0}}}}\, = {\rm I}m{\left[ {Y\left( z \right)} \right]_z} = {e^{j0}};\,\, - \pi \le \theta < \pi \cr} $$
2
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha $$ is a real constant $$\left( {\sin \,c\left( x \right) = {{\sin \left( {\pi x} \right)} \over {\pi x}}} \right)$$ is the input to a linear Time invariant system whose impulse response $$h\left( t \right) = \sin c\left( {\beta t} \right)$$ where $$\beta $$ is a real constant. If $$\min \left( {\alpha ,\,\,\beta } \right)$$ denotes the minimum of $$\alpha $$ and $$\beta $$, and similarly $$\max \left( {\alpha ,\,\,\beta } \right)$$ denotes the maximum of $$\alpha $$ and $$\beta $$, and $$K$$ is a constant, which one of the following statements is true about the output of the system?
A
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\min \left( {\alpha ,\,\,\beta } \right)$$
B
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\max \left( {\alpha ,\,\,\beta } \right)$$
C
It will be of the form $$K$$ $$\sin c\left( {\alpha t} \right)$$
D
It cannot be a $$sinc$$ type of signal
3
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ The steady state value of the output of this system for a unit impulse input applied at time instant $$t=1$$ will be
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
4
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
A system with input $$x(t)$$ and output $$y(t)$$ is defined by the input $$-$$ output relation:
$$y\left( t \right) = \int\limits_{ - \infty }^{ - 2t} {x\left( \tau \right)} d\tau .$$ The system will be
A
causal, time $$-$$ invariant and unstable
B
causal, time $$-$$ invariant and stable
C
non $$-$$ causal, time $$-$$ invariant and unstable
D
non $$-$$ causal, time $$-$$ variant and unstable
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