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 2009
MCQ (Single Correct Answer)
+2
-0.6
A cascade of 3 Linear Time Invariant systems is casual and unstable. From this, we conclude that
A
each system in the cascade is individually casual and unstable
B
at least one system is unstable and atleast one system is casual
C
at least one system is casual and all systems are unstable
D
the majority are unstable and the majority are casual