1
GATE EE 2009
MCQ (Single Correct Answer)
+1
-0.3
A linear Time Invariant system with an impulse response $$h(t)$$ produces output $$y(t)$$ when input $$x(t)$$ is applied. When the input $$x\left( {t - \tau } \right)$$ is applied to a system with response $$h\left( {t - \tau } \right)$$, the output will be
A
$$y\left( t \right)$$
B
$$y\left( {2\left( {t - \tau } \right)} \right)$$
C
$$y\left( {t - \tau } \right)$$
D
$$y\left( {t - 2\tau } \right)$$
2
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}
3
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
The Fourier Series coefficients, of a periodic signal $$x\left( t \right),$$ expressed as $$x\left( t \right) = \sum {_{k = - \infty }^\infty {a_k}{e^{j2\pi kt/T}}}$$ are given by
$${a_{ - 2}} = 2 - j1;\,\,{a_{ - 1}} = 0.5 + j0.2;\,\,{a_0} = j2;$$
$${a_1} = 0.5 - j0.2;\,\,{a_2} = 2 + j1;\,\,$$ and
$${a_k} = 0;$$ for $$|k|\,\, > 2.$$

Which of the following is true?

A
$$x(t)$$ has finite energy because only finitely many coefficients are non $$-$$ zero
B
$$x(t)$$ has zero average value because it is periodic
C
the imaginary part of $$x(t)$$ is constant
D
The real part of $$x(t)$$ is even
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