1
GATE ECE 2016 Set 3
+2
-0.6
A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrelation function of $$X(t)$$ is $${R_x}\left( \tau \right),$$ then the autocorrelation function $${R_x}\left( \tau \right),$$ of the output $$Y(t)$$ is equal to
A
$$2{R_X}\left( \tau \right) + {R_X}\left( {\tau - {T_0}} \right) + {R_X}\left( {\tau + {T_0}} \right)$$
B
$$2{R_X}\left( \tau \right) - {R_X}\left( {\tau - {T_0}} \right) - {R_X}\left( {\tau + {T_0}} \right)$$
C
$$2{R_X}\left( \tau \right) + 2{R_X}\left( {\tau - 2{T_0}} \right)$$
D
$$2{R_X}\left( \tau \right) - 2{R_X}\left( {\tau - 2{T_0}} \right)$$
2
GATE ECE 2016 Set 1
+2
-0.6
An antenna pointing in a certain direction has a noise temperature of 50K. The ambient temperature is 290K. The antenna is connected to a pre-amplifier that has a noise figure of 2dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature Te for the amplifier and the noise power Pao at the output of the preamplifier, respectively, are
A
$${T_e} = 169.36K\,\,\,$$ and $${P_{ao}} = 3.73 \times {10^{ - 10}}\,\,W$$
B
$${T_e} = 170.8K\,\,\,$$ and $${P_{ao}} = 4.56 \times {10^{ - 10}}\,\,W$$
C
$${T_e} = 182.5K\,\,\,$$ and $${P_{ao}} = 3.85 \times {10^{ - 10}}\,\,W$$
D
$${T_e} = 160.62K\,\,\,$$ and $${P_{ao}} = 4.6 \times {10^{ - 10}}\,\,W$$
3
GATE ECE 2015 Set 2
+2
-0.6
A zero mean white Gaussian noise having power spectral density $${{{N_0}} \over 2}$$ is passed through an $$LTI$$ filter whose impulse response $$h(t)$$ is shown in the figure. The variance of the filtered noise at $$t = 4$$ is
A
$${3 \over 2}{A^2}{N_0}$$
B
$${3 \over 4}{A^2}{N_0}$$
C
$${A^2}{N_0}$$
D
$${1 \over 2}{A^2}{N_0}$$
4
GATE ECE 2015 Set 2
+2
-0.6
$$\mathop {\left\{ {{X_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty }$$ is an independent and identically distributed (i.i.d) random process with $${X_n}$$ equally likely to be $$+1$$ or $$-1$$. $$\mathop {\left\{ {{Y_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } \,$$ is another random process obtained as $${Y_n} = {X_n} + 0.5{X_{n - 1}}.\,\,\,$$
The autocorrelation function of $$\mathop {\left\{ {{Y_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty }$$, denoted by $${r_y}\left[ K \right],$$ is
A
B
C
D
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