1
GATE ECE 2016 Set 2
Numerical
+2
-0
An information source generates a binary sequence $$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$ can take one of the two possible values −1 and +1 with equal probability and are statistically independent and identically distributed. This sequence is pre-coded to obtain another sequence $$\left\{ {{\beta _n}} \right\},$$ as $${\beta _n} = {\alpha _n} + k{\mkern 1mu} {\alpha _{n - 3}}$$ . The sequence $$\left\{ {{\beta _n}} \right\}$$ is used to modulate a pulse $$g(t)$$ to generate the baseband signal

$$x\left( t \right) = \sum\limits_{n = - \infty }^\infty {{\beta _n}g\left( {t - nT} \right),}$$ where $$g\left( t \right) = \left\{ {\matrix{ {1,} & {0 \le t \le T} \cr 0 & {otherwise} \cr } } \right.$$

If there is a null at $$f = {1 \over {3T}}$$ in the power spectral density of $$X(t)$$, then $$k$$ is _________.

Your input ____
2
GATE ECE 2016 Set 2
Numerical
+2
-0
Consider random process $$X(t) = 3V(t) - 8$$, where $$V$$ $$(t)$$ is a zero mean stationary random process with autocorrelation $${R_v}\left( \tau \right) = 4{e^{ - 5\left| \tau \right|}}$$. The power of $$X(t)$$ is _______.
Your input ____
3
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+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
$$2{R_X}\left( \tau \right) - 2{R_X}\left( {\tau - 2{T_0}} \right)$$
4
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+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 $${P_{ao}} = 4.6 \times {10^{ - 10}}\,\,W$$
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