1
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 $${P_{ao}} = 4.6 \times {10^{ - 10}}\,\,W$$
2
GATE ECE 2016 Set 1
Numerical
+2
-0
Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right\}$$ and respective probabilities of occurrence $$P = \left\{ {{1 \over 2},\,{1 \over 4},\,{1 \over 8},\,{1 \over {16}},\,{1 \over {32}},......} \right\}$$. The entropy of the source (in bits) is__________.
Your input ____
3
GATE ECE 2016 Set 1
Numerical
+2
-0
A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1, Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is _______
Your input ____
4
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density $${{{N_0}} \over 2}$$. The received signal is passed through a filter with impulse response h(t). Let $${E_s}$$ and $${E_n}$$ denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter $$\left( {SN{R_{\max }}} \right)$$, which of the following holds?
A
$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{2{E_s}} \over {{N_0}}}$$
B
$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{{E_s}} \over {2{N_0}}}$$
C
$${E_s} > \,\,{E_h};\,\,SN{R_{\max }} > \,\,{{2{E_s}} \over {{N_0}}}$$
D
$${E_s} < \,\,{E_h};\,\,SN{R_{\max }} = \,\,{{2{E_h}} \over {{N_0}}}$$
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