1
GATE ECE 2016 Set 1
+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
$${E_s} < \,\,{E_h};\,\,SN{R_{\max }} = \,\,{{2{E_h}} \over {{N_0}}}$$
2
GATE ECE 2015 Set 2
+2
-0.6
Consider a binary, digital communication system which uses pulses g (t) and − g (t)for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?
A
B
C
D
3
GATE ECE 2015 Set 1
Numerical
+2
-0
The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is _______.
4
GATE ECE 2015 Set 1
+2
-0.6
A source emits bit 0 with probability $${1 \over 3}$$ and bit 1 with probability $${2 \over 3}$$. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as
$${f_{\left. R \right|o}}\,(r) = \left\{ {\matrix{ {{1 \over 4},} & { - \,3\,\, \le \,\,x\,\, \le \,\,1,\,} \cr 0 & {otherwise,} \cr } } \right.and$$
$${f_{R/o}}\,(r) = \left\{ {\matrix{ {{1 \over 6},} & { - \,1\,\, \le \,\,x\,\, \le \,\,5\,,} \cr 0 & {otherwise.} \cr } } \right.$$

The minimum decision error orobability is

A
0
B
1/12
C
1/9
D
1/6
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