1
GATE ECE 2014 Set 1
Numerical
+2
-0
Let $$Q\left( {\sqrt y } \right)$$ be the BER of a BPSK system over an AWGN channel with two - sided noise power spectral density N0/2. The parameter 𝛾 is a function of bit energy and noise power spectral density. A system with two independent and identical AWGN channels with noise power spectral density N0/2 is shown in the figure. The BPSK demodulator receives the sum of outputs of both the channels GATE ECE 2014 Set 1 Communications - Random Signals and Noise Question 42 English

If the BER of this system is $$Q\left( {b\sqrt y } \right),$$ then the value of b is -----------.

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2
GATE ECE 2014 Set 3
Numerical
+2
-0
A real band-limited random process $$X( t )$$ has two -sided power spectral density $$${S_x}\left( f \right) = \left\{ {\matrix{ {{{10}^{ - 6}}\left( {3000 - \left| f \right|} \right)Watts/Hz} & {for\left| f \right| \le 3kHz} \cr 0 & {otherwise} \cr } } \right.$$$

Where f is the frequency expressed in $$Hz$$. The signal $$X( t )$$ modulates a carrier cos $$16000$$ $$\pi t$$ and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of $$8kHz$$ and band-width of $$2kHz$$. The output power (in Watts) is ______.

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3
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$. If $$Y(t)$$ is the process defined as $$Y(t) = X(2t - 1)$$, the power spectral density $${S_y}\left( f \right)$$ is .
A
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j\pi f}}$$
B
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j\pi f/2}}$$
C
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right)$$
D
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j2\pi f}}$$
4
GATE ECE 2014 Set 3
Numerical
+2
-0
Let $${X_1},\,{X_2},$$ and $${X_3}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,\,1} \right]$$. The probability $$P\left\{ {{X_1} + {X_2} \le {X_3}} \right\}$$ is ___________ .
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