1
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
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j2\pi f}}$$
2
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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3
GATE ECE 2014 Set 2
Numerical
+2
-0
The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \right| > W} \cr } } \right.$$$

The value of the expectation $$$E\left[ {\pi X\left( t \right)X\left( {t - {1 \over {4W}}} \right)} \right]$$$
is ---------------.

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4
GATE ECE 2013
MCQ (Single Correct Answer)
+2
-0.6
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. GATE ECE 2013 Communications - Random Signals and Noise Question 45 English

If the detection threshold is 1, the BER will be

A
$${1 \over 2}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${1 \over 16}$$
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