1
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
$$\mathop {\left\{ {{X_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } $$ is an independent and identically distributed (i.i.d) random process with $${X_n}$$ equally likely to be $$+1$$ or $$-1$$. $$\mathop {\left\{ {{Y_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } \,$$ is another random process obtained as $${Y_n} = {X_n} + 0.5{X_{n - 1}}.\,\,\,$$
The autocorrelation function of $$\mathop {\left\{ {{Y_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } $$, denoted by $${r_y}\left[ K \right],$$ is
A
GATE ECE 2015 Set 2 Communications - Random Signals and Noise Question 36 English Option 1
B
GATE ECE 2015 Set 2 Communications - Random Signals and Noise Question 36 English Option 2
C
GATE ECE 2015 Set 2 Communications - Random Signals and Noise Question 36 English Option 3
D
GATE ECE 2015 Set 2 Communications - Random Signals and Noise Question 36 English Option 4
2
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $$X \in \left\{ {0,1} \right\}$$ and $$Y \in \left\{ {0,1} \right\}$$ be two independent binary random variables.

If $$P\left( {X\,\, = 0} \right)\,\, = p$$ and $$P\left( {Y\,\, = 0} \right)\,\, = q,$$ then $$P\left( {X + Y \ge 1} \right)$$ is equal to

A
$$pq + \left( {1 - p} \right)\left( {1 - q} \right)$$
B
$$pq$$
C
$$p\left( {1 - q} \right)$$
D
$$1 - pq$$
3
GATE ECE 2015 Set 2
Numerical
+1
-0
A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is _________ .
Your input ____
4
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+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
GATE ECE 2015 Set 2 Communications - Noise In Digital Communication Question 12 English Option 1
B
GATE ECE 2015 Set 2 Communications - Noise In Digital Communication Question 12 English Option 2
C
GATE ECE 2015 Set 2 Communications - Noise In Digital Communication Question 12 English Option 3
D
GATE ECE 2015 Set 2 Communications - Noise In Digital Communication Question 12 English Option 4
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