Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 6th Sem New 2161001 Digital Communication Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2161001 Date:16/11/2018
Subject Name:Digital Communication
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) What is conditional probability? Explain it with suitable example. 03
(b) Compare Polar, On-off and Bipolar signalling with respect to desirable properties
of line codes.
04
(c) State and prove sampling theorem in time domain. Explain aliasing and Nyquist
rate.
07
Q.2 (a) State the Shannon?s theorem of channel capacity. What is its importance? 03
(b) Explain the difference between source coding and channel Coding. 04
(c) A source emits three equi-probable messages randomly and independently.
i. Find the source entropy.
ii. Find a compact ternary code, the average length of the code word, the code
efficiency and the redundancy.
iii. Repeat part (ii) for binary code.
iv. To improve the efficiency of a binary code, we now the code the second
extension of the source. Find a compact binary code, the average length of
the code word, the code efficiency and the redundancy.
07
OR
(c) A source emits one of four messages randomly every 1 microsecond. The
probabilities of these messages 0.5, 0.3, 0.1, 0.1. Messages are generated
independently.
i. Find the source entropy.
ii. Obtain compact binary code and determine the average length of the code
word, the code efficiency and the redundancy of the code.
iii. Repeat part (ii) for compact ternary code.
07
Q.3 (a) Explain the frame structure of T1 system in brief. 03
(b)
The random variable X have uniform distribution as,
f
X
(x) =
?
?
?
k (1 ? x
2
)
0
0 ? x ? 1
otherwise
Then find : (i) k (ii) CDF (iii) P (0 ? x < 2)
04
(c) Explain Delta modulation and demodulation technique and list the merits and
demerits of this technique.
07
OR
Q.3 (a) Draw the block diagram of regenerative repeater and briefly explain the function
of each block.
03
(b)
A random variable X has PDF :
f
X
(x) =
?
?
?
6x ? 6x
2
0
0 ? x ? 1
otherwise
Find constant b such that: P (X ? b) = P (X > b), Where b is constant 0 ? b ? 1.
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2161001 Date:16/11/2018
Subject Name:Digital Communication
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) What is conditional probability? Explain it with suitable example. 03
(b) Compare Polar, On-off and Bipolar signalling with respect to desirable properties
of line codes.
04
(c) State and prove sampling theorem in time domain. Explain aliasing and Nyquist
rate.
07
Q.2 (a) State the Shannon?s theorem of channel capacity. What is its importance? 03
(b) Explain the difference between source coding and channel Coding. 04
(c) A source emits three equi-probable messages randomly and independently.
i. Find the source entropy.
ii. Find a compact ternary code, the average length of the code word, the code
efficiency and the redundancy.
iii. Repeat part (ii) for binary code.
iv. To improve the efficiency of a binary code, we now the code the second
extension of the source. Find a compact binary code, the average length of
the code word, the code efficiency and the redundancy.
07
OR
(c) A source emits one of four messages randomly every 1 microsecond. The
probabilities of these messages 0.5, 0.3, 0.1, 0.1. Messages are generated
independently.
i. Find the source entropy.
ii. Obtain compact binary code and determine the average length of the code
word, the code efficiency and the redundancy of the code.
iii. Repeat part (ii) for compact ternary code.
07
Q.3 (a) Explain the frame structure of T1 system in brief. 03
(b)
The random variable X have uniform distribution as,
f
X
(x) =
?
?
?
k (1 ? x
2
)
0
0 ? x ? 1
otherwise
Then find : (i) k (ii) CDF (iii) P (0 ? x < 2)
04
(c) Explain Delta modulation and demodulation technique and list the merits and
demerits of this technique.
07
OR
Q.3 (a) Draw the block diagram of regenerative repeater and briefly explain the function
of each block.
03
(b)
A random variable X has PDF :
f
X
(x) =
?
?
?
6x ? 6x
2
0
0 ? x ? 1
otherwise
Find constant b such that: P (X ? b) = P (X > b), Where b is constant 0 ? b ? 1.
04
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2
(c) A television signal (video and audio) has a bandwidth of 4.5 MHz. This signal is
sampled, quantized and binary coded to obtain a PCM signal.
i. Determine the sampling rate if the signal is to be sampled at a rate 20%
above the Nyquist rate.
ii. If the samples are quantized into 1024 levels, determine the number of
binary pulse required to encode each sample.
iii. Determine the binary pulse rate (bits per second) of binary coded signal
and the minimum bandwidth required to transmit the signal.
07
Q.4 (a) Define the terms Mean, Central moment and Variance of a Random Variable. 03
(b) Derive the formula for signal to quantization noise ratio for PCM. 04
(c) Explain coherent detection of Frequency-Shift keying (FSK) signal with
necessary equations.
07
OR
Q.4 (a) What are the types of random variables? Explain them. 03
(b) Explain the concept of scrambling. 04
(c) Explain QPSK with waveforms, constellation diagram and mathematical
representation.
07
Q.5 (a) What is Burst error? Explain Burst error correction. 03
(b) Explain the Convolution code with suitable example. 04
(c) For a systematic linear block code, the three parity check digits,
C
4
, C
5
and C
6
are given by:
C
4
= d
1
? d
2
? d
3
C
5
= d
1
? d
2
C
6
= d
1
? d
3
i. Construct generator matrix.
ii. Construct code generated by this matrix.
iii. Determine error correcting capability.
iv. Prepare a suitable decoding table.
v. Decode the received words 101100,000110 and 101010.
07
OR
Q.5 (a) Define the following terms
i. Hamming distance
ii. Code rate
iii. Weight of code
03
(b) Explain Cyclic code with suitable example. 04
(c) A binary channel matrix is given by :
y1 y2 ? outputs
inputs ?
x1
x2
?
?
?
?
?
?
?
?
2 / 3
1 / 10
1 / 3
9 / 10
p ( x
1
) = 1/3 and p ( x
2
) = 2/3 Determine H (X), H (X/Y), H (Y/X) and mutual
information I (X ; Y)
07
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This post was last modified on 20 February 2020