School of Electronics Engineering (Sense) : Answer Any Three Questions

SCHOOL OF ELECTRONICS ENGINEERING (SENSE)
Winter Semester 2020–21

Continuous Assessment Test – I
ECE4001 – Digital Communication Systems
Duration: 50 minutes Max. Marks: 30

Slot: F2 Programme: B. Tech ECE
Answer Any three Questions
S. Questions Marks
No
1 Assume an analog signal x(t), sampled by a train of impulses at a sampling rate of f s= 2fm, 10
a) where fm is the maximum frequency. Derive the expression for the sampled signal in the
frequency domain. Explain the spectrum of the sampled signal with fs= 2fm, fs > 2fm and fs <
2fm.
1 Consider an audio signal x(𝑡), which is to be sampled, quantized, encoded and transmitted 10
b) through the channel.
i) Calculate the Nyquist rate?
ii) Consider any arbitrary spectrum for x(𝑡). Draw the spectrum of the sampled
audio signal.
iii) If the signal is sampled below the Nyquist rate, what is the corresponding effect?
Explain the effect using spectral analysis.
iv) Consider that a power line signal with a maximum frequency of 40 kHz is
added to the audio signal. Assume that the resultant signal is sampled using
critical sampling. Is there any possibility of aliasing effect? If yes, how can it be
rectified?
v) How the original audio signal can be reconstructed at the receiver? What type of
filter you will prefer? Specify the ideal and practical bandwidths of the required
filter.
2 1) A 56MB hard disk is used to store PCM data. The signal is sampled at 8 KHz and the 5+5
a) encoded PCM is to have an average signal to noise ratio of at least 28 dB. For how
many minutes the PCM data can be stored on the hard disk?
SQN=1.8+6n,,,,28dB=1.8+6n
n=5 bits
Signaling Rate=nfs=40 kbps
In PCM=56MB/40 kbps=186 mins or 11200 secs
2) Consider a delta modulation system designed to accommodate analog message
signals limited to bandwidth of 5 kHz. A sinusoidal test signal of amplitude is 1 volt
and frequency of 1 kHz is applied to the system. The sampling rate of system is 50
kHz.
1. Calculate the step size required to minimize slope overload.
2. Calculate the signal to noise ratio of the system for the

specified sinusoidal test signal.
= 950 or 29 dB
2 a) A waveform, x(t)=10 cos (1000t+π/3)+20 cos(2000t+ π /6) is to be uniformly sampled for 5+5
b) digital transmission.
(i) What is the maximum allowable time interval between sample values that will
ensure perfect signal reproduction?
(ii) If we want to reproduce 1 hour of this waveform, how many samples values need
to be stored?
b) Name the Line coding method and draw the corresponding line coded signal for a binary bit
stream ‘00101101’, where ‘a’ is the peak amplitude, and ‘T’ is duration of one bit
𝑡
() {
𝑡
𝑡
() {
𝑡
𝑡
() {
𝑡
POLAR NRZ, MANCHESTER FORMAT, UNIPLOAR NRZ
3 A Discrete time signal x[n] is given in figure 1 and it consists of 11 samples. All the samples 10
transmitted through a Delta modulator. Delta modulator is using a two level quantizer as shown
a) figure 2. Find the delta modulator transmitter and receiver output. Check the error between original
sample amplitude and decoded sample amplitude.
10 v
9.5 v 9.5 v
8.09 v
8.09 v
5.87 v
5.87 v
3.09 v
3.09 v
0v 0v
Figure 1 (Discrete time Signal with 11 Samples)
output
2.5
Input
-2.5
Figure 2 (Two level quantizer with δ = 2.5)

3 Sketch a DPCM system with suitable diagrams and write the necessary equations. Also find 10
b) the DPCM Transmitter and Receiver output of the following signal x(k)= {0.3, 1.5, 0.7, 1,
2.3, 3.7, 2.8, 3.4, 2.8, 0} by considering midtread type Quantizer with Δ=1V.
DPCM block Diagram
Quantized output -------0, 1,0,0,1,2,-1,0,0,-3
RX output------0111243330
4 5+5
a) a) Sketch the Manchester format, differential code and polar quaternary signals for the
following binary sequence {1 0 0 1 0 1 1 1 0 0}.
4 a) For a delta modulation system, a sinusoidal analog signal x(t)=0.1sin2π (103)t is sampled 5+5
b) at fs = 20000Hz. Find out whether slope overload distortion occurs for the following step
size
a) 4mV and b) 60mV

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SCHOOL OF ELECTRONICS ENGINEERING (SENSE)

Winter Semester 2020–21

Duration: 50 minutes Max. Marks: 30

2. Calculate the signal to noise ratio of the system for the

POLAR NRZ, MANCHESTER FORMAT, UNIPLOAR NRZ

Figure 1 (Discrete time Signal with 11 Samples)

Figure 2 (Two level quantizer with δ = 2.5)

DPCM block Diagram

Quantized output -------0, 1,0,0,1,2,-1,0,0,-3

a) 4mV and b) 60mV

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