212 Ete 2023

DEPT.
OF ELECTRONICS & COMMUNICATION ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
ECN-212: Communication Systems & Techniques
Spring Semester 2023 End-Term Examination Maximum Marks : 75
1. (a) Consider a message signal m(t) = cos(2πfm t + ϕ) and the corresponding DSB-SC (5)
signal s(t) = Am(t) cos(2πfc t), where fc > fm .
i. Determine and sketch the spectrum of the corresponding LSB and USB sig-
nals (if the spectrum is complex-valued, sketch the real and imaginary parts
separately).
ii. Determine the time-domain expressions for the LSB and USB signals.
iii. Determine the time-domain expressions for the complex envelope of the LSB
and USB signals.
(b) A modulated signal can be expressed as (5)
s(t) = a(t) cos [2πfc t + θ(t)] ,
where a(t) and θ(t) are the envelope and phase, respectively.
i. Starting with a time-domain expression of SSB in terms of the message signal
m(t), and its Hilbert transform, determine a(t) and θ(t).
ii. Determine an expression for the instantaneous frequency of the modulated signal
from (i) above and comment on the dependence of envelope and instantaneous
frequency on m(t). Compare DSB-FC, DSB-SC and SSB in this regard.
(c) Consider a quadrature-carrier multiplex system. Suppose that the local carrier (5)
available for demodulation has a phase error ϕ with respect to the carrier source
used in the transmitter. What is the effect of the phase error on the demodulated
signals? Justify your answer.
2. (a) Consider an FM signal s(t) of carrier frequency fc , which is produced by a modu- (4)
lating signal m(t). Assume that fc is large enough to justify treating this FM signal
as a narrowband signal. Find expressions for the following:
i. Complex envelope of s(t).
ii. Pre-envelope of s(t).
iii. Hilbert transform of s(t).
(b) Consider the single-tone FM modulation with fc = 1 MHz, message signal frequency (5)
fm = 3 kHz, and peak frequency deviation ∆f = 10 kHz.
i. Sketch the spectrum (inside the Carson’s bandwidth) of the FM signal.
ii. If the amplitude of the message signal is doubled and its frequency is reduced
to 2 kHz, how is the modulated signal bandwidth modified?
(c) With the help of block diagram explain the working of Costas loop for demodu- (8)
lating DSB-SC signals. What is the advantage of Costas loop over synchronous
demodulation of DSB-SC signals?
3. (a) Consider the random process (4)
X(t) = A cos(2πf0 t + Θ)
where f0 is a constant, A is a random variable uniformly distributed in the range

[−3, 3], and Θ is a random variable uniformly distributed in the range [−π/2, 3π/2].
The random variables A and Θ are statistically independent.
i. Is X(t) a WSS process?
ii. Is X(t) ergodic?
Justify your answers.
(b) Let the WSS random process X(t) is defined by (7)
∞
X t − t0 − k · ta
X(t) = Ak g ,
b
k=−∞
where 0 < b < ta < ∞, g(t) = u(t)−u(t−1), t0 is a random variable that is uniformly
distributed from 0 to ta , and Ak = ±1 with equal probability and independent for
each k.
i. Sketch two sample functions of the process X(t).
ii. Find the autocorrelation function of X(t).
(c) White Gaussian noise of zero mean and power spectral density N0 /2 is applied (5)
to the filtering scheme shown in the figure. The random variable Θ is uniformly
distributed in the range [0, 2π].

i. Find the power spectral density and the autocorrelation function of the output
process n(t).
ii. Find the average power of n(t).
iii. What is the maximum sampling rate at which n(t) can be sampled so that the
resulting samples are uncorrelated? Justify your answer.
Page 2
4. (a) An unmodulated carrier of amplitude Ac and frequency fc , and band-limited white (4)
noise are summed and then passed through an ideal envelope detector. Assume the
noise spectral density to be of height N0 /2 and bandwidth 2W , centered about the
carrier frequency fc . Determine the output SNR for the case when the carrier-to-
noise ratio is high.
(b) The input to an FM reciever consists of an FM modulated signal plus narrowband (6)
additive white noise of power spectral density N0 /2. The bandwidth of the filter
preceeding the discriminator (pre-detection bandpass filter) satisfies Carson’s rule.
i. Draw a phasor diagram for the pre-detection bandpass filter output signal.
ii. Determine an expression for the phase deviation introduced due to the noise.
(Assume that the carrier-to-noise ratio is high)
iii. Derive an expression for the noise spectrum at the receiver output.
(c) With the help of a block diagram, explain the working of superheterodyne receiver. (8)
What is the main advantage of superheterodyne architecture as compared to using
only a single tunable bandpass filter? What is high-end tuning? What is image
frequency and how it is removed?
5. Answer any three of the following: (9)

(a) What is the Quadrature null effect in DSB-SC?
(b) Show that the theoretical bandwidth of an angle modulated signal is infinite.
(c) Explain the Capture range and lock range of PLL.
(d) What is need for Pre-emphasis and De-emphasis in FM Systems?
(e) Why AM is preferred over FM in air traffic control communication?
Page 3

212 Ete 2023

Uploaded by

Copyright:

Available Formats

212 Ete 2023

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

212 Ete 2023

Uploaded by

Copyright:

Available Formats

DEPT.

OF ELECTRONICS & COMMUNICATION ENGINEERING

s(t) = a(t) cos [2πfc t + θ(t)] ,

3. (a) Consider the random process (4)

where f0 is a constant, A is a random variable uniformly distributed in the range

distributed in the range [0, 2π].

5. Answer any three of the following: (9)

You might also like