Beijing-Dublin International

College

SEMESTER II FINAL EXAMINATION - 2018/2019

School of Electrical and Electronic Engineering

EEEN3005J: Communication Theory

Prof. Peter Kennedy

Dr. Deepu John

Time Allowed: 120 minutes

Instructions for Candidates

Answer ANY 3 of the 4 questions. All questions carry equal marks. Only the 3 highest scoring

answers will contribute to final grade.

BJUT Student ID: UCD Student ID:

I have read and clearly understand the Examination Rules of both Beijing University of Technology

and University College Dublin. I am aware of the Punishment for Violating the Rules of Beijing

University of Technology and/or University College Dublin. I hereby promise to abide by the

relevant rules and regulations by not giving or receiving any help during the exam. If caught

violating the rules, I accept the punishment thereof.

Honesty Pledge: (Signature)

Instructions for Invigilators

Non-programmable calculators are permitted.

No rough-work paper is to be provided for candidates.

BDIC Semester II Academic Year (2018/2019)

Question 1:

Score

Obtained A baseband signal, g (t) , with bandwidth 10 kHz, is such that its amplitude satisfies |g (t)| <

0.8 V, and has average power = 0.1 Watts. This signal is connected to a circuit composed of

a mixer and an adder as shown in Figure 1 below. The resulting signal, s˜(t) , is transmitted

through a channel as shown. The scaling factor, α , represents a signal power attenuation of

120 dB, and w (t) is additive white Gaussian noise with single-sided power spectral density

(PSD) N0= -174 dBm/Hz. The receiver applies an ideal band pass filter having bandwidth

just sufficient to capture the whole of the received modulated signal.

[Note that if the power of a signal is Pm mWatts, then its power in dBm is = 10 log10(Pm)

dBm.]

Figure 1: Circuit to be considered in question 1

1. Sketch the time-domain signal, s˜(t), showing numbers and units on both axes. What

name is given to this type of modulation?

2. Calculate the signal-to-noise ratio (SNR) in dB at point “A”. Do not count the carrier

component as contributing to the “signal power” here, as it bears no information.

3. What do we mean when we say that a random signal is wide-sense stationary?

4. What is meant by the Energy Spectral Density (ESD) of a deterministic energy sig-

nal?Consider a signal,x (t), with one-sided ESD given by:

S

′

x(f) =

{

4f2 if 0 < f < 10 kHz

0 otherwise

Determine the fraction of the signal’s energy that lies in the frequency range 0 < f < 5

kHz

Question 2:

Score

Obtained Consider the circuit in Figure 2 where the control signal c (t), that is guaranteed to be either±1 V, is used to control the position of the two switches as shown.

Figure 2: Circuit to be considered in question 2

1. Write a simple expression for the circuit’s output, vout(t), in terms of c (t) and s˜(t),

explaining your answer by clearly describing the operation of the circuit when c (t) =

+1 V and when c (t) = -1 V.

2. Let s˜(t) be a bandpass signal with centre frequency fc Hz, and c (t) be a square wave

signal alternating between ±1 V also with frequency fc Hz. In this case

Page 2 of 5

BDIC Semester II Academic Year (2018/2019)

• sketch a possible power spectral density (PSD) for s˜(t)

• sketch the PSD of c (t)

• sketch the resulting PSD of vout(t)

3. Provide a clear definition of “Double SideBand Suppressed Carrier (DSB-SC)” modu-

lation. Your answer should contain the mathematical expressions and derivations of a

DSB-SC signal in the time and frequency domain. You should also include sketches of

an example DSB-SC signal in both domains.

4. Explain how the circuit in Figure 2 could be used, in conjunction with some additional

circuit elements, to demodulate a DSB-SC signal.

5. The process of demodulating a DSB-SC signal often suffers from local oscillator “phase

and/or frequency mismatch” errors. Explain the meaning of this statement

Question 3:

Score

Obtained 1. What is the instantaneous frequency fi (t) of an arbitrary signal A (t) cos (φ (t))?

2. If a modulated signal can be written as Ac cos (2pifct+ θ (t)) give an expression for the

instantaneous frequency.

3. What is Frequency Modulation (FM)? your answer should derive an expression for s˜ (t),

the FM signal, in terms of g (t) the modulating signal, and kf the frequency sensitivity.

4. Let g (t) be a sine wave with amplitude Am and frequency fm kHz.

• Derive an expression for s˜ (t) in terms of Am and fm.

• What is the modulation index β and modify the above expression to include β.

• Derive an expression for whats called ”the peak frequency deviation” ∆f . Hint:

∆f is should really be called the ”peak instantaneous frequency deviation”

• Why is the spectrum of this sinusoidal modulation FM signal, s˜ (t) a line spectra?

• The Fourier series for s˜ (t) is:

s˜ (t) = AcJ0 (β) cos (2pifct) +Ac

∞∑

n=1

J2n (β) [cos {2pi (fc + 2nfm) t}+ cos {2pi (fc − 2nfm) t}]

+Ac

∞∑

n=1

J2n−1 (β) [cos {2pi (fc + (2n− 1) fm) t} − cos {2pi (fc − (2n− 1) fm) t}]

where Jn (β) is the n

th order Bessel function of the first kind.

Let fm = 8kHz, and fc = 100MHz:

– Using Figure 3 sketch the spectra for β = 0.1

– If Am = 1Volt, what approximate value of frequency sensitivity kf would result

in the spectral component at fc being zero? You answer should use the correct

units for kf.

Page 3 of 5

BDIC Semester II Academic Year (2018/2019)

0 1 2 3 4 5 6 7 8 9 10

−0.5

0

0.5

1

β

J n

(β)

J0(β)

J1(β)

J2(β)

J3(β)

J4(β)

Figure 3: Some Bessel functions for use in question 3.

Question 4:

Score

Obtained Consider the system shown in Figure 4.

p(τ)bk ∈ {±1}

y(t)

y(kT )

every T seconds kT

Figure 4: System to be considered in question 4

1. Write an expression for y (t).

2. Hence, or otherwise, derive (don’t just quote) a time domain criteria on p (τ) such that

the collection of samples {y (kT )} are all ISI-free.

3. Derive (don’t just quote) the frequency domain version of the criteria derived in part 2.

Let T = 1 and P (f), as shown in Figure 5(a), be the Fourier transform of p (τ):