Semester II of Academic Year 2016/17 of BJUT Midterm exam
Semester II of Academic Year 2016/17 of BJUT ≪EEEN3005J: Communication Theory≫ Midterm exam
Exam Instructions: Answer ANY 2 out of 3 Questions in 1.5hrs
Honesty Pledge:
I have read and clearly understand the Examination Rules of Beijing University of Technology and am aware of the Punishment for Violating the Rules of Beijing University of Technology. 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 would accept the punishment thereof.
Pledger: Class No:
BJUT Student ID: UCD Student ID:
Notes: The exam paper has 3 questions parts on 3 pages, with a full score of 100 points
composed of the 2 highest scoring answers.
Total Score of the Exam Paper (For teachers’ use only)
Question
1
2
3
Total Score
Full Score
50%
50%
50%
Obtained score
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Semester II of Academic Year 2016/17 of BJUT Midterm exam
Question 1:
Let g (t) be a low-pass signal with maximum frequency 4kHz and no DC component. Let s (t) be the “FM” modulated version of g (t), with carrier frequency FcHz.
1. What is Frequency Modulation (FM)?
2. Write an expression for s (t) in terms of g (t).
3. Explain how a Phase Modulator (PM) can be used to implement an FM modulator.
Consider the PLL shown in Figure 1:
PLL input vi(t) vo(t) PLL output
Figure 1: A PLL demodulator for use in question 1.
4. What does a PLL do?
Your answer should clearly explain its operation in terms of the frequency and phase of the input and output signals vi (t) and vo (t) respectively.
5. How can a PLL be used to demodulate an FM signal?
Question 2:
1. With reference to Figure 2:
• Write an expression for the output s ̃(t).
• What kind of modulation is this?
• IfX(f)andY(f)aretheFouriertransformsofx(t)andy(t)respectivelywhatis
S ̃(f), the Fourier transform of s ̃(t)?
• How does the amplitude spectrum of this s ̃(t) differ from that of a DSB-SC signal?
2. Draw a circuit diagram for a demodulator for the signal in Figure 2 and explain in detail (with equations) how is can recover estimates of both x (t) and y (t).
3. If the transmission channel introduces a delay of τ seconds, how would that effect the performance of your demodulator from part 2.2 on the estimate of x (t)?
Score Obtained
PLL
Phase Detector
vdet (t)
LPF
VCO
Score Obtained
x(t)
Ac cos(2πfct) c(t)
−Ac sin(2πfct)
s ̃(t)
π
2
y(t)
Figure 2: The modulator in question 2.
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Semester II of Academic Year 2016/17 of BJUT Midterm exam
Question 3:
Figure 3 shows a receiver for a “Full AM” signal. The received signal r (t) is given by: r (t) = Ar [1 + kag (t)] cos (2πfct)
Score Obtained
where the power of the zero-mean, low-pass, information signal, g(t), is Pg. w(t)
r(t)
gˆ(t)
Figure 3: System to be considered in question 3
As shown in Figure 3 the channel also adds White Gaussian Noise, w (t), with (double sided)
power spectral density 1 No Watts/Hz. The demodulation is implemented using an envelope
2
1. What is the purpose of the bandpass filter?
2. Draw a circuit for the envelope detector. Explain the operation of the circuit, using appropriate voltage waveforms to explain its operation. You should also explain how to select the component values in the circuit.
3. Given that the equivalent noise bandwidth of the bandpass filter is BN Hertz, derive an equation for the input average signal-to-noise power ratio at the input to the envelope detector (the input SNR).
4. Assuming an ideal envelope detector and high input SNR, derive an expression for the output SNR, i.e. the SNR at the output of the envelope detector.
5. Show that for low input SNR there is no useful output from the detector.
6. Can the circuit (in the figure) be used for the demodulation of a “DSB-SC” signal ? If not how would you minimally modify it to achieve DSB-SC demodulation?
oOo
detector (as shown).
Receiver
Bandpass Filter
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Envelope Detector