ELEC0006 2019



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Physical constants:
Ambient temperature T=300 K
Boltzmann’s constant k=1.38x10-23 WK-1Hz-1.

You may assume the following identities:

cos(A + B) = cos A cos B ─ sin A sin B
cos(A ─ B) = cos A cos B + sin A sin B
sin(A + B) = sin A cos B + cos A sin B
sin(A ─ B) = sin A cos B ─ cos A sin B


cosAcosB = 12 cos(A+B)+ cos(A−B)[ ]

ELEC0006 2019



CONTINUED Page 2 of 4
Answer ALL six questions in section A. Answer ONE question from section B.

SECTION A
Answer ALL questions in this section.

1. Sketch an example of the time domain waveform of a ASK signal transporting the following
data sequence:
0 1 1 0 1 1 0 0 0 1
[5 marks]

2. Draw the double-sided frequency spectrum that results from finding the Fourier transform of a
time domain signal that is a square pulse with a pulse width of T. Demonstrate how the
resulting spectrum changes if T increases or decreases.

[5 marks]

3. What are three key design criteria of a receiver filter (e.g a matched filter) that is designed to
maximise the signal to noise ratio of a received signal?
[5 marks]

4. Briefly explain the meanings of the following communications terms:
(i) Angle modulation
(ii) FM modulation index
(iii) Carrier
(iv) Sideband
(v) Bandwidth
[5 marks]

5. Sketch diagrams illustrating a carrier that is (a) phase modulated and (b) frequency modulated
by a sinusoidal modulating signal, showing the sinusoidal modulating signal and the two
modulated signals, as a function of time.
[5 marks]

6. A radio receiver with a noise figure of 3 dB (corresponding to a noise factor of 2) has an input
signal of amplitude 1 µV rms. The receiver input impedance is 50 W. Calculate the signal-to-
noise ratio (SNR) in a 50 kHz bandwidth. Give your answer in dBs.

You may assume N = kTBF, an ambient temperature of 300 K and take Boltzmann's constant,
k, as 1.38x10-23 WK-1Hz-1.
[5 marks]


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Page 3 of 4 TURN OVER

SECTION B
Answer ONE question from this section.


7. (a) Why do we not use perfectly square pulses to transmit data in a practical communications
system?
[3 marks]

(b) A sequence of binary data is to be transmitted using 8-PSK. Sketch the constellation
showing how the data can be assigned to the symbols to minimise the bit error rate (BER).
Describe how this minimises the BER.
[3 marks]

(c) Determine the Fourier transform of the signal shown in figure 7.1. You may use known
Fourier relationships (these must be stated) to derive your answer if you wish.



8

4


-4 -2 2 4

Figure 7.1
[6 marks]

(d) Calculate the Fourier transform of the following signals and sketch the magnitude as a
function of frequency, including both positive and negative frequencies.

i) ( − 3)
ii) !"#() where () is the unit step function.
[8 Marks]



f (Hz)
V(f)

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END OF PAPER Page 4 of 6
8. (a) Sketch a circuit that may be used to perform amplitude demodulation.
[3 marks]

(b) Sketch a circuit that may be used to perform frequency demodulation.
[4 marks]

(c) Starting with the general equation for a sinusoidally-modulated FM signal, show that the
sideband levels relative to the carrier tend to one half of the modulation index, b, when b is
small, i.e. the modulation is narrowband FM.
[5 marks]

(d) Sketch the spectrum of a narrowband FM signal with a carrier amplitude of 0.25 V, a carrier
frequency of 9.5 MHz, an FM modulation index, b, of 0.1, and 3.5 kHz modulating
frequency. Indicate clearly the amplitudes and frequencies of all components.
[5 marks]

(e) If the above FM signal is applied to a x15 frequency multiplier then what is the change, if
any, in the above parameters (carrier frequency, FM modulation index and modulating
frequency)?
[3 marks]