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TELE3113 Analogue and Digital Communications
Tutorial 2
Semester 2, 2009
Question 1
A carrier signal
c(t) = 10 cos(2π · 1000t)
is modulated by a single-tone message signal
m(t) = 2 sin(2π · 50t)
to form the AM signal
s(t) = (10 + 2 sin(2π · 50t)) cos(2π · 1000t).
1) Sketch c(t), m(t) and s(t) and their corresponding spectra.
2) What is the modulation index?
3) What bandwidth is required to transmit the AM signal?
4) What is the power efficiency of the AM signal?
Question 2
Consider the following sinusoidal message and carrier signals,
m(t) = Am cos(2πfm t)
c(t) = Ac cos(2πfc t)
1) Write down expression for the DSB-SC modulated signal for the above message and carrier.
Show the spectra of the DSB-SC modulated signal.
2) The DSB-SC modulated signal is domodulated using a coherent detection. Draw a block
diagram of the coherent detection.
3) If the demodulation local oscillator has a phase error φ, find the demodulation output. Is
the demodulated signal the same as m(t) when φ = π/2?

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Question 3
Which of the following statement is CORRECT?
1) DSB-SC modulated signals have no carrier component, but the information is carried in
the sidebands.
2) Standard AM and DSB-SC both require the transmission bandwidth to be equal to the
message bandwidth.
3) SSB modulated signal can reduce the transmission bandwidth to the message bandwidth.
4) SSB demodulation can be achieved through coherent detection.
5) VSB modulation is used for transmitting TV signals, because TV signals have significantly
low frequency components.
6) In VSB modulation, one sideband is passed almost completely, while just a vestige of the
other sideband is not retained.
Question 4
Let m(t) denote the message signal and m(t) its Hilbert transform.
ˆ
1) Consider a linear time-invariant system of impulse response h(t) with input m(t) and
1
output m(t). Show that h(t) =
ˆ πt
.
2) Show that the frequency response of the system is H(f ) = −jsgn(f ).
1
m (t ) h (t ) = m(t )
ˆ
πt
Illustration of Hilbert transform in time domain
M(f ) H ( f ) = − j sgn( f ) ˆ
M(f )
Illustration of Hilbert transform in frequency domain
Question 5
Sort the bandwidth of standard AM, DSB-SC, SSB and VSB modulations of the same message
signal m(t) in ascending order.