1 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?
2 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 messagesignal m(t) in ascending order.