Question

signals and communications 2

Make sure you show all working and describe each step in your calculations. 1. A signum function is defined as sgn(t) = { 1、12 0 1 t 0, plot the signal a) x(t)-e"u(t)-eul-t). 2 marks b) Determine the Fourier transform of x(). XGa), and plot IXGo)l. 8 marks An SSB-AM modulator is shown in fig. 1, where the SSB filter removes the upper sideband. 5. cos(2 π 10% m(o)-4 cos 2T.5x10'r SSB Filter Figure 1 a) Write down an expression for the SSB-AM signal o 12 marks ) A synchronous demodulator is shown in fig. 2. Show that by setting the frequency of the local oscillator to the carrier frequency of the SSB-AM signal from part a, the demodulator output will contain the original messago. 4 marks cos(2m10 1) v,(t) ourlt) Figure 2 An FM signal is to be produced using a V/F converter with a frequency conversion factor, α Hz per volt. The modulation index is-2 when the carrier is modulated by the signal 6. m(t) = 5 cos(2π x 103 t). a) The spectrum of the FM signal may be expressed by: Sketch accurately, the band-limited spectrum of the FM signal showing all significant sidebands, if V 5 Volts and fe 5MHz. 6 marks power in 3 marks Determine the average power in the unmodulated carrier and the average the band-limited FM signal if the load resistance R1 is 50Ω. b) 7. A schematic diagram for a quadrature phase shift keying (QPSK) modulator is shown in fig. 3. The modulator has two digital messages, d() and d(), both of which have two voltage levels:+Vn and-, corresponding to a bit value of I and 0 respectively Derive the equation for the output, v(). a) 2 marks Sketch a suitable QPSK demodulator and show how the binary messages, h() and d:(0), are separately recovered. What are the advantages of QPSK modulation over PSK modulation? b) 6 marks c) 2 marks) cos(2Tf1) v, (t) sin(2rf t Figure 3

Answer 1