(a) Consider double sideband suppressed carrier (DSB-SC) amplitude modulation, where the message signal is m(t) = cos(10t) + 2 sin (8t + 7), and the carrier signal is ve(t) = 20 cos(8000). (i) Find the time domain and frequency domain representations of the modulated signal. (7 marks) (ii) Draw the amplitude spectrum of the modulated signal. Draw the phase spectrum of the modulated signal. (5 marks) (b) Consider conventional amplitude modulation (AM). The modulated signal is u(t) = (1 + 0.4 cos(10t)) cos (2 fet + 7). The peak amplitude of the message signal is 1. (i) Determine the ratio of the power in the sidebands to the power in the carrier. (ii) (iii) (3 marks) What is the modulation index of the signal? What is the message signal? Can the modulated signal be demodulated using an envelope detector? Why? (3 marks) Show that u(t) can be demodulated using a synchronous detector. If the cosine signal generated by the local oscillator in the synchronous detector has a carrier frequency of f Hz and a phase shift of what is the output of the synchronous detector? (7 marks)