In a double-sideband suppressed-carrier amplitude modulation (DSB-SC AM) system, the modulating signal is given as m(t) = cos(20nt) + 2 cos(26t). The modulating signal is to be transmitted by the carrier signal cos(200t). Denote XDSB-Sc(t) as the DSB-SC AM signal specified above. a. Provide an expression for XDSB-Sc(t). (4 marks) b. Plot the frequency spectrum of XDSB-Sc(t). Clearly label all relevant parameters in the plot. (8 marks) c. Suppose coherent detection is carried out to demodulate m(t). Plot a circuit diagram that can carry out coherent detection. (4 marks) d. Assume we can use an ideal lowpass filter (LPF) for coherent detection. Plot the frequency response of the ideal LPF that can recover m(t), where the LPF should have the minimum possible bandwidth. (3 marks) e. To enable the use of envelope detector at the receiver side, the carrier signal is transmitted together with XDSB-Sc(t). Determine the minimum amplitude of the carrier signal such that an envelope detector may recover m(t). (3 marks) f. Determine the amplitude of the carrier signal when the modulation index is 0.5. (3 marks)