1. Hw week 5 1. Let the message signal m(t) = 4 + 2cos(2 103t), carrier wave xc(t) = 8cos(2 106t) (a) For DSB-SC systems, draw the frequency domain representation of m(t), xc(t) and the modulation output x(t)=m(t) xc(t) ; (b) Draw the block diagram of the demodulation system diagram. if low pass filter is used in the demodulator, what is the minimum bandwidth required to fully recover the signal? (c) What is the frequency and time domain representation of the demodulator output? 2. The bandwidth of human voice signals is about 8 kHz. If the government allocates the spectrum between 100 kHz to 700 kHz for you to use, how many AM radio talk shows can you have at the same time, assuming DSB-SC modulation? 3. For a conventional AM system with power carrier amplitude Ac and message signal m(t)= Amcosmt, (a) Calculate the modulation index for Am = Ac (b) Determine the transmission efficiency when Am = Ac and when Am = Ac/2

2. Hw week 5 4. The following figure shows the transmitter output of a conventional AM system. (a) Calculate the modulation index; (b) If the original message m(t) is a sinusoid, what is the amplitude of m(t)? What is the amplitude of the unmodulated power carrier? (c) Sketch the spectrum of x(t); (d) What is the transmission efficiency?

3. Hw week 5 5. For this question we will look at the SNR for DSB-SC systems. n(t) are the noise introduced in the system with PSD Sn()=/2 (shown in the figure below) low-pass filter h(t), H(w) Channel Receiver Transmitter • In the output y(t), what is the average power of the signal component? • If ideal low-pass filter with transfer function H() given by the figure on the right, what is the average power of the noise component n0(t) at the output? • What is the SNR of this system?