Suppose we would like to send the two messages mi(t), i = 1; 2, created in Problem 12 using the same bandwidth and to recover them separately. To implement this consider the QAMapproach where the transmitted signal is

s(t) = m₁(t) cos(50t) + m₂(t) sin(50t)

Suppose that at the receiver we receive s(t) and that we demodulate it to obtain m_i(t), i = 1, 2. This is a discretized version of the processing, similar to that in Problem 12. Use the functions AFT and AIFT given there to compute Fourier transform and inverse.

(a) Sample s(t) using Ts = 5=512 and obtain its magnitude spectrum |S(Ω)| using the functions AFT. The sampled messages coincide with those in Problem 12.

(b) Multiply s(t) by cos(50t), and filter the result using the low-pass filter designed in Problem 12.

(c) Multiply s(t) by sin(50t), and filter the resulting signal using the low-pass filter designed in Problem 12.

(d) Use the function plot to plot the spectrum of s(t) and the recovered messages. Comment on your results.