(Solved): Question 6 Consider the following simplified model of a communication system. Assume you have two ...

Question 6 Consider the following simplified model of a communication system. Assume you have two signals that are transmitted, \( x_{1}(t) \) and \( x_{2}(t) \), with Fourier Transforms depicted below. Signal 1 is transmitted with a carrier frequency of 7 and signal 2 is transmitted with a carrier frequency of 10. Assume you have an ideal filter with frequency response, \( H(j \omega) \), shown below. a) Show the frequency response of the signal \( y(t)=x_{1}(t) \cos (7 t)+x_{2}(t) \cos (10 t) \) b) Show the frequency response of the signal \( y_{1}(t)=y(t) \cos (7 t) \) c) Show the frequency response of the signal \( y_{2}(t)=y(t) \cos (10 t) \) d) Show the frequency response of the output signal when \( y_{1}(t) \) is passed through the filter. e) Show the frequency response of the output signal when \( y_{2}(t) \) is passed through the filter.