Problem: Consider the following system shown in Fig. 1. Assume: xz(t) = 2 (), z(t) = 3 A(3t - 12),cz(t) = 4 cos (120nt), and Cz(t) = 2 cos (80nt). a. Write the signals x (t), and xz(t) in terms of singularity functions. b. Write Matlab Code to validate your solution in part a. c. Write Matlab Code to plot and determine the Fourier transform of the signals: x (t), xz(t), (t), and cz(t). d. Determine the output signals y.(6), y(t), and v(t). e. Write Matlab code to determine and plot the Fourier transform of the signals evaluated in part d. f. Design the system in Black box which generates the output signal r(t) = y(t), Explain your design xy(t) x y(t) v(t) r(t) Black Box (t) x2(0) yz(t) cz(t) Fig. 1: System Model