The continuous time system with OLTF A s + Bs + C can be converted to discrete time G[q] using the code nn= dd= [num,den]= G(s): A; [1 B C]; c2dm(nn,dd,T,'zoh'); = % continuous-time system dynamics % discrete-time system dynamics 1. A continuous system with damping ratio and undamped frequency w, is being sampled at fs. a. Express the forward gain K, 3, and w, in terms of a, b, and c b. Determine the poles of G(s) c. Using the sq transformation, derive the formula for G [q] algebraically. d. Assign values to A, B, and C, so that 0.5 0.8 and 3 w 5. e. Assign a value to 5 f 10. Use Matlab to verify your answer to Question I.b 2. Using the values in Question I, a. Express G[q] in polar coordinates. b. Determine the poles of G[q]. c. Compare the poles of G (s) and G[q]. Comment if the CT2DT analogy is correct. 3. Use Matlab to plot, in the q-plane a. The constant, and w, line b. The poles of G[q] c. Change fs, 5, and w, and comment how the poles change on the plot. 4. In Matlab, obtain the unit pulse response of the discrete system. Plot a. The unit pulse response b. The autocorrelation of the response c. The cross-correlation of the input and the response d. The Power Spectrum of the response e. Use the Blackman-Tuckey weighing function to estimate the response. 5. Write your report in IMRAD format. You will be graded on a. The completeness of the mathematical expressions; b. Your communication skills (clarity, organization, objectivity, completeness, etc.), and c. Your orthographic qualities (punctuation, spelling, grammar).