Write magnitude and phase expressions for bode plots

Question

Problem 1: Consider the causal CT systems with transfer functions

H₁(s) = (s + 1)/((s + 2)(s² + s + 16))

H₂(s) = s/((s+ 10)(s + 1))

H₃(s) = 1/((s - 1)(s + 1))

H₄(s) = s/(s + 1)(s² + s + 16)

Part 1: Write magnitude and phase expressions for their Bode plots and sketch their asymptotes. Verify using MATLAB.

Part 2: Compute their steady-state response to cos(5t) u(t) + 3u(t) + cos(10t) e-tu(t).

Problem 2: Consider the causal DT systems with transfer functions:

H₁(z) = z/((z 0.5)(z - 0.7))

H₂(z) = 0.9z-1/((z - 1)(z - 0.8))

H₃(z) = 1/((0.5z - 1)(z + 0.7))

H₄(z) = (z-1)/(z - 0.9)(z² - 1.8z + 0.9)

Part 1: Write magnitude and phase expressions for their Bode plots and sketch their asymptotes (or approximate asymptotes). Verify using MATLAB.

Part 2: Compute their steady-state response to sin (0.1 n) u(n - 10) + 2u(n).