Linear time-invariant discrete-time system

Question

Assignment:

Question 1. A linear time-invariant discrete-time system has transfer function

H (z)  =  Z² - Z - 2/ Z² - 1.5z - 1

a. Use MATLAB to obtain the poles of the system. Is the system stable? Explain.
b. Compute the step response using MATLAB commands like conv and residue.
c. Plot the first seven values of the step response. Is the response increasing or decreasing with time? Is this what you would expect, and why?

Question 2. a. Plot the Bode plots (both magnitude and phase) for the given transfer function

H (s) = 1000(s + 1)/(s+20)²

Use the command semilogx to make your plots.

b. What kind of filter is this? What is the bandwidth of the filter?

Question 3. Consider the system given by the following transfer function:

H(s) =  242.5(s +8)/(s + 2)[(s + 4)² + 81](s + 10)

a. Identify the poles and zeros of the system.
b. Is the system stable? Why or why not?
c. What is the steady-state value for the step response.
d. Use Simulink to simulate the step response. Use the 'Zero-Pole' continuous model for the system with a gain of 242.5. For the sink, you can use the step function provided. Please include a copy of the model along with a plot of the output either from the scope or the simout variables.
e. Is the steady-state value from the simulation the same as in part c?
f. Is the response more like a first-order system or a second-order system?