Use MATLAB to compute and plot the frequency response of the system of(a) Problem(b) Probl...

Use MATLAB to compute and plot the frequency response of the system of

(a) Problem

---

(b) Problem

---

(c) Problem

---

(d) Problem (e)

---

(e) Problem (f)

Consider the digital filter shown in Figure.

(a) Derive the z-transform of the unit-step response, Y(z).

---

(b) Find the steady-state output in response to a unit-step input.

---

(c) Find the time-domain unit-step response, y[n].

---

(d) Use the result of Part (c) to verify your result from Part (b).

---

(e) Use MATLAB to calculate and plot the unit step response of the system.

(a) The difference equation

y[n] – y[n – 1] + 0.5y[n – 2] = x[n]

models an LTI system. Find the system transfer function.

---

(b) Find the unit step response for the system of Part (a).

---

(c) Use MATLAB to check the partial-fraction expansion in Part (b).

---

(d) From Part (b), give the values of y[0], y[1], and y[2].

---

(e) Verify the results of Part (d) by solving the difference equation iteratively.

---

(f) Verify the results in Part (e) by calculating the system’s unit-step response using MATLAB.

Consider the block diagram shown in Figure.

(a) Find the difference equation model for this system.

---

(b) Find the system transfer function.

---

(c) Determine the stability of the system.

---

(d) Find the unit-step response of the system.

---

(e) If the unit-step response has a finite final value, calculate the final value.

---

(f) Use MATLAB to calculate and plot the step response. Compare the response computed by MATLAB with your results from Parts (d) and (e).

Consider the block diagram of a discrete-time system given in Figure.

(e) Let a = 0.5. Find the unit step response for this system.

---

(f) Let a = 2.0. Find the unit step response for this system.