Consider the block diagram of a discrete-time system given in Figure.(a) Find the differen...

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

(a) Find the difference-equation model of this system.

---

(b) Find the system transfer function.

---

(c) Determine the range of the parameter a for which this system is BIBO stable.

---

(d) Find the impulse response of this system. Is the answer to Part (c) evident from the impulse response? Why?

---

(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.

---

(g) Check the results of Parts (e) and (f) using MATLAB.