A find the characteristic polynomial az for this system b

Question

Problem 1: Let

y(k) - y(k -1) = x(k) + x(k - 1)/2

a. Find the characteristic polynomial, a(z), for this system.

b. Find the input polynomial, b(z) for this system.

c. If x(k) = .2^ku(k), calculate y_zs(k), the zero state response of the system.

Problem 2:

Let

x(k) = [2 3] and y(k) = [2 4 6 3]

Calculate r_yx = D(x)y for this system.

Problem 3: Let

x(k) = 2δ(k) + 6δ(k - 1) - 3δ(k - 2) and h(k)  = [3 0 2]

a. Write the summation for y(k) = x(k) * h(k).

b. Calculate y(k).

Problem 5: Let

y(k) = 2^-ku(k - 2)

a. Is y(k) periodic? If so, what is the period?

b. Is y(k) bounded or unbounded?

c. Is y(k) finite or infinite?

d. Is y(k) causal?

e. Calculate the energy of y(k). Is it finite or infinite?