Q4. Consider the following linear time-invariant discrete-time system S.

y(k) = y(k 1) .24y(k 2) + 3x(k) 2x(k 1)

1. Find the characteristic polynomial a(z) and the input polynomial b(z).
2. Suppose the input is the unit step, x(k) = (k). Write down the general form of the zero-state response, y_zs(k).
3. Find the zero-state response to the unit step input.