For the difference equation,
y(k)= 0.9744 y(k−1)− 0.2231 y(k−2)− 0.3225 u(k−2)+ 0.5712 u(k−3) (1)
derive its discrete transfer function and step response for U(z) = \frac {1}{1-z^{-1}}. Use long division to obtain Y(z) for k=0 to k=9. Compare this result with simulating the original difference equation, Equation (1) , and a unit step change in u(k) at k=0. Assume y(0)=0.