Problem 5. Recall the system from Homework 5, Problem 2: y[n]=y[n-1]-0.25 y[n-2]+x[n], \quad n \geq 0 a. Find the transfer function, H(z) =Y(z)/X(z) b. Determine the impulse response h[n] = Z^-1{H(z)}. (Note: You will need to use a special case of the PFE when you have repeated roots) c. How does your result in b. compare with the answer you obtained for the analytical impulse response in Homework 5 Problem 2.d?

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5