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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?

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