The reflection coefficients corresponding to a third-order

Question

The reflection coefficients corresponding to a third-order all-pole model are and the modeling error is given by

(a) Find the direct form filter coefficients, a₃(k), for this third-order model.

(b) Find the autocorrelation values r_x(0), r_x(1), r_x(2), and r_x(3) that led to this model.

(c) If a fourth-order model were found for x(n), what value or values for r_x(4) result in the minimum model error, ?₄?

(d) Repeat part (c) and find the value or values for r_x(4) that produce the maximum error, ?₄.