As discussed in Section 11.7.3, Burg (1975) proposed computing the k parameters so as to...

As discussed in Section 11.7.3, Burg (1975) proposed computing the k parameters so as to minimize the sum of the forward and backward prediction errors at the i^th stage of the lattice filter; i.e.,

where the sum is over the fixed interval i ≤ n ≤ M.

a) Substitute the lattice filter signals into (P11.30-1) and show that the value of k_i that minimizes B⁽ⁱ⁾ is

(b) Prove that − 1 < k ^B _i < 1.

Hint: Consider the expression where x[n] and y[n] are two distinct sequences.

(c) Given a set of Burg coefficients how would you obtain the coefficients of the corresponding prediction error filter A^(p)(z)?