VLSI Digital Signal Processing Systems: Design and Implementation

12.5    DERIVATION OF NORMALIZED LATTICE FILTER

The structure of an N-th order normalized lattice filter is shown in Fig. 12.14. Consider an N-th order IIR transfer function H_N(z) = N_N(z)/D_N(z). Then, initialize the N-th order Schur polynomial Φ_N(z) as Φ_N(z)= D_N(z), where

From Φ_N(z), form the polynomial Φ_N−1 (z) by the Schur algorithm as

where

with i = N. Also, , the reverse polynomial of Φ_N−1(z) is

From (12.67),

Using (12.65) and (12.68), Φ_N−1(z) can be expressed as a function of Φ_N(z) and as

An implementation of (12.68) and (12.69) is shown in Fig. 12.15(a), which is the same as the feedback part of module N of the normalized lattice filter in Fig. 12.14 if

By repeatedly applying the ...