VLSI Digital Signal Processing Systems: Design and Implementation

12.4    DERIVATION OF ONE-MULTIPLIER LATTICE FILTER

By choosing s_i = 1 − _ik_iin (12.36), the Schur algorithm can be expressed as

Fig. 12.8    (a) Implementation of (12.52) and (b) implementation of H_N(z) = Ψ_N(z).

Fig. 12.9    A 3rd-order FIR lattice filter in Example 12.3.3.

where _i is called a sign parameter and is either 1 or −1. 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 ∧_N(z) as ∧_N(z) = D_N(z). From ∧_N(z), form the polynomial ∧_N−1(z) by the Schur algorithm as

where

With i = N,

From (12.56),

Using (12.54) and (12.57 ...