12.4 DERIVATION OF ONE-MULTIPLIER LATTICE FILTER
By choosing si = 1 − ikiin (12.36), the Schur algorithm can be expressed as
Fig. 12.8 (a) Implementation of (12.52) and (b) implementation of HN(z) = ΨN(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 HN(z) = NN(z)/DN(z). Then, initialize the N-th order Schur polynomial ∧N(z) as ∧N(z) = DN(z). From ∧N(z), form the polynomial ∧N−1(z) by the Schur algorithm as
where
With i = N,
From (12.56),
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