12.4    DERIVATION OF ONE-MULTIPLIER LATTICE FILTER

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

image

image

Fig. 12.8    (a) Implementation of (12.52) and (b) implementation of HN(z) = ΨN(z).

image

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

where imagei 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

image

where

image

With i = N,

image

From (12.56),

image

Using (12.54) and (12.57 ...

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