Filter Realizations - Introduction to Digital Signal Processing and Filter Design - page 333

X(z)

Σ Σ Σ Σ Σ

− K 5 K 5 − K 4 K 4 − K 3 K 3 − K 2 K 2 − K 1 K 1

Σ

z − 1 z − 1 z − 1 z − 1 z − 1 Σ Σ Σ Σ

v 4 v 3 v 2 v 1 v 0

Σ Σ Σ

Y(z)

( a )

X(z)

Y(z)

Σ Σ Σ

− K 3 K 3 − K 2 K 2 − K 1 K 1

V(z)

z − 1 z − 1 z − 1

Σ Σ Σ

( b )

Figure 6.19 (a) Lattice-ladder structure for an IIR filter (ARMA model); (b) lattice
structure for an all-pole IIR filter Y(z)/X(z) (AR model) and an allpass filter V(z)/X(z) .

-0.5745
0.5238
-0.1866
v=
0.3831
0.3164
0.2856
0.1532
0.1000
0

Example 6.16

In order to illustrate the derivation of a lattice structure for an all-pole (AR model)
filter, we select a transfer function

1

H(z − 1 )

=

(6.66)

1 − 0 . 2051 z − 1 − 0 . 0504 z − 2 + 0 . 0154 z − 3

and use the MATLAB function [k] = tf2latc(1,den) to get the vector output
for the lattice coefficients as shown below:

k =− 0 . 2145

− 0 . 0473
0 . 0154