Quantized Filter Analysis - Introduction to Digital Signal Processing and Filter Design - page 367

and the quantized filter, it allows us to make a suboptimal choice of the filter.
This is illustrated by the following example.

7.5 QUANTIZATION ANALYSIS OF IIR FILTERS

Let us select the same fifth-order IIR lowpass elliptic filter that was considered
in Example 6.17. Its transfer function G(z) is given by

0 . 1397
1 . 965

G(z) =

( 1 + 1 . 337 z − 1 + 2 . 251 z − 2 + 2 . 251 z − 3 + 1 . 337 z − 4 z − 5 ) +

×

( 1 − 1 . 629 z − 1 + 2 . 256 z − 2 − 1 . 597 z − 3 + 0 . 8096 z − 4 − 0 . 1866 z − 5 )

(7.9)

The frequency specifications for the filter are given as ω p = 0 . 4, ω s = 0 . 6,
A p = 0 . 3dB,and A s = 35 dB. The transfer function G(z) was decomposed as
the sum of two allpass filters A 1 (z) and A 2 (z) such that G(z) = 2 [ A 1 (z) + A 2 (z) ],

where

0 . 5089 − 0 . 6763 z − 1 z − 2 +

A 1 (z) = (7.10)

−

0 . 6763 z − 1

+

0 . 5089 z − 2 1

and

0 . 8805 − 0 . 5368 z − 1

+ 0 . 8805 z − 2 − 0 . 4165 + 1 − 0 . 4165 z − 1

z − 2 z − 1 +

A 2 (z) = (7.11)

1 − 0 . 5367 z − 1

Recollect the following lattice coefficients used to realize the lattice structures
for A 1 (z) and A 2 (z) computed in Chapter 6:
For A 1 (z) :

−

0 . 4482
0 . 5089

K1 =

⎡
⎣

⎤
⎦

0
0
1

V1 =

For A 2 (z) :

−

0 . 2855
0 . 8805

K2 =

⎡ ⎤

0
0
1

⎣ ⎦

V2 =