Filter Realizations - Introduction to Digital Signal Processing and Filter Design - page 339

H

Transfer function:
0.8603 z^5 - 2.469 z^4 + 4.021 z^3 - 4.021 z^2 + 2.469 z
- 0.8603
----------------------------------------------------------
1.965 z^5 - 3.202 z^4 + 4.435 z^3 - 3.14 z^2 + 1.591 z
- 0.3667

Sampling time: 1

We rewrite the transfer function G(z − 1 ) in the following form for reference in
the next chapter:
0 . 1397
1 . 965

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

( 1 + + + + +

− 0 . 1866 z − 5 )
(6.68)
The magnitude response of the lowpass elliptic filter G(z) , the magnitude
response of the parallel connection G(z)

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

1

=

2 [ A 1 (z)

+ A 2 (z) ], and that of the

1

highpass filter H(z)

=

2 [ A 1 (z)

− A 2 (z) ] are shown in Figures 6.20, 6.21, and

6.22, respectively.
The two allpass filter functions (6.69) and (6.71) obtained in the example
above are expressed in the form of (6.70) and 6.72, respectively. The function
A 1 (z) can be realized in the direct form, and A 2 (z) can be realized in many
of the structures that we have already discussed, for example, the direct form,

Magnitude of specified LP filter

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized frequency

Figure 6.20 Magnitude response of the elliptic lowpass filter G(z) .