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Analog-to-Digital Filter Transformations 439
1
0.8913
Magnitude Response
1
Phase Response
|H|
π units
0
0.1778
0
0 0.2 0.3 1
frequency in π units
−1
0 0.2 0.3 1
frequency in π units
0
1
Magnitude in dB
15
Group Delay
decibels
15
Samples
10
5
0 0.2 0.3 1
frequency in π units
0
0 0.2 0.3 1
frequency in π units
FIGURE 8.27
Digital Chebyshev-I lowpass filter using bilinear transformation
The desired filter is a 4th-order filter and has 4 zeros at z = −1. The system
function is
0.0018 ( 1+z −1) 4
H(z) =
(1 − 1.4996z −1 +0.8482z −2 )(1− 1.5548z −1 +0.6493z −2 )
The frequency response plots are given in Figure 8.27 which are similar to those
in Figure 8.22.
□
□ EXAMPLE 8.19 Design the digital Chebyshev-II filter of Example 8.13. The specifications are
ω p =0.2π, R p =1dB
ω s =0.3π, A s =15dB
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