Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 320

Table 8.5 Chebyshev Lowpass Prototype Transfer Functions with 1 dB Ripple ( ε ¼ 0 : 5088 Þ
n H P ðsÞ

1:9652
s þ

1

1 : 9652

0 : 9826

2

s

2

þ 1 : 0977 s þ 1 : 1025

0 : 4913

3

s

3

þ 0 : 9883 s

2

þ 1 : 2384 s þ 0 : 4913

0 : 2456

4

s

4

þ 0 : 9528 s

3

þ 1 : 4539 s

2

þ 0 : 7426 s þ 0 : 2756

0 : 1228

5

s

5

þ 0:9368s

4

þ 1:6888s

3

þ 0:9744s

2

þ 0:5805s þ 0:1228

0 : 0614

6

s

6

þ 0:9283s

5

þ 1:9308s

4

þ 1:20121s

3

þ 0:9393s

2

þ 0:3071s þ 0:0689

10 0 : 1 A s 1
ε

log 10

2

n (8.29)

½ 2 $ log 10 ðv s Þ

where ε is the absolute ripple specification.
The magnitude response function of a Chebyshev lowpass prototype with order n is shown in
Figure 8.14 , where the magnitude response jH P ðvÞj versus the normalized frequency v is given by

1
1 þ ε

jH P ðvÞj ¼ q (8.30)

v

2 2

n

C

where

C n v s ¼ cosh n cosh 1 v s

(8.31)

Hv

P ()

1

Hv ()

1 P

1

22

v

n

1

1

2

n 1

n

A s

n 3 2

v

v p 1

v s

0

FIGURE 8.13
Normalized Butterworth magnitude response function.