Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 334

2. Then, carrying out the prototype transformation (lowpass to bandstop) using the first-order lowpass prototype
filter given by

H P s ¼

1
s þ 1

it follows that

s 2 þ u 0
s 2 þ Ws þ u 0

HðsÞ¼H P ðsÞ sW
s 2 þu 0

¼

Substituting the values of u 0 and W yields

s 2 þ 5:7341 10 8
s 2 þ 4; 149s þ 5:7341 10 8

HðsÞ¼

3. Hence, applying the BLT leads to

s¼16;000ðz1Þ=ðzþ1Þ

s 2 þ 5:7341 10 8
s 2 þ 4; 149s þ 5:73411 10 8

HðzÞ¼

After algebra, we get

HðzÞ¼ 0:9259 þ 0:7078 z 1 þ 0:9249 z 2
1 þ 0:7078z 1 þ 0:8518z 2

10

0

-10

-20

-30

-40

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

100

50

0

-50

-100

0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hertz)

FIGURE 8.21
Frequency responses of the designed digital filter for Example 8.12.