11.4 IIR Filter Design 671FIGURE 11.17
Equal-order(N= 15 )(a) Butterworth
and (b) Chebyshev filters for filtering of
acoustic signal. (b)
(a)− 1 0 1− 1−0.500.51Real partImaginary part
0 2000400060008000
0246810|H(f)|f(Hz)0 2000400060008000− 40− 30− 20− 100<H(f
)f(Hz)0− 20− 1001020α(ω)dBf(Hz)2000 4000 6000 8000− (^101)
− 1
−0.5
0
0.5
1
Real part
Imaginary part
0 2000400060008000
0
2
4
6
8
10
|H
(f
)|
f(Hz)
0 2000400060008000
− 40
− 30
− 20
− 10
0
<H
(f
)
f(Hz)
0 2000400060008000
− 20
− 10
0
10
20
α
(ω
)dB
f(Hz)
Design a Butterworth and a Chebyshev low-pass filters of the same order and compare their
frequency responses.
Solution
The specifications of the discrete filter are:
dc gain= 10 ⇒α(ej^0 )=−20 dB
Half-power frequency:ωhp= 2 πfhp( 1 /fs)=0.4πrad
Band-stop frequency:ωst= 2 πfst( 1 /fs)=0.5πrad