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394 Chapter 8 IIR FILTER DESIGN
Imaginary Part
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
Pole–zero Plot
2
–1 –0.5 0 0.5 1
Real Part
FIGURE 8.5
Decibel
Radians / π
10
0
Magnitude Response
–50
–1 0 1
1
0.5
0
–0.5
Phase Response
–1
–1 0 1
ω in π units
Frequency response of a typical notch filter
around the desired null are severely attenuated. To reduce the bandwidth
of the null, we may resort to the more sophisticated, longer FIR
filter designed according to the optimum equiripple design method described
in Chapter 7. Alternatively, we could attempt to improve the frequency
response of the filter by introducing poles in the system function.
Imaginary Part
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
Pole–zero Plot
2
–1 –0.5 0 0.5 1
Real Part
Decibel
Radians / π
10
0
Magnitude Response
–50
–1 –1/4 0 1/4 1
1
0.5
0
–0.5
Phase Response
–1
–1 –1/4 0 1/4 1
ω in π units
FIGURE 8.6 Frequency response of a notch filter with ω 0 = π/4
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