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390 Chapter 8 IIR FILTER DESIGN
8.2 SOME SPECIAL FILTER TYPES
In this section we consider the design of several special types of digital
filters and describe their frequency response characteristics. We begin by
describing the design and characteristics of a digital resonator.
8.2.1 DIGITAL RESONATORS
A digital resonator is a special two-pole bandpass filter with a pair of
complex-conjugate poles located very near the unit circle, as shown in
Figure 8.3a. The magnitude of the frequency response of the filter is shown
in Figure 8.3b. The name resonator refers to the fact that the filter has a
large magnitude response in the vicinity of the pole position. The angle of
the pole location determines the resonant frequency of the filter. Digital
resonators are useful in many applications, including simple bandpass
filtering and speech generation.
Let us consider the design of a digital resonator with a resonant peak
at or near ω = ω 0 . Hence, we select the pole position as
p 1,2 = re ±jω0 (8.6)
Imaginary Part
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
Digital Resonator Responeses
Pole–zero Plot
Magnitude Response
–1 –0.5 0 0.5 1
2
Real Part
Magnitude
Radians / π
1
0.8
0.6
0.4
0.2
0
–1 –1/3 0 1/3 1
0.5
0
Phase Response
–0.5
–1 –1/3 0 1/3 1
ω in π units
FIGURE 8.3 Pole positions and frequency response of a digital resonator with
r =0.9 and ω 0 = π/3
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