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Problems 461<br />

1<br />

0.8913<br />

Magnitude Response<br />

1<br />

Phase Response<br />

phase in π units<br />

0.5<br />

0<br />

−0.5<br />

0<br />

0 0.25 0.4 0.7 0.8 1<br />

Digital frequency in π units<br />

−1<br />

0 0.25 0.4 0.7 0.8 1<br />

Digital frequency in π units<br />

0<br />

Magnitude in dB<br />

15<br />

Group Delay<br />

10<br />

5<br />

−40<br />

0 0.25 0.4 0.7 0.8 1<br />

Digital frequency in π units<br />

0<br />

0 0.25 0.4 0.7 0.8 1<br />

Digital frequency in π units<br />

FIGURE 8.34 Digital Chebyshev-II bandstop filter in Example 8.30<br />

A = 1.0000 1.3041 0.8031<br />

1.0000 0.8901 0.4614<br />

1.0000 0.2132 0.2145<br />

1.0000 -0.4713 0.3916<br />

1.0000 -0.8936 0.7602<br />

This is also a 10th-order filter. The frequency domain plots are shown in<br />

Figure 8.34.<br />

□<br />

8.7 PROBLEMS<br />

P8.1 A digital resonator is to be designed with ω 0 = π/4 that has 2 zeros at z =0.<br />

1. Compute and plot the frequency response of this resonator for r =0.8, 0.9, and 0.99.<br />

2. For each case in part 1, determine the 3 dB bandwidth and the resonant frequency ω r<br />

from your magnitude plots.<br />

3. Check if your results in part 2 are in agreement with the theoretical results.<br />

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