Signals and Systems - Electrical Engineering

408 C H A P T E R 6: Application to Control and Communications

n passband frequencies [10, 20] rad/sec

n unit gain in the passband

(b) Using theellipmethod, design a band-stop filter with unit gain in the passbands and the

following specifications:

n orderN= 20

n α()=0.1 dB in the passband

n α()=40 dB in the stopband

n passband frequencies [10, 11] rad/sec

The following script is used.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Example 6.12 --- general filter design

%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;clf

N = 10;

[b, a] = ellip(N/2, 0.1, 40, [10 11], ’stop’, ’s’) % elliptic band-stop

%[b, a] = cheby2(N, 60, [10 20], ’s’) % cheby2 bandpass

W = 0:0.01:30;

H = freqs(b, a, W);

Notice that the order given toellipis 5 and 10 tocheby2since a quadratic transformation will be

used to obtain the notch and the band-pass filters from a prototype low-pass filter. The magnitude

and phase responses of the two designed filters are shown in Figure 6.27. n

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Ω

|H

(Ω

)|

0 5 10 15 20 25 30

−10

−5

0

5

10

Ω

<H

(Ω

)

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Ω

|H

(Ω

)|

0 5 10 15 20 25 30

−10

−5

0

5

10

Ω

<H

(Ω

)

(a) (b)

FIGURE 6.27

Design of (a) a notch filter using ellip and of (b) a band-pass filter using cheby2.