Continuous-time filters - Continuous and Discrete Time Signals and Systems - page 363

Fig. 7.15. Magnitude spectrum
of the Butterworth bandstop
filter designed in Example 7.12.

1

0.7943

0.6

0.4

0.1

0

0 50 100 150 200 250 300 350 400 450 500

with the transfer function of the bandstop filter is given by

H ( s ) = H ( S )

S = 270 s / s 2 + 3 . 7 10 4

1 . 8640

= ,

3 + 2 . 4641 2 + 3 . 0292

270 s
s 2 + 3 . 7 10 4

270 s
s 2 + 3 . 7 10 4

270 s
s 2 + 3 . 7 10 4

+ 1 . 8640

which reduces to
H ( s ) = s 6 + 1 . 11 10 5 s 4 + 4 . 107 10 9 s 2 + 5 . 065 10 13

s 6 + 4 . 388 10 2 s 5 + 2 . 0737 10 5 s 4 + 4 . 302 10 7 s 3 + 7 . 673 10 9 s 2 + 6 10 11 s + 5 . 065 10 13 .
The magnitude spectrum of the bandstop filter is included in Fig. 7.15, which
confirms that the given specifications are satisfied.

7.4.3.1 M ATL AB code for designing bandstop filters

The M ATLAB code for the design of the bandstop filter required in
Example 7.12 using the Butterworth, Type I Chebyshev, Type II Chebyshev,
and elliptic implementations is as follows:

%M ATLAB code for designing bandstop filter
>> wp=[100 370]; ws=[150 250]; Rp=2; Rs=20;
% Specifications

>> % Butterworth Filter
>> [N, wn] = buttord(wp,ws,Rp,Rs,'s');
>> [num1,den1] = butter(N,wn, 'stop','s');
>> H1 = tf(num1,den1);
>> % Type I Chebyshev filter
>> [N, wn] = cheb1ord(wp,ws,Rp,Rs,'s');
>> [num2,den2] = cheby1(N,Rp,wn, 'stop','s');
>> H2 = tf(num2,den2);
>> % Type II Chebyshev filter
>> [N,wn] = cheb2ord(wp,ws,Rp,Rs,'s');
>> [num3,den3] = cheby2(N,Rs,wn, 'stop','s');
>> H3 = tf(num3,den3);
>> % Elliptic filter
>> [N,wn] = ellipord(wp,ws,Rp,Rs,'s');
>> [num4,den4] = ellip(N,Rp,Rs,wn, 'stop','s');
>> H4 = tf(num4,den4);