PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 623

MATLAB Solution

% Script file: butt _ chev

Rp = 1 ; % in db (passband ripple)

Rs = 1 ; % in db (stopband ripple)

Wp = 1 ; % pass band edge

% Butterworth LPF.

n = 5; % order

% transfer function, But. LPF.

[num1, den1] = butter (n, Wp, ‘s’);

% plot the frequency response Butterworth. LPF

w = [0:.1: 5];

h1 = freqs (num1, den1, w);

gain1 = 20 * log10 (abs (h1));

figure(1);

subplot(1,3,1);

plot(w,gain1);axis([0 5 -80 20]);

title (‘Butterworth LPF, N = 5’)

xlabel (‘ frequency w (rad/sec)’)

ylabel (‘gain, db’)

% Chebyshev LPF, type 1

[num2, den2] = Cheby1 ( n, Rp, Wp, ‘s’);

% plot the frequency response, Chebyshev 1 LPF

h2 = freqs (num2,den2,w);

gain2 = 20 * log10 (abs(h2));

subplot (1, 3, 2);

plot (w, gain2);

title (‘ Chebyshev 1 LPF, N=5’); axis([0 5 -100 20]);

xlabel (‘frequency w (rad/sec)’);

ylabel (‘gain, db’)

% Chebyshev LPF, type 2.

Wn = 1;% cut off norm. freq.

[num3, den3] = Cheby2 (n, Rs, Wn, ‘s’);

h3 = freqs (num3, den3, w);

gain3 = 20 * log10 (abs(h3));

subplot (1, 3, 3);

plot (w, gain3);

title (‘Chebyshev 2 LPF, N=5’);axis([0 2 -50 10]);

xlabel (‘ frequency w (rad/sec)’);

ylabel (‘gain, db’)

figure(2) % Butterworth phase

phase1=angle(h1);

subplot(1,3,1);

plot(w,phase1);axis([0 3 -4 4]);

xlabel (‘freq w(rad/sec)’);

ylabel(‘phase in rad’);

title(‘Butterworth, phase plot’)

% Chebyshev1 phase

phase2=angle(h2);

subplot(1,3,2)

plot(w,phase2);axis([0 2 -4 4]);

xlabel(‘freq w(rad/sec)’);

ylabel(‘phase in rad’);

title(‘Chebyshev 1, phase plot ‘)

% Chebyshev2 phase