PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 647

MATLAB Solution

% Script file: IIR-yul

% IIR/YULE-WALKER

% for N = 4, 6, 8, and 10

f = [0:.1:1.0];

omega = 0:1/512:511/512;

mag = [1 1 1 .707 zeros(1,7)];

[num4,den4] = yulewalk(4,f,mag);

[num6,den6] = yulewalk(6,f,mag);

[num8,den8] = yulewalk(8,f,mag);

[num10,den10] = yulewalk(10,f,mag);

h4 = freqz(num4,den4);

h6 = freqz(num6,den6);

h8 = freqz(num8,den8);

h10 = freqz(num10,den10);

figure(1)

subplot(2,2,1)

plot(f,mag,’o’,omega,abs(h4))

ylabel(‘Magnitude(H)’)

title(‘Order=4’)

subplot(2,2,2)

plot(f,mag,’o’,omega,abs(h6))

ylabel(‘Magnitude(H)’)

title(‘Order=6’)

subplot(2,2,3)

plot(f,mag,’o’,omega,abs(h8))

FIGURE 6.72

Gain and phase plots of the transfer function of the fi lter of Example 6.17.

0

Gain in db

 50

 100

 150

 200

 250

2.5 1.5 0.5 0.5 1.5 2.5



104

104

 10

Magnitude of [H(f)] versus f

Phase of [H(f)] versus f

f in Hertz

f in Hertz

 2 12

100

50

 50

 100

0

Angle in degrees

2.5  2 1.5 101 20.5 0.5 1.5 2.5

See Figure 6.72.