PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 631

disp(Pz2)

disp(‘The denominator coefficients are:’); disp(Qz2)

disp(‘********************************************’)

[mag1, phase1] = freqz (Pz1,Qz1,Wz);

[mag2, phase2] = freqz (Pz2,Qz2,Wz);

subplot (2,2,1)

plot (Wz, mag1)

title (‘Mag of Cheby. type/1, HPF’);

axis([0 5 0 1.1]);

xlabel (‘ W in rad’)

ylabel (‘Magnitude’)

subplot (2,2,2)

plot (Wz, phase1* 180/pi)

title (‘Phase of Cheby. type/1,HPF ‘)

ylabel (‘Angle in degrees’)

xlabel (‘ W in rad’)

subplot (2,2,3)

plot (Wz, mag2)

title (‘Mag.of Cheby. type/2, HPF’); axis([0 1 0 1.5]);

xlabel (‘W in rad’); ylabel (‘Magnitude’)

subplot (2,2,4)

plot (Wz, phase2 * 180/ pi);

xlabel (‘W in rad’)

ylabel (‘Angle in degrees’)

title(‘Phase. of Cheby. type/2, HPF’)

disp(‘****** FILTERS TRANSFER FUNCTIONS*******’)

disp(‘********************************************’)

disp(‘Chebyshev type 1’)

tf(Pz2,Qz2,T)

disp(‘^^^^^^^^^^^^^^^^^^^’)

disp(‘Chebyshev type 2’)

tf(Pz1,Qz1,T)

disp(‘****************************************************’)

The script fi le cheby_HPF is executed and the results are shown as follows (Figure 6.59):

>> cheby _ HPF

********************************************

************* R E S U L T S ***************

********************************************

For the transfer function H(z) of the Cheby/type1 HPF

the numerators coefficients are:

0.8006 -2.4019 2.4019 -0.8006

The denominator coefficients are:

1.0000 -2.5767 2.2067 -0.6217

For the transfer function H(z) of the Cheby/type2 HPF

The numerators coefficients are:

0.9564 -2.8530 2.8530 -0.9564

The denominator coefficients are:

1.0000 -2.8943 2.8098 -0.9147