PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

630 Practical MATLAB® Applications for Engineers

Example 6.9

Create the script fi le cheby_HPF that returns the coeffi cients of the digital transfer func-

tion and the magnitude and phase plots of a third-order Chebyshev type-1 and -2 digi-

tal HPFs with the following specs:

1. wc = 0.5 rad/s


2. T = 0.3


3. Rp = 2 dB


4. Rs = 3 dB
   MATLAB Solution
   % Script file: cheby _ HPF
   N =3; % order
   Rp = 2; Rs = 3; % ripples
   T = .3; % sampling period
   Wc = .5; % cut off frequency
   Wz = -2pi:.01pi:3pi;
   wzc = WcT/pi; % normalized dig. frequency
   [Pz1, Qz1] = cheby1(N, Rp, wzc, ‘high’);
   disp(‘****’)
   disp(‘*R E S U L T S *****’)
   disp(‘****’)
   disp(‘For the transfer function H(z) of the Cheby/type1 HPF’)
   disp(‘the numerators coefficients are:’)
   disp(Pz1)
   disp(‘The denominator coefficients are:’)
   disp(Qz1)
   [Pz2, Qz2] = cheby2(N, Rs, wzc, ‘high’);
   disp(‘ For the transfer function H(z) of the Cheby/type2 HPF’)
   disp(‘The numerators coefficients are:’)

FIGURE 6.58
Magnitude and phase plots of H(z) of Example 6.8.

− (^505)
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Mag.of digital LPF
magnitude
− 2 − 1 0 1 2
− 30
− 20
− 10
0
10
20
30
Phase of digital LPF versus w
W in rad W in rad
phase in degrees