PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

644 Practical MATLAB® Applications for Engineers

MATLAB Solution

% Script file : butt _ implem

[z,p,k] = buttap(3);

disp(‘ ******* R E S U L T S ********’)

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

disp(‘the poles are :’);disp(p);

[Pn,Qn] = zp2tf(z,p,k); % returns the transf. function

disp(‘The coefficients of the numerator of Hn(s) are: ‘); disp(Pn);

disp(‘The coefficients of the denominator of Hn(s) are: ‘); disp(Qn);

system = tf(Pn,Qn);

system

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

w =-3:.1:3;

hn = freqs(Pn,Qn,w);

gain=20*log10(abs(hn));

subplot(1,2,1)

plot(w,gain)

xlabel(‘w in rad/sec’)

ylabel(‘gain in db’)

title(‘Normalize filter/magnitude’)

subplot(1,2,2)

plot(w,angle(hn)*180/pi);

xlabel(‘w in rad/sec’);ylabel(‘Phase in degrees’)

title(‘Normalize filter/phase’)

Back in the command window the script fi le butt_implem is executed and the results are

shown as follows (Figure 6.69):

>> butt _ implem

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

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

the poles are :

-0.5000 + 0.8660i

-0.5000 - 0.8660i

-1.0000

The coefficients of the numerator of Hn(s) are:

0 0 0 1.0000

The coefficients of the denominator of Hn(s) are:

1.0000 2.0000 2.0000 1.0000

Transfer function:

1

---------------------

s^3 + 2 s^2 + 2 s + 1

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

FIGURE 6.68
Filter’s structure of Example 6.17.

1 Ω

C

Vi(s) Vo(s)

L 1 L 2