PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 613

disp(‘Coefficients of the denominator of the transf. function

[butter/wc=2rad/sec]’)

disp(Ql)

tf(Pl,Ql)

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

figure(5)

w =0:.1:5;

Hl =freqs(Pl,Ql,w);

mag5=abs(Hl);

phase5=angle(Hl);

subplot(1,2,1)

plot(w,mag5)

xlabel(‘frequency in rad/sec’);

ylabel(‘Magnitude’);

title(‘Magnitude of H(w) vs. w [Butter/wc=2]’);

subplot(1,2,2)

plot(w,phase5*180/pi)

xlabel(‘frequency in rad/sec’);

ylabel(‘Angle in degrees’);

title(‘Phase of H(w) vs. w [Butter/wc=2]’)

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

shown as follows (Figures 6.38 through 6.42):

>> shifting _ LPF

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

******* M A T L A B ***** R E S U L T ************

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

Solution to part (c)

Coefficients of numerator of trans. function [LPF/ with

L=C=1/2,R=1]

1

Coefficients of denominator of trans. function [LPF/lp2lp/wc=2]

0.2500 0.5000 1.0000

Transfer function:

1

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

0.25 s^2 + 0.5 s + 1

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

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

Solution to part (e)

Coefficients of the numerator of the trans. function [wc=1]

4

Coefficients of the denominator of the trans. function [wc=1]

1.0000 2.0000 4.0000

Transfer function:

4

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

s^2 + 2 s + 4

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