PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

658 Practical MATLAB® Applications for Engineers

plot(w,abs(H7));axis([0 4 -.5 1.5]);

ylabel(‘magnitude’)

title(‘Butt. BS,center freq,=2,stopband=1Butt.’)

subplot(2,2,2);

plot(w,angle(H7)*180/pi)

ylabel(‘phase (deg)’)

title(‘Butt.BSF’)

[num8,den8] = lp2bs(num2,den2,2,1);

H8 = freqs(num8,den8,w);

subplot(2,2,3)

plot(w,abs(H8));axis([0 6 -.5 1.5]);

ylabel(‘magnitude’)

xlabel(‘frequency(rad/sec)’)

title(‘Cheb.BS ,cent freq=2,BW stopband=1’)

subplot(2,2,4);

plot(w,angle(H8)*180/pi)

ylabel(‘phase (deg)’)

xlabel(‘frequency (rad/sec)’)

title(‘Cheb. BSF’)

Back in the command window, the script fi le revisit_analog_fi lters is executed and the

results are as follows (Figures 6.81 through 6.84):

>> revisit _ analog _ filters

Example 6.23

Indicate the steps and compute by hand the discrete IIR fi lter’s transfer function from

the analog RC-LPF of Example 6.1 (R = 1 Ω and C = 1 F) by employing a sampling period

of T = 0.01 s.

ANALYTICAL Solution

The solution follows the steps indicated:

1. Determine the analog fi lter’s transfer function H(s).


2. From the transfer function H(s), obtain the system impulse response h(t) = £−^1 [H(s)].

FIGURE 6.81
Four-pole analog Butterworth and Chebyshev/type-1 normalized LPFs of Example 6.22.

0 2 4 6

Butt. norm. LPF

0 2 4 6

− 200

− 100

0

0

100

200

phase (deg)

− 200

− 100

100

200

phase (deg)

Butt. LPF

0 2 4 6

0

0.2

0.4

0.6

0.8

1

magnitude

0

0.2

0.4

0.6

0.8

1

magnitude

Cheb. norm. LPF

frequency (rad/sec)

0246

frequency (rad/sec)

Cheb. LPF