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122 Chapter 4 THE z-TRANSFORM
Pole–Zero Plot
1
0.8
0.6
0.4
Imaginary part
0.2
0
−0.2
0
0.9
−0.4
−0.6
−0.8
−1
−1 −0.5 0 0.5 1
Real Part
FIGURE 4.7 Pole-zero plot of Example 4.11a
Note that we specified b=[1,0] instead of b=1 because the zplane function
assumes that scalars are zeros or poles. The resulting pole-zero plot is shown
in Figure 4.7.
b. Using (4.23) and (4.24), we can determine the magnitude and phase of
H(e jω ). Once again we will use MATLAB to illustrate the use of the freqz
function. Using its first form, we will take 100 points along the upper half of
the unit circle.
MATLAB Script:
>> [H,w] = freqz(b,a,100); magH = abs(H); phaH = angle(H);
>> subplot(2,1,1);plot(w/pi,magH);grid
>> xlabel(’frequency in pi units’); ylabel(’Magnitude’);
>> title(’Magnitude Response’)
>> subplot(2,1,2);plot(w/pi,phaH/pi);grid
>> xlabel(’frequency in pi units’); ylabel(’Phase in pi units’);
>> title(’Phase Response’)
The response plots are shown in Figure 4.8. If you study these plots carefully,
you will observe that the plots are computed between 0 ≤ ω ≤ 0.99π and
fall short at ω = π. This is due to the fact that in MATLAB the lower half
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