Digital Signal Processing Reference
In-Depth Information
H
(
j
)
1.0
0.5
0
1
2
3
4
5
6
H
(
j
)
1
2
3
4
5
6
0
45
Figure 4.19
Frequency response for
90
Example 4.7.
The system in Example 4.7 has the transfer function
H(s) = 1/(s + 1)
and is
low pass. At the harmonic frequencies
kv
0
= k,
from Example 4.7,
1
tan
-1
(-k).
H(jkv
0
)
|
v
0
= 1
=
1 + k
2
∠
(4.44)
2
The plot of this function in Figure 4.19 shows graphically the system frequency re-
sponse. This plot can be verified with the following MATLAB program:
n = [0 1];
d = [1 1];
w = 0:0.25:5;
h = freqs(n, d, w);
hmag = abs(h);
hphase = angle(h)*180/pi;
plot(w, hmag)
plot(w, hphase)
[w', hmag', hphase']
The last statement gives a table of frequency, and the magnitude and phase of the
frequency response.
The low-pass nature of the system is evident from Figure 4.19, because
(called the system
gain
at the frequency ) approaches zero as ap-
proaches infinity. As shown in Figure 4.19, only isolated points have meaning for
periodic inputs. However, as shown in Chapters 5 and 6, the total frequency re-
sponse has meaning with respect to aperiodic inputs. Table 4.7 gives the frequency
response for the system of Example 4.7, as calculated by the MATLAB program.
ƒ
H(jkv
0
)
ƒ
kv
0
kv
0
