Digital Signal Processing Reference
In-Depth Information
1
5.0625
0.0008s
2
0.0882s
5.0625
0.5
Signal
Generator
Butterworth Filter
Scope 1
0
0.5
1
0.1
0.15
Time (second)
0.2
0.25
Scope 2
(a)
(b)
1
0.5
0
0.5
1
0.1
0.15
Time (second)
0.2
0.25
0
50
100
150
200
250
300
350
400
450
Frequency (rad/s)
(c)
(d)
Figure 6.16
S
IMULINK
diagram and plots for Example 6.6.
Scope 2 displays the filter's input signal. Scope 1 displays the filter's output signal. The
filter input and output signals are shown in Figure 6.16(b) and (c), respectively.
Figure 6.16(d) shows an approximation of the magnitude frequency spectra of the filter
input and output. The stem plot shows the magnitude frequency spectrum of the output sig-
nal. The dashed curve indicates the magnitude frequency spectrum of the input signal. From
the plots in Figure 6.16(d), it is seen that the high-frequency components
(v 7 200 rad/s)
of
the output signal are reduced in magnitude by the filter.
■
It can be confirmed that each of the low-pass Butterworth filters described can
be converted to a high-pass Butterworth filter with the same cutoff frequency by re-
placing each capacitor with an inductor so that
1
C
i
v
2
,
L
i
=
(6.5)
