Digital Signal Processing Reference
In-Depth Information
G
4
( )
3
3
1200
1200
800
0
800
(a)
G
3
( )
5
5
5
5
1200
c
800
800
1200
0
(b)
H
1
( )
0.6
1200
c
800
0
800
1200
c
(c)
Figure 6.4
Figure for Example 6.1.
Application of an ideal low-pass filter
EXAMPLE 6.2
We work with the signals from Example 6.1. Assume this time that an application requires a
signal
g
5
(t) = 4 cos(800pt).
This can be obtained from
g
3
(t)
by a low-pass filter. The Fourier transform of
g
5
(t)
is
G
5
(v) = 4p[d(v - 800p) + d(v + 800p)]
.
The frequency spectrum of is shown in Figure 6.5. To pass the frequency components of
at with an output amplitude of requires a gain of 0.8, as shown in
the ideal low-pass filter in Figure 6.6. Again, the filtering process is written as
g
5
(t)
G
3
(v)
v =+-800p
4p
G
5
(v) = G
3
(v)H
2
(v),
G
5
()
4
4
Figure 6.5
Frequency spectrum for
800
800
Example 6.2.
