Digital Signal Processing Reference
In-Depth Information
v
1
(
t
)
Ideal
low-pass
filter
v
2
(
t
)
(a)
V
1
( )
Information
signal
V
0
Noise
Noise
c
c
(b)
H
( )
A
c
c
(c)
V
2
( )
Information
signal
AV
0
c
c
Figure 6.2
An ideal low-pass filter used to
eliminate noise.
(d)
Therefore, from Table 5.2, its impulse response is
h(t) = F
-1
5
6
H(v)
= (v
c
/p) sinc(v
c
t),
as sketched in Figure 6.3. It is seen that the impulse response for this ideal filter be-
gins long before the impulse occurs at (theoretically, at ). Systems
such as this, which respond to an input before the input is applied, are called
noncausal systems
, as discussed in Chapters 2 and 3. Of course, the physical exis-
tence of noncausal systems is impossible. However, the concept of noncausal sys-
tems, such as ideal filters, can be useful during the initial stages of a design or
analysis effort. The following examples illustrate some applications of the
ideal filter
concept:
t =-
q
t = 0
