Digital Signal Processing Reference
In-Depth Information
3
c
x
(
t
)
c
c
(a)
2
T
t
0
T
3
T
−
c
−
c
matched
filter
(b)
β
(
t
)
t
0
3α
w
(
t
)
=
(
β
x
)(
t
)
*
α
α
(c)
t
3
T
2
T
T
0
−α
−α
Figure 2.41
. (a) The signal
x
(
t
) at the receiver input, (b) matched filter impulse
response, and (c) matched filter output (signal component).
x(t)
t
3
T
0
T
2
T
Figure 2.42
. The transmitted signal
x
(
t
) with overlapping pulses
p
(
t − nT
)
.
2.
Channel impulse response.
In the preceding discussions we assumed that
the received signal is equal to the transmitted signal
x
(
t
) plus noise. In
practice the transmitted signal is also distorted by the channel frequency
response
H
(
jω
)
.
Thus the effective pulse is the convolution of
p
(
t
)with
the channel impulse response
h
(
t
), and the channel output has the form
s
(
n
)(
h
∗
p
)(
t
−
nT
)
,
(2
.
91)
n
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