Digital Signal Processing Reference
In-Depth Information
steady state reached
h
(0) +
h
(1) +
h
(2)
output =
h
(0) +
h
(1) −
h
(2)
1 1
−
1 1
−
h
(0) +
h
(1)
+
h
(2)
1
−
1
(a)
−
1
−
1
−
h
(0)
−
h
(1)
+
h
(2)
−
h
(0)
−
h
(1)
−
h
(2)
h
(0)
−
h
(1)
−
h
(2)
four states
time
n
0
1
2
3
4
5
6
h
(0) +
h
(1)
+
h
(2)
−
h
(0) +
h
(1)
+
h
(2)
h
(0) +
h
(1)
−
h
(2)
1 1
−
1 1
h
(0) −
h
(1)
−
h
(2)
(b)
−
h
(0) +
h
(1)
+
h
(2)
1
−
1
−
1
−
1
−
h
(0)
−
h
(1)
+
h
(2)
Figure 5.15
. (a) The trellis diagram for the channel
H
(
z
)=
h
(0)+
h
(1)
z
−
1
+
h
(2)
z
−
2
,
with one-bit PAM constellation (symbol values
±
1). (b) A specific path through the
trellis corresponding to the input sequence [
−
1
−
1111
−
1]
.
In the figure, heavy
arrows represent input symbol 1
,
and the light arrows represent input symbol
−
1
.
The
labels on the edges represent filter outputs corresponding to the present state and
present input. For example if the present input is
−
1 and the state is [
−
1
,
1]
,
then the
filter output is
−
h
(0)
−
h
(1) +
h
(2)
.
Showing the noise-free outputs
Given an input
s
(
n
)andastatevector
x
(
n
)attime
n,
the inputs to all the
multipliers
h
(
k
) in Fig. 5.14 are determined. This determines the output
y
(
n
)
completely. All the branches in the trellis are labeled with the output value
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