Digital Signal Processing Reference
In-Depth Information
s
(
n
)
s
(
n
)
R
(
z
)
0
E
(
z
)
0
R
(
z
)
1
R
(
z
)
1
E
(
z
)
1
−
R
(
z
)
0
A
(
z
)
can be arbitrary
channel part
equalizer part
Figure 4.31
. The FSE schematic for
L
= 2, with the redundant transfer function
A
(
z
) included. In the absence of channel noise the ouput
s
(
n
) is unaffected by the
choice of
A
(
z
). Thus in the presence of noise,
A
(
z
) offers an extra degree of freedom
that can be optimized such that
s
(
n
)isascloseto
s
(
n
) as possible.
H
(
j
ω
)
c
(a)
ω
−π
/T
0
π
/T
j
ω
C
(
e
)
L
(b)
ω
−π
/L
0
π
/L
π
−π
Figure 4.32
. (a) A continuous-time channel without excess bandwidth, and (b) the
oversampled version with oversampling ratio
L.
Summarizing, when there is no excess bandwidth, (i.e.,
H
c
(
jω
) is bandlimited
to
ω
<π/T
), there is no benefit to oversampling. The benefits of FSE arise when
there is excess bandwidth, which is usually the case in practice. In Chap. 10 we
shall briefly revisit this issue in the context of optimal pre- and post-filtering in
transceivers.
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