Digital Signal Processing Reference
In-Depth Information
s
(
n
)
L
C
(
z
)
L
G
(
z
)
L
s
(
n
)
L
(a)
s
(
n
)
R
(
z
)
0
L
E
(
z
)
0
s
(
n
)
L
z
-
1
z
R
(
z
)
1
L
E
(
z
)
1
L
z
z
-
1
z
-
1
z
(b)
R
(
z
)
L
L
L
E
(
z
)
L
−1
−
1
s
(
n
)
R
(
z
)
0
E
(
z
)
0
s
(
n
)
R
(
z
)
1
E
(
z
)
1
(c)
R
(
z
)
L
E
(
z
)
L
−
1
−
1
channel
equalizer
Figure 4.23
. (a) The oversampled channel
C
L
(
z
) and fractionally spaced equalizer
G
L
(
z
), (b) polyphase representation, and (c) simplified equivalent.
4.8.2 Comparing SSE and FSE with examples
For the special case where the fractionally spaced equalizer uses an oversampling
rate
L
= 2, Fig. 4.24(a) shows the equalizer system and Fig. 4.24(b) shows the
corresponding polyphase representation.
The noise sources
q
2
,
0
(
n
)and
q
2
,
1
(
n
) are the even and odd samples of the
oversampled channel noise
q
2
(
n
)
.
Consider a second-order FIR channel
2
ρ
cos
θz
−
1
+
ρ
2
z
−
2
C
1
(
z
)=1
−
with a complex conjugate pair of zeros at
ρe
±jθ
,
and assume
ρ
=0
.
999
,
θ
=0
.
2
π.
So 1
/C
1
(
z
)haspoles0
.
999
e
±
0
.
2
jπ
very close to the unit circle.
Assume the
channel noise
q
(
n
) is white Gaussian with zero mean and variance
σ
q
=10
−
5
.
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