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25 July 2008
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Table 1 & 2
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Soft Radios and Modems on FPGAs
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TABLE 1: A pattern evolves from J-filter responses.
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y
a
= x
1
h
0
+ x
2
h
4
+ x
3
h
8
+ x
4
h
12
+ x
5
h
15
+ x
6
h
11
+ x
7
h
7
+ x
8
h
3
y
b
= x
2
h
3
+ x
3
h
7
+ x
4
h
11
+ x
5
h
15
+ x
6
h
12
+ x
7
h
8
+ x
8
h
4
+ x
9
h
0
y
c
= x
2
h
2
+ x
3
h
6
+ x
4
h
10
+ x
5
h
14
+ x
6
h
13
+ x
7
h
9
+ x
8
h
5
+ x
9
h
1
y
d
= x
2
h
1
+ x
3
h
5
+ x
4
h
9
+ x
5
h
13
+ x
6
h
14
+ x
7
h
10
+ x
8
h
6
+ x
9
h
2
y
e
= x
2
h
0
+ x
3
h
4
+ x
4
h
8
+ x
5
h
12
+ x
6
h
15
+ x
7
h
11
+ x
8
h
7
+ x
9
h
3
y
f
= x
3
h
3
+ x
4
h
7
+
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TABLE 2: The modulated filter response.
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Y
b
= x
I2
h
3
+ x
I3
h
7
+ x
I4
h
11
+ x
I5
h
15
+ x
I6
h
12
+ x
I7
h
8
+ x
I8
h
4
+ x
I9
h
0
Y
c
= x
Q2
h
2
+ x
Q3
h
6
+ x
Q4
h
10
+ x
Q5
h
14
+ x
Q6
h
13
+ x
Q7
h
9
+ x
Q8
h
5
+ x
Q9
h
1
Y
d
= - [ x
I2
h
1
+ x
I3
h
5
+ x
I4
h
9
+ x
I5
h
13
+ x
I6
h
14
+ x
I7
h
10
+ x
I8
h
6
+ x
I9
h
2
]
Y
e
= - [ x
Q2
h
0
+ x
Q3
h
4
+ x
Q4
h
8
+ x
Q5
h
12
+ x
Q6
h
15
+x
Q7
h
11
+ x
Q8
h
7
+ x
Q9
h
3
]
Y
f
= x
I3
h
3
+ x
I4
h
7
+
..
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Soft Radios and Modems on FPGAs
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