9
overflow. The maximum number of terms depends also on
the number system and the distribution of the coefficient and
data values. Then maximum numbers of terms in the sum
products are:
For practical FIR filters, the coefficients are never all near
maximum value, so even larger vectors are possible in
practice.
Basic FIR Operation
A simple, 30MHz 8-tap filter example serves to illustrate
more clearly the operation of the DF. The sequence table
(Table 1) shows the results of the multiply accumulate in
each cell after each clock. The coefficient sequence, Cn,
enters the DF on the left and moves from left to right through
the cells. The data sample sequence, Xn, enters the DF from
the top, with each cell receiving the same sample
simultaneously. Each cell accumulates the sum of products
for one output point. Eight sums of products are calculated
simultaneously, but staggered in time so that a new output is
available every system clock.
NUMBER SYSTEM
MAX #
OF TERMS
Two Unsigned Vectors
1032
Two Two's Complement:
Two Positive Vectors
Negative Vectors
One Positive and One Negative Vector
2080
2047
2064
One Unsigned and One Two's Complement
Vector:
Positive Two's Complement Vector
Negative Two's Complement Vector
1036
1028
TABLE 1. 30MHz, 8-TAP FIR FILTER SEQUENCE
CLK
CELL 0
CELL 1
CELL 2
CELL 3
CELL 4
CELL 5
CELL 6
CELL 7
SUM/CLR
0
C
7
x X
0
0
0
0
-
1
+C
6
x X
1
C
7
x X
1
0
0
-
2
+C
5
x X
2
+C
6
x X
2
C
7
x X
2
0
-
3
+C
4
x X
3
+C
5
x X
3
+C
6
x X
3
C
7
x X
3
-
4
+C
3
x X
4
+C
4
x X
4
+C
5
x X
4
+C
6
x X
4
C
7
x X
4
-
5
+C
2
x X
5
C
3
x X
5
+C
4
x X
5
+C
5
x X
5
+C
6
x X
5
C
7
x X
5
-
6
+C
1
x X
6
+C
2
x X
6
+C
3
x X
6
+C
4
x X
6
+C
5
x X
6
+C
6
x X
6
C
7
x X
6
-
7
+C
0
x X
7
+C
1
x X
7
+C
2
x X
7
+C
3
x X
7
+C
4
x X
7
+C
5
x X
7
+C
6
x X
7
C
7
x X
7
Cell 0 (Y7)
8
C
7
x X
8
+C
0
x X
8
+C
1
x X
8
+C
2
x X
8
+C
3
x X
8
+C
4
x X
8
+C
5
x X
8
+C
6
x X
8
Cell 1 (Y8)
9
+C
6
x X
9
C
7
x X
9
+C
0
x X
9
+C
1
x X
9
+C
2
x X
9
+C
3
x X
9
+C
4
x X
9
+C
5
x X
9
Cell 2 (Y9)
10
+C
5
x X
10
+C
6
x X
10
C
7
x X
10
+C
0
x X
10
+C
1
x X
10
+C
2
x X
10
+C
3
x X
10
+C
4
x X
10
Cell 3 (Y10)
11
+C
4
x X
11
+C
5
x X
11
+C
6
x X
11
C
7
x X
11
+C
0
x X
11
+C
1
x X
11
+C
2
x X
11
+C
3
x X
11
Cell 4 (Y11)
12
+C
3
x X
12
+C
4
x X
12
+C
5
x X
12
+C
6
x X
12
C
7
x X
12
+C
0
x X
12
+C
1
x X
12
+C
2
x X
12
Cell 5 (Y12)
13
+C
2
x X
13
+C
3
x X
13
+C
4
x X
13
+C
5
x X
13
+C
6
x X
13
C
7
x X
13
+C
0
x X
13
+C
1
x X
13
Cell 6 (Y13)
14
+C
1
x X
14
+C
2
x X
14
+C
3
x X
14
+C
4
x X
14
+C
5
x X
14
+C
6
x X
14
+C
7
x X
14
+C
0
x X
14
Cell 7 (Y14)
15
+C
0
x X
15
+C
1
x X
15
+C
2
x X
15
+C
3
x X
15
+C
4
x X
15
+C
5
x X
15
+C
6
x X
15
C
7
x X
15
Cell 0 (Y15)
X
15
...X
9,
X
8,
X
7
...X
1,
X
0
C
0
...C
6,
C
7,
C
0
...C
6,
C
7
HSP43881
Y
15
...Y
14,
...Y
8,
Y
7
HSP43881