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HSP43881

Digital Filter

Intersil 

HSP43881

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:

NUMBER SYSTEM

Two Unsigned Vectors

Two Two's Complement:

• Two Positive Vectors

• Negative Vectors

• One Positive and One Negative Vector

One Unsigned and One Two's Complement

Vector:

• Positive Two's Complement Vector

• Negative Two's Complement Vector

MAX #

OF TERMS

1032

2080

2047

2064

1036

1028

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.

CLK

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

TABLE 1. 30MHz, 8-TAP FIR FILTER SEQUENCE

X15...X9, X8, X7...X1, X0

C0...C6, C7, C0...C6, C7

HSP43881

Y15...Y14,...Y8, Y7

CELL 0

C7 x X0

+C6 x X1

+C5 x X2

+C4 x X3

+C3 x X4

+C2 x X5

+C1 x X6

+C0 x X7

C7 x X8

+C6 x X9

+C5 x X10

+C4 x X11

+C3 x X12

+C2 x X13

+C1 x X14

+C0 x X15

CELL 1

0

C7 x X1

+C6 x X2

+C5 x X3

+C4 x X4

C3 x X5

+C2 x X6

+C1 x X7

+C0 x X8

C7 x X9

+C6 x X10

+C5 x X11

+C4 x X12

+C3 x X13

+C2 x X14

+C1 x X15

CELL 2

0

0

C7 x X2

+C6 x X3

+C5 x X4

+C4 x X5

+C3 x X6

+C2 x X7

+C1 x X8

+C0 x X9

C7 x X10

+C6 x X11

+C5 x X12

+C4 x X13

+C3 x X14

+C2 x X15

CELL 3

0

0

0

C7 x X3

+C6 x X4

+C5 x X5

+C4 x X6

+C3 x X7

+C2 x X8

+C1 x X9

+C0 x X10

C7 x X11

+C6 x X12

+C5 x X13

+C4 x X14

+C3 x X15

CELL 4

C7 x X4

+C6 x X5

+C5 x X6

+C4 x X7

+C3 x X8

+C2 x X9

+C1 x X10

+C0 x X11

C7 x X12

+C6 x X13

+C5 x X14

+C4 x X15

CELL 5

C7 x X5

+C6 x X6

+C5 x X7

+C4 x X8

+C3 x X9

+C2 x X10

+C1 x X11

+C0 x X12

C7 x X13

+C6 x X14

+C5 x X15

CELL 6

C7 x X6

+C6 x X7

+C5 x X8

+C4 x X9

+C3 x X10

+C2 x X11

+C1 x X12

+C0 x X13

+C7 x X14

+C6 x X15

CELL 7

C7 x X7

+C6 x X8

+C5 x X9

+C4 x X10

+C3 x X11

+C2 x X12

+C1 x X13

+C0 x X14

C7 x X15

SUM/CLR

-

-

-

-

-

-

-

Cell 0 (Y7)

Cell 1 (Y8)

Cell 2 (Y9)

Cell 3 (Y10)

Cell 4 (Y11)

Cell 5 (Y12)

Cell 6 (Y13)

Cell 7 (Y14)

Cell 0 (Y15)

9

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