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Table 3 Tested digital filters

From: Bounded model checking for fixed-point digital filters

#

Filter

N

M

\(\sum |h_{k}|\)

Input

Bits

Bound

1

LP-IIR

2

1

2

[−1,1]

<2,4>

6

2

LP-Butterworth-IIR

3

3

1.2

[−1.6,1.6]

<2,5>

6

3

LP-IIR

3

1

4

[−1,1]

<3,4>

6

4

LP-IIR

3

1

1.56

[−1,1]

<2,4>

6

5

HP-ChebyshevI-IIR

3

3

1.33

[−1,1]

<2,6>

6

6

BP-Elliptic-IIR

3

3

1.24

[−1,1]

<2,8>

6

7

BS-Butterworth-IIR

3

3

1.81

[−1.1,1.1]

<2,8>

6

8

BP-Elliptic-IIR

5

5

0.91

[−1.1,1.1]

<1,7>

10

9

HP-Butterworth-IIR

5

5

1.58

[−1.27,1.27]

<2,6>

10

10

BP-ChebyshevI-IIR

5

5

1.51

[−1.33,1.33]

<2,6>

10

11

HP-Elliptic-IIR

7

7

5.39

[−1,1]

<3,11>

14

12

HP-Cascade-IIR

6

6

12.4

[−1,1]

<5,5>

14

13

BS-Cascade-IIR

9

9

2.45

[−1,1]

<3,5>

19

14

LP-Parallel-IIR

6

6

16.6

[−1,1]

<5,5>

13

15

LP-Cascade-IIR

6

6

7.64

[−1,1]

<4,4>

13

16

Multiband-Parallel-IIR

9

9

2.75

[−1,1]

<4,4>

19

17

LP-FIR

1

31

1.94

[−1,1]

<2,6>

31

18

Multiband-FIR

1

9

2.18

[−1,1]

<2,6>

13

19

Multiband-FIR

1

25

1.47

[−1,1]

<2,8>

25

20

LP-WiFi-FIR

1

21

2.92

[−1,1]

<3,5>

21