Upper and lower cutoff frequency of the 1/1, 1/3 octave band

There are three types in the frequency characteristics of the band pass filter, such as Ⅰ type (for simple measurement), Ⅱ type (for normal measurement) and Ⅲ type (for precision measurement). The moderateness of cutoff frequency is in order of Ⅰ>Ⅱ>Ⅲ. According to the JIS C 1513-1983, Ⅰ and Ⅱ types are applicable to the 1/1 octave band pass filter, and Ⅱ and Ⅲ types are applicable to the 1/3 octave band pass filter. It is also prescribed in the ANCI CLASS Ⅲ.

 

The band number, central frequency, and cutoff frequency (upper and lower frequency) can be obtained in the following formula, and results are described in the following table.

 

Calculation formula of the cutoff frequency

fm: Central frequency
f1: Lower limit of the cutoff frequency
f2: Upper limit of the cutoff frequency

 

(1) In the 1/1 octave band pass filter

f1 = fm / √2 ≒ fm÷1.4142
f2 = √2 ×fm ≒ 1.4142 × fm
f2 = 2 × f1

 

(2) In the 1/3 octave band pass filter

f1 = fm / 6√2 ≒ fm ÷ 1.1225
f2 = 6√2 × fm≒ 1.1225 × fm
f2 = 3√2 × f1 ≒ 1.2599 × f1

 

 

Band number
1/1 octave (Hz)
Central frequency fm
Lower limit of the frequency f1
Upper limit of the frequency f2
0
1
0.71
1.41
3
2
1.41
2.83
6
4
2.83
5.66
9
8
5.66
11.31
12
16
11.3
22.6
15
31.5
22.3
44.5
18
63
44.5
89.1
21
125
88.4
176.8
24
250
176.8
353.6
27
500
353.6
707.1
30
1000
707.1
1414.2
33
2000
1414.2
2828.4
36
4000
2828.5
5656.8
39
8000
5656.9
11313.6
42
16000
11313.8
22627.2

 

Band number
1/3 octave (Hz)
Central frequency fm
Lower limit of the frequency f1
Upper limit of the frequency f2
-2
0.63
0.56
0.71
-1
0.8
0.71
0.90
0
1
0.89
1.12
1
1.25
1.11
1.40
2
1.6
1.43
1.80
3
2
1.78
2.25
4
2.5
2.23
2.81
5
3.15
2.81
3.54
6
4
3.56
4.49
7
5
4.45
5.61
8
6.3
5.61
7.07
9
8
7.13
8.98
10
10
8.9
11.2
11
12.5
11.1
14.0
12
16
14.3
18.0
13
20
17.8
22.5
14
25
22.3
28.1
15
31.5
28.1
35.4
16
40
35.6
44.9
17
50
44.5
56.1
18
63
56.1
70.7
19
80
71.3
89.8
20
100
89.1
112.3
21
125
111.4
140.3
22
160
142.5
179.6
23
200
178.2
224.5
24
250
222.7
280.6
25
315
280.6
353.6
26
400
356.3
449.0
27
500
445.4
561.3
28
630
561.2
707.2
29
800
712.7
898.0
30
1000
890.9
1122.5
31
1250
1113.6
1403.1
32
1600
1425.4
1796.0
33
2000
1781.7
2245.0
34
2500
2227.2
2806.3
35
3150
2806.2
3535.9
36
4000
3563.5
4490.0
37
5000
4454.3
5612.5
38
6300
5612.5
7071.8
39
8000
7126.9
8980.0
40
10000
8908.7
11225.0
41
12500
11135.9
14031.3
42
16000
14253.9
17960.0
43
20000
17817.4
22450.0
44
25000
22271.7
28062.5
45
31500
28062.4
35358.8
46
40000
35634.7
44900.0
47
50000
44543.4
56125.0
48
63000
56124.7
70717.5
49
80000
71269.5
89800.0
50
100000
89086.9
112250.

Revised:2002.06.17


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