Octave

Two frequencies are an octave apart if the ratio of the higher frequency to the lower frequency is two.

Band NumberNominal Centre Frequency HzExact Centre Frequency HzPassband Hz
322.001.41 - 2.82
643.982.82 - 5.62
987.945.62 - 11.2
121615.8511.2 - 22.4
1531.531.6222.4 - 44.7
186363.1044.7 - 89.1
21125125.8989.1 - 178
24250251.19178 - 355
27500501.19355 - 708
3010001000.0708 - 1410
3320001995.31410 - 2820
3640003981.12820 - 5620
3980007943.35620 - 11200
421600015848.911200 - 22400

1/3 Octave Bands
Preferred centre frequencies and passbands are defined by ISO R 266 and ANSI S1.6-1984. The nominal centre frequencies are used to identify the bands and are normally what is reported. The true centre frequencies are calculated using
where
fc = true centre frequency [Hz]
n = band number

1/3 octave filters are sometimes referred to as 1/10 decade filters.

For convenience, 1/3-octave bands are sometimes numbered from band No. 1 (1.25 Hz third-octave centre frequency, which cannot be heard by humans) to band No. 43 (20000 Hz third-octave centre frequency).

Band NumberNominal Centre Frequency HzExact Centre Frequency HzPassband Hz
11.251.261.12 - 1.41
21.61.581.41 - 1.78
322.001.78 - 2.24
42.52.512.24 - 2.82
53.153.162.82 - 3.55
643.983.55 - 4.47
755.014.47 - 5.62
86.36.315.62 - 7.08
987.947.08 - 8.91
101010.08.91 - 11.2
1112.512.5911.2 - 14.1
121615.8514.1 - 17.8
132019.9517.8 - 22.4
142525.1222.4 - 28.2
1531.531.6228.2 - 35.5
164039.8135.5 - 44.7
175050.1244.7 - 56.2
186363.1056.2 - 70.8
198079.4370.8 - 89.1
20100100.0089.1 - 112
21125125.89112 - 141
22160158.49141 - 178
23200199.53178 - 224
24250251.19224 - 282
25315316.23282 - 355
26400398.11355 - 447
27500501.19447 - 562
28630630.96562 - 708
29800794.33708 - 891
3010001000.0891 - 1120
3112501258.91120 - 1410
3216001584.91410 - 1780
3320001995.31780 - 2240
3425002511.92240 - 2820
3531503162.32820 - 3550
3640003981.13550 - 4470
3750005011.94470 - 5620
3863006309.65620 - 7080
3980007943.37080 - 8910
401000010000.08910 - 11200
411250012589.311200 - 14100
421600015848.914100 - 17800
432000019952.617800 - 22400

For 1/3 octave filters the time required for the amplitude to approach the final value is ~1/B where B=filter bandwidth. For 100Hz centre, 23.1Hz bandwidth 1/B=1/23=0.04s.

For broadband random signals the standard deviation of each 1/3 octave band can be estimated by:

where
σ = standard deviation [dB]
B = bandwidth of the signal [Hz], this is 23.1% of the 1/3 octave centre frequency
T = measurement time [s]

This shows that the level of the higher frequency 1/3 octave bands stabilises much quicker than the lower centre frequency bands. For the 100Hz 1/3 octave centre frequency a measurement time of 82 seconds is required for a standard deviation of 0.1dB.

See also: Bandwidth Time Product, Constant Percentage Bandwidth Filter, Frequency.

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Subjects: Noise & Vibration