Physics:Octave band
An octave band is a frequency band that spans one octave (
Play (help·info)). In this context an octave can be a factor of 2[1] or a factor of 100.3.[2][3] 2/1 = 1200 cents ≈ 100.301.
Fractional octave bands such as 1⁄3 or 1⁄12 of an octave are widely used in engineering acoustics.[4]
Analyzing a source on a frequency by frequency basis is possible. [5] Alternatively, the whole frequency range can be divided into sets of frequencies called bands. Each band covers a specific range of frequencies. For this reason, a scale of octave bands and one-third octave bands has been developed. A band is said to be an octave in width when the upper band frequency is twice the lower band frequency. A one-third octave band is defined as a frequency band whose upper band-edge frequency (f2) is the lower band frequency (f1) times the cube root of two.
Octave bands
Calculation
If [math]\displaystyle{ f_c }[/math] is the center frequency of an octave band, one can compute the octave band boundaries as
[math]\displaystyle{ f_c = \sqrt{2} f_{min} = \frac{f_{max}}{\sqrt{2}} }[/math],
where [math]\displaystyle{ f_{min} }[/math] is the lower frequency boundary and [math]\displaystyle{ f_{max} }[/math] the upper one.
Naming
| Band Number | Nominal Frequency[6] | Calculated Frequency | A-Weighting Adjustment |
|---|---|---|---|
| -1 | 16 Hz | 15.625 Hz | |
| 0 | 31.5 Hz | 31.250 Hz | -39.4 dB |
| 1 | 63 Hz | 62.500 Hz | -26.2 dB |
| 2 | 125 Hz | 125.000 Hz | -16.1 dB |
| 3 | 250 Hz | 250.000 Hz | -8.6 dB |
| 4 | 500 Hz | 500.000 Hz | -3.2 dB |
| 5 | 1 kHz | 1000.000 Hz | 0 dB |
| 6 | 2 kHz | 2000.000 Hz | 1.2 dB |
| 7 | 4 kHz | 4000.000 Hz | 1 dB |
| 8 | 8 kHz | 8000.000 Hz | -1.1 dB |
| 9 | 16 kHz | 16000.000 Hz | -6.6 dB |
One-third octave bands
Base 2 calculation
%% Calculate Third Octave Bands (base 2) in Matlab fcentre = 10^3 * (2 .^ ([-18:13]/3)) fd = 2^(1/6); fupper = fcentre * fd flower = fcentre / fd
Base 10 calculation
%% Calculate Third Octave Bands (base 10) in Matlab fcentre = 10.^(0.1.*[12:43]) fd = 10^0.05; fupper = fcentre * fd flower = fcentre / fd
Naming
| Band Number | Nominal Frequency | Base-2 Calculated Frequency | Base-10 Calculated Frequency |
|---|---|---|---|
| 1 | 16 Hz | 15.625 Hz | 15.849 Hz |
| 2 | 20 Hz | 19.686 Hz | 19.953 Hz |
| 3 | 25 Hz | 24.803 Hz | 25.119 Hz |
| 4 | 31.5 Hz | 31.250 Hz | 31.623 Hz |
| 5 | 40 Hz | 39.373 Hz | 39.811 Hz |
| 6 | 50 Hz | 49.606 Hz | 50.119 Hz |
| 7 | 63 Hz | 62.500 Hz | 63.096 Hz |
| 8 | 80 Hz | 78.745 Hz | 79.433 Hz |
| 9 | 100 Hz | 99.213 Hz | 100 Hz |
| 10 | 125 Hz | 125.000 Hz | 125.89 Hz |
| 11 | 160 Hz | 157.490 Hz | 158.49 Hz |
| 12 | 200 Hz | 198.425 Hz | 199.53 Hz |
| 13 | 250 Hz | 250.000 Hz | 251.19 Hz |
| 14 | 315 Hz | 314.980 Hz | 316.23 Hz |
| 15 | 400 Hz | 396.850 Hz | 398.11 Hz |
| 16 | 500 Hz | 500.000 Hz | 501.19 Hz |
| 17 | 630 Hz | 629.961 Hz | 630.96 Hz |
| 18 | 800 Hz | 793.701 Hz | 794.43 Hz |
| 19 | 1 kHz | 1000.000 Hz | 1000 Hz |
| 20 | 1.25 kHz | 1259.921 Hz | 1258.9 Hz |
| 21 | 1.6 kHz | 1587.401 Hz | 1584.9 Hz |
| 22 | 2 kHz | 2000.000 Hz | 1995.3 Hz |
| 23 | 2.5 kHz | 2519.842 Hz | 2511.9 Hz |
| 24 | 3.150 kHz | 3174.802 Hz | 3162.3 Hz |
| 25 | 4 kHz | 4000.000 Hz | 3981.1 Hz |
| 26 | 5 kHz | 5039.684 Hz | 5011.9 Hz |
| 27 | 6.3 kHz | 6349.604 Hz | 6309.6 Hz |
| 28 | 8 kHz | 8000.000 Hz | 7943.3 Hz |
| 29 | 10 kHz | 10079.368 Hz | 10 kHz |
| 30 | 12.5 kHz | 12699.208 Hz | 12.589 kHz |
| 31 | 16 kHz | 16000.000 Hz | 15.849 kHz |
| 32 | 20 kHz | 20158.737 Hz | 19.953 kHz |
See also
- Octave
- Octave (electronics)
References
- ↑ Crocker 1997
- ↑ IEC 61260-1:2014
- ↑ IANSI S1-6-2016
- ↑ "Octave-Band Center Frequencies". Archived from the original on 2017-05-14. https://web.archive.org/web/20170514010527/http://www.cross-spectrum.com/audio/articles/center_frequencies.html. Retrieved 2017-11-23.
- ↑ "Fast Fourier Transformation FFT - Basics". https://www.nti-audio.com/en/support/know-how/fast-fourier-transform-fft. Retrieved 2024-01-09.
- ↑ "ANSI S1.11: Specification for Octave, Half-Octave, and Third Octave Band Filter Sets". p. 13. https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.11.2004.pdf. Retrieved 7 March 2018.
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