1/N octave analysis
PrintSpectrum analysis using filters whose bandwidth is a fractional ratio of the center frequency of the filter. For example, a 1/3 octave filter centered at 1000 Hz would have a bandwidth of 260 Hz (26% equals 1/3 octave). Bandwidth (relative to a normalized center frequency of 1) is computed as 2(1/N)-1. The typical bandwidths used (primarily for acoustical and vibration ananlysis) are 1/1 octave, 1/3, 1/12, and 1/24 octave.
Octave band filters do not have infinitely steep skirts. Therefore, an isolated tone may produce a reading in adjacent octave bands. Also, a tone at the nominal boundary between two bands produces an equal reading in both. (For example, a 60 dB tone at 707.1 Hz would give readings of 57 dB each in the 500 Hz and 1000 Hz octave bands.) Note also that filters designed according to ANSI S1.11 and IEC 1260 filters have different skirts. Bands adjacent to a strong tone may have different numerical readings with the two types of filters. The actual filter band center frequencies are typically developed as a series of powers of 21/3 times 1000 Hz, and therefore, may not correspond precisely to the nominal band center frequencies.
1/N octave filters have a constant relative bandwidth, which means that the Q factor of the filters are the same. In many respects, this is similar to many natural systems, which tend to have a similar behavior and are best viewed on a logarithmic frequency axis. For example, the frequency response of a simple (first order) low-pass filter looks like a straight line when plotted on a logarithmic frequency axis.
The following is a table of octave and third-octave filter center frequencies:
ISO Band Numbers | Octave Band Center Frequency | One-Third Octave Band Center Frequencies |
11, 12, 13 | 16 Hz | 12.5 Hz, 16 Hz, 20 Hz |
14, 15, 16 | 31.5 Hz | 25 Hz, 31 Hz, 40 Hz |
17, 18, 19 | 63 Hz | 50 Hz, 63 Hz, 80 Hz |
20, 21, 22 | 125 Hz | 100 Hz, 125 Hz, 160 Hz |
23, 24, 25 | 250 Hz | 200 Hz, 250 Hz, 315 Hz |
26, 27, 28 | 500 Hz | 400 Hz, 500 Hz, 630 Hz |
29, 30, 31 | 1000 Hz | 800 Hz, 1000 Hz, 1250 Hz |
32, 33, 34 | 2000 Hz | 1600 Hz, 2000 Hz, 2500 Hz |
35, 36, 37 | 4000 Hz | 3150 Hz, 4000 Hz, 5000 Hz |
38, 39, 40 | 8000 Hz | 6300 Hz, 8000 Hz, 10000 Hz |
41, 42, 43 | 16000 Hz | 12500 Hz, 16000 Hz, 20000 Hz |
V or dB vs.1/Oct (Hz)
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