Octave band

An octave band is a frequency band that spans one octave (). In this context an octave can be a factor of 2 or a factor of 10^0.3. 2/1 = 1200 cents ≈ 10.

Fractional octave bands such as or of an octave are widely used in engineering acoustics.

Analyzing a source on a frequency by frequency basis is possible but time-consuming. The whole frequency range is 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 $f_c$ is the center frequency of an octave band, one can compute the octave band boundaries as

$f_c = \sqrt f_ = \frac$,

where $f_$ is the lower frequency boundary and $f_$ the upper one.

Naming

One-third octave bands

Base 2 calculation

%% Calculate Third Octave Bands (base 2) in Matlab
fcentre = 10^3 * (2 .^ ( 18:133))
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.* 2:43
fd = 10^0.05;
fupper = fcentre * fd
flower = fcentre / fd

Naming

See also

*Octave
*Octave (electronics)

References

Acoustics

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