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 100.3. 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 formula_1 is the center frequency of an octave band, one can compute the octave band boundaries as
formula_2,
where formula_3 is the lower frequency boundary and formula_4 the upper one.
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