The spectral centroid is a measure used in
digital signal processing to characterise a
spectrum. It indicates where the
center of mass of the spectrum is located. Perceptually, it has a robust connection with the impression of
brightness of a sound.[1] It is sometimes called center of spectral mass.[2]
Calculation
It is calculated as the
weighted mean of the frequencies present in the signal, determined using a
Fourier transform, with their magnitudes as the weights:[3]
where x(n) represents the weighted frequency value, or magnitude, of
bin number n, and f(n) represents the center frequency of that bin.
Alternative usage
Some people use "spectral centroid" to refer to the
median of the spectrum. This is a different statistic, the difference being essentially the same as the difference between the unweighted median and
mean statistics. Since both are
measures of central tendency, in some situations they will exhibit some similarity of behaviour. But since typical audio spectra are not
normally distributed, the two measures will often give strongly different values. Grey and Gordon in 1978 found the mean a better fit than the median.[1]
Applications
Because the spectral centroid is a good predictor of the "brightness" of a sound,[1] it is widely used in digital audio and music processing as an automatic measure of musical
timbre.[4]
References
^
abcGrey, John M.; Gordon, John W. (1978). "Perceptual effects of spectral modifications on musical timbres". The Journal of the Acoustical Society of America. 63 (5). Acoustical Society of America (ASA): 1493–1500.
doi:
10.1121/1.381843.
ISSN0001-4966.