Spectral centroid

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The spectral centroid is a measure used in digital signal processing to characterise an audio spectrum. It indicates where the "center of mass" of the spectrum is. Perceptually, it has a robust connection with the impression of "brightness" of a sound.^[1] It is calculated as the weighted mean of the frequencies present in the signal, with their magnitudes as the weights^[2]:

$Centroid = \frac{\sum_{n=0}^{N-1}f(n)x(n)}{\sum_{n=0}^{N-1}x(n)}$

where x(n) represents the magnitude of bin number n, and f(n) represents the center frequency of that bin.

[edit] 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.

[edit] References

^ Schubert, E., Wolfe, J. and Tarnopolsky, A. (2004) Spectral centroid and timbre in complex, multiple instrumental textures, in Proceedings of the International Conference on Music Perception and Cognition, North Western University, Illinois
^ A Large Set of Audio Features for Sound Description - technical report published by IRCAM in 2003. Section 6.1.1 describes the spectral centroid.