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| 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. Perceptually, it has a robust connection with the impression of "brightness" of a sound.<ref name="greygordon78">Grey, J. M., Gordon, J. W., 1978. Perceptual effects of spectral modifications on musical timbres. Journal of the Acoustical Society of America 63 (5), 1493–1500, {{doi|10.1121/1.381843}}</ref>
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| 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:<ref>[http://recherche.ircam.fr/equipes/analyse-synthese/peeters/ARTICLES/Peeters_2003_cuidadoaudiofeatures.pdf A Large Set of Audio Features for Sound Description] - technical report published by [[IRCAM]] in 2003. Section 6.1.1 describes the spectral centroid.</ref>
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| :<math>
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| Centroid = \frac{
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| \sum_{n=0}^{N-1}
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| f \left ( n \right )
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| x \left ( n \right )
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| } {
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| \sum_{n=0}^{N-1}
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| x \left ( n \right )
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| }
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| </math>
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| where ''x(n)'' represents the weighted frequency value, or magnitude, of [[Histogram|bin]] number ''n'', and ''f(n)'' represents the center frequency of that bin.
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| ==Alternative usage==
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| 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 [[Average|measures of central tendency]], in some situations they will exhibit some similarity of behaviour. But since typical audio spectra are not [[normal distribution|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.<ref name="greygordon78"/>
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| ==Applications==
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| Because the spectral centroid is a good predictor of the "brightness" of a sound,<ref name="greygordon78"/> it is widely used in digital audio and music processing as an automatic measure of musical [[timbre]].<ref>
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| {{cite conference
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| | last1 = Schubert
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| | first1 = Emery
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| | last2 = Wolfe
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| | first2 = Joe
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| | last3 = Tarnopolsky
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| | first3 = Alex
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| | others = Lipscomb, S.D.; Ashley, R.; Gjerdingen, R. O.; Webster, P. (Eds.)
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| | year = 2004
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| | url = http://icmpc8.umn.edu/proceedings/ICMPC8/PDF/AUTHOR/MP040215.PDF
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| | title = Spectral centroid and timbre in complex, multiple instrumental textures
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| | conference = International Conference on Music Perception & Cognition
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| | conferenceurl = http://www.icmpc8.umn.edu/index_all.htm
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| | booktitle = Proceedings of the 8th International Conference on Music Perception & Cognition, North Western University, Illinois
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| | publisher = School of Music and Music Education; School of Physics, University of New South Wales
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| | location = Sydney, Australia
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| }}</ref>
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| ==References==
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| <references/>
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| [[Category:Digital signal processing]]
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| {{Signal-processing-stub}}
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