Contraction (operator theory): Difference between revisions
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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> | |||
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> | |||
:<math> | |||
Centroid = \frac{ | |||
\sum_{n=0}^{N-1} | |||
f \left ( n \right ) | |||
x \left ( n \right ) | |||
} { | |||
\sum_{n=0}^{N-1} | |||
x \left ( n \right ) | |||
} | |||
</math> | |||
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. | |||
==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 [[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"/> | |||
==Applications== | |||
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> | |||
{{cite conference | |||
| last1 = Schubert | |||
| first1 = Emery | |||
| last2 = Wolfe | |||
| first2 = Joe | |||
| last3 = Tarnopolsky | |||
| first3 = Alex | |||
| others = Lipscomb, S.D.; Ashley, R.; Gjerdingen, R. O.; Webster, P. (Eds.) | |||
| year = 2004 | |||
| url = http://icmpc8.umn.edu/proceedings/ICMPC8/PDF/AUTHOR/MP040215.PDF | |||
| title = Spectral centroid and timbre in complex, multiple instrumental textures | |||
| conference = International Conference on Music Perception & Cognition | |||
| conferenceurl = http://www.icmpc8.umn.edu/index_all.htm | |||
| booktitle = Proceedings of the 8th International Conference on Music Perception & Cognition, North Western University, Illinois | |||
| publisher = School of Music and Music Education; School of Physics, University of New South Wales | |||
| location = Sydney, Australia | |||
}}</ref> | |||
==References== | |||
<references/> | |||
[[Category:Digital signal processing]] | |||
{{Signal-processing-stub}} | |||
Revision as of 11:12, 26 October 2012
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.[1]
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:[2]
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.[3]
References
- ↑ 1.0 1.1 1.2 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, 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ A Large Set of Audio Features for Sound Description - technical report published by IRCAM in 2003. Section 6.1.1 describes the spectral centroid.
- ↑
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