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Spectral skewness for audio signals and auditory spectrograms

`skewness = spectralSkewness(x,f)`

`skewness = spectralSkewness(x,f,Name,Value)`

`[skewness,spread,centroid] = spectralSkewness(___)`

specifies options using one or more `skewness`

= spectralSkewness(`x`

,`f`

,`Name,Value`

)`Name,Value`

pair arguments.

The spectral skewness is calculated as described in [1]:

$$\text{skewness}=\frac{{\displaystyle \sum _{k={b}_{1}}^{{b}_{2}}{\left({f}_{k}-{\mu}_{1}\right)}^{3}{s}_{k}}}{{\left({\mu}_{2}\right)}^{3}{\displaystyle \sum _{k={b}_{1}}^{{b}_{2}}{s}_{k}}}$$

where

*f*is the frequency in Hz corresponding to bin_{k}*k*.*s*is the spectral value at bin_{k}*k*.*b*_{1}and*b*_{2}are the band edges, in bins, over which to calculate the spectral skewness.*μ*_{1}is the spectral centroid, calculated as described by the`spectralCentroid`

function.*μ*_{2}is the spectral spread, calculated as described by the`spectralSpread`

function.

[1] Peeters, G. "A Large Set of Audio Features for Sound Description (Similarity and Classification) in the CUIDADO Project." Technical Report; IRCAM: Paris, France, 2004.