Spectral kurtosis for audio signals and auditory spectrograms

`kurtosis = spectralKurtosis(x,f)`

`kurtosis = spectralKurtosis(x,f,Name,Value)`

`[kurtosis,spread,centroid] = spectralKurtosis(___)`

specifies options using one or more `kurtosis`

= spectralKurtosis(`x`

,`f`

,`Name,Value`

)`Name,Value`

pair arguments.

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

$$\text{kurtosis}=\frac{{\displaystyle \sum _{k={b}_{1}}^{{b}_{2}}{\left({f}_{k}-{\mu}_{1}\right)}^{4}{s}_{k}}}{{\left({\mu}_{2}\right)}^{4}{\displaystyle \sum _{k={b}_{1}}^{{b}_{2}}{s}_{k}}}$$

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.