# spectralKurtosis

Spectral kurtosis for signals and spectrograms

## Syntax

## Description

specifies options using one or more name-value arguments.`kurtosis`

= spectralKurtosis(`x`

,`f`

,`Name=Value`

)

`spectralKurtosis(___)`

with no output arguments plots
the spectral kurtosis.

If the input is in the time domain, the spectral kurtosis is plotted against time.

If the input is in the frequency domain, the spectral kurtosis is plotted against frame number.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

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`

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

(Audio Toolbox) function.

## References

[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.

## Extended Capabilities

## Version History

**Introduced in R2019a**

## See Also

`spectralCentroid`

(Audio Toolbox) | `spectralSpread`

(Audio Toolbox) | `spectralSkewness`

### Topics

- Spectral Descriptors (Audio Toolbox)