# spectralKurtosis

Spectral kurtosis for signals and spectrograms

## Syntax

## Description

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

= spectralKurtosis(`x`

,`f`

,`Name=Value`

)

`[___,`

returns the spectral kurtosis threshold using the confidence level `threshold`

] = spectralKurtosis(___,`ConfidenceLevel`

=p)`p`

.
`threshold`

represents the range within which the spectral kurtosis
indicates that the input signal is Gaussian and stationary.* (since R2024b)*

`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

## More About

## Algorithms

The spectral kurtosis is calculated as described in [3]:

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

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] Antoni, J. "The Spectral Kurtosis:
A Useful Tool for Characterising Non-Stationary Signals." *Mechanical Systems and
Signal Processing*. Vol. 20, Issue 2, 2006, pp. 282–307.

[2] Antoni, J., and R. B. Randall.
"The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating
Machines." *Mechanical Systems and Signal Processing*. Vol. 20, Issue 2,
2006, pp. 308–331.

[3] 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

`kurtogram`

| `pspectrum`

| `spectralCentroid`

(Audio Toolbox) | `spectralEntropy`

| `spectralSkewness`

| `spectralSpread`

(Audio Toolbox)

### Topics

- Spectral Descriptors (Audio Toolbox)