Spectral flatness

Spectral flatness is a measure used in digital signal processing to characterise an audio spectrum. A high spectral flatness indicates that the spectrum has a similar amount of power in all spectral bands - this would sound similar to white noise, and the graph of the spectrum would appear relatively flat and smooth. A low spectral flatness indicates that the spectral power is concentrated in a relatively small number of bands - this would typically sound like a mixture of sine waves, and the spectrum would appear "spiky".

The spectral flatness is calculated by dividing the geometric mean of the power spectrum by the arithmetic mean of the power spectrum, i.e.:

:$Flatness\; =\; frac\{sqrt\; [N]\; \{prod\_\{n=0\}^\{N-1\}x(n)\{(frac\{sum\_\{n=0\}^\{N-1\}x(n)\}\{N\})\}$

where "x(n)" represents the magnitude of bin number "n".

This measurement is one of the many audio descriptors used in the MPEG-7 standard, in which it is labelled "AudioSpectralFlatness".

The spectral flatness can also be measured within a specified subband, rather than across the whole band.

References

* [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 9.1 describes spectral flatness.
* J. D. Johnston, [http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=39&arnumber=608 Transform coding of audio signals using perceptual noise criteria] , Selected Areas in Communications, IEEE Journal on, 6 (1988), pp. 314–323.