Spectral flatness or tonality coefficient,[1][2] also known as Wiener entropy,[3][4] is a measure used in digital signal processing to characterize an audio spectrum. Spectral flatness is typically measured in decibels, and provides a way to quantify how noise-like a sound is, as opposed to being tone-like.[2]
The meaning of tonal in this context
is in the sense of the amount of peaks or resonant structure in a power spectrum, as opposed to flat spectrum of a white noise. A high spectral flatness
(approaching 1.0 for white noise) 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 (approaching 0.0 for a pure tone) 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".[5]
The spectral flatness is calculated by
dividing the geometric mean of the power spectrum by the arithmetic mean of
the power spectrum, i.e.:
![{\mathrm {Flatness}}={\frac {{\sqrt[ {N}]{\prod _{{n=0}}^{{N-1}}x(n)}}}{{\frac {\sum _{{n=0}}^{{N-1}}x(n)}{N}}}}={\frac {\exp \left({\frac {1}{N}}\sum _{{n=0}}^{{N-1}}\ln x(n)\right)}{{\frac {1}{N}}\sum _{{n=0}}^{{N-1}}x(n)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/11508079a0c7aa6a86e8db802359974a0fccb60e)
where x(n) represents the magnitude of bin
number n. Note that a single (or more) empty bin
yields a flatness of 0, so this measure is most useful when bins are generally
not empty.
The ratio produced by this calculation is often
converted to a decibel scale
for reporting, with a maximum of 0 dB and a minimum of −∞ dB.
The spectral flatness can also be measured within a
specified subband, rather than across the whole band.
출처: <https://en.wikipedia.org/wiki/Spectral_flatness>
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