Spectral flatness

Spectral flatness or tonality coefficient, also known as Wiener entropy, 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 tone-like a sound is, as opposed to being noise-like. 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 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.:

$\mathrm{Flatness} = \frac{\sqrt[N]{\prod_{n=0}^{N-1}x(n)}}{\frac{\sum_{n=0}^{N-1}x(n)}{N}} = \frac{\exp\left(\frac{1}{N}\sum_{n=0}^{N-1} \ln x(n)\right)}{\frac{1}{N} \sum_{n=0}^{N-1}x(n)}$

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.

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

Applications

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

In birdsong research, it has been used as one of the features measured on birdsong audio, when testing similarity between two excerpts.