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