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| [[File:White noise spectrum.svg|thumb|Maximum spectral flatness (approaching 1) is achieved by white noise.]]
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| '''Spectral flatness''' or '''tonality coefficient''',<ref name="johnston88">
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| {{cite journal
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| |author=J. D. Johnston
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| |title=Transform coding of audio signals using perceptual noise criteria
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| |journal=IEEE Journal on Selected Areas in Communications
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| |volume=6
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| |issue=2 |pages=314–332
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| |year=1988
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| |doi=10.1109/49.608
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| }}</ref><ref name="Signal Processing Letters">
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| {{cite journal
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| |author=Shlomo Dubnov
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| |title=Generalization of Spectral Flatness Measure for Non-Gaussian Linear Processes
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| |journal=Signal Processing Letters
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| |volume=11
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| |issue=8 |pages=698–701
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| |year=2004
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| |issn=1070-9908
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| |doi=10.1109/LSP.2004.831663
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| }}</ref> also known as '''Wiener entropy''',<ref>[http://soundanalysispro.com/manual-1/chapter-4-the-song-features-of-sap2/wiener-entropy The Song Features › Wiener entropy] "defined as the ratio of geometric mean to arithmetic mean of the spectrum"</ref><ref>[http://luscinia.sourceforge.net/page19/page8/page33/page33.html Luscinia parameters] "Wiener entropy is an alternative measure of the noisiness of a signal. It is defined as the ratio of the geometric mean to the arithmetic mean of the power spectrum."</ref> 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 [[Pitch (music)|tone]]-like a sound is, as opposed to being [[noise]]-like.<ref name="Signal Processing Letters" />
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| 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 wave]]s, and the spectrum would appear "spiky".<ref>[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</ref>
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| The spectral flatness is calculated by dividing the [[geometric mean]] of the power spectrum by the [[arithmetic mean]] of the power spectrum, i.e.:
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| :<math> | |
| \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)}
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| </math>
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| where ''x(n)'' represents the magnitude of [[histogram|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.
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| 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.
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| The spectral flatness can also be measured within a specified subband, rather than across the whole band.
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| == Applications ==
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| This measurement is one of the many audio descriptors used in the [[MPEG-7]] standard, in which it is labelled <nowiki>"AudioSpectralFlatness"</nowiki>.
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| In [[bird vocalization|birdsong]] research, it has been used as one of the features measured on birdsong audio, when testing similarity between two excerpts.<ref>Tchernichovski, O., Nottebohm, F., Ho, C. E., Pesaran, B., Mitra, P. P., 2000. A procedure for an automated measurement of song similarity. Animal Behaviour 59 (6), 1167–1176, {{doi|10.1006/anbe.1999.1416}}.</ref>
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| == References == | |
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| {{Reflist}}
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| [[Category:Digital signal processing]]
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