Spectral flatness or tonality coefficient, also known as Wiener entropy, is a measure used in

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...

to characterize an audio

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...

. Spectral flatness is typically measured in

decibels The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whose ...

, and provides a way to quantify how much a sound resembles a

pure tone Pure may refer to: Computing * A pure function * A pure virtual function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify tool * Pure-FTPd, F ...

, as opposed to being

noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...

-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 In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, ...

. 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 A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...

s, and the spectrum would appear "spiky". The spectral flatness is calculated by dividing the

geometric mean In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...

of the power spectrum by the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...

of the power spectrum, i.e.: :

\mathrm = \frac = \frac

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 The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...

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. Dubnov has shown that spectral flatness is equivalent to information theoretic concept of

mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such ...

that is known as dual total correlation.

Applications

This measurement is one of the many audio descriptors used in the

MPEG-7 MPEG-7 is a multimedia content description standard. It was standardized in ISO/ IEC 15938 (Multimedia content description interface). This description will be associated with the content itself, to allow fast and efficient searching for material th ...

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. Spectral flatness has also been used in the analysis of electroencephalography (EEG) diagnostics and research, and psychoacoustics in humans.

References

{{Reflist Digital signal processing