Spectral flux is a measure of how quickly the

power spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...

of a

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

is changing, calculated by comparing the power spectrum for one frame against the power spectrum from the previous frame. More precisely, it is usually calculated as the L2-norm (also known as the

Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...

) between the two normalised spectra. Calculated this way, the spectral flux is not dependent upon overall power (since the spectra are normalised), nor on phase considerations (since only the magnitudes are compared). The spectral flux can be used to determine the

timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...

of an audio signal, or in

onset Onset may refer to: *Onset (audio), the beginning of a musical note or sound *Onset, Massachusetts Onset is a census-designated place (CDP) in the town of Wareham, Massachusetts, United States. The population was 1,573 at the 2010 census. Geog ...

detection, among other things.

Variations

Some implementations use the L1-norm rather than the L2-norm (i.e. the sum of absolute differences rather than the sum of squared differences). Some implementations do not normalise the spectra. For onset detection, increases in energy are important (not decreases), so some algorithms only include values calculated from bins in which the energy is increasing.

References

Digital signal processing {{Signal-processing-stub