1/f noise

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It has been suggested that this article or section be merged with Pink noise. (Discuss)

$1 / f$ noise, or more accurately $1 / f α$ noise, is a signal or process with a power spectral density proportional to $1 / f α$ ,

$S(f) = \frac{\textrm{constant}}{f^\alpha}$

where $f$ is the frequency. Typically use of the term focuses on noises with exponents in the range 0 < α < 2, that is, fluctuations whose structure falls in-between white ( $α = 0$ ) and brown ( $α = 2$ ) noise. Such " $1 / f$ -like" noises are widespread in nature and a source of great interest to diverse scientific communities.

The "strict $1 / f$ " case of α = 1 is also referred to as pink noise, although the precise definition of the latter term^[1] is not a $1 / f$ spectrum per se but that it contains equal energy per octave, which is only satisfied by a $1 / f$ spectrum. The name stems from the fact that it lies in the middle between white ( $1 / f 0$ ) and red ( $1 / f 2$ , more commonly known as Brown or Brownian) noise^[2].

The term flicker noise is sometimes used to refer to $1 / f$ noise, although this is more properly applied only to its occurrence in electronic devices due to a direct current. Mandelbrot and Van Ness proposed the name fractional noise (sometimes since called fractal noise) to emphasise that the exponent of the spectrum could take non-integer values and be closely related to fractional Brownian motion, but the term is very rarely used.

1 Description
- 1.1 Pink noise
- 1.2 Relationship to fractional Brownian motion
2 References
- 2.1 Notes
- 2.2 Bibliography

[edit] Description

In the most general sense, noises with a $1 / f α$ spectrum include white noise, where the power spectrum is proportional to $1 / f 0$ = constant, and Brownian noise, where it is proportional to $1 / f 2$ . The term black noise is sometimes used to refer to $1 / f α$ noise with an exponent α > 2.

[edit] Pink noise

^[1]

[edit] Relationship to fractional Brownian motion

The power spectrum of a fractional Brownian motion of Hurst exponent H is proportionnal to: $1 / f 2 H + 1$

[edit] References

[edit] Notes

^ ^a ^b Federal Standard 1037C and its successor, American National Standard T1.523-2001.
^ Confusingly, the term "red noise" is sometimes used instead to refer to pink noise. In both cases the name springs from analogy to light with a $1 / f α$ spectrum: as α increases, the light becomes darker and darker red.