# 1-f noise

*Due to technical limitations, this article uses an unusual title. It should be called*

**1/f noise**.

** ( "one over f " ) noise**, or more accurately

**noise**, is a signal or process with a power spectral density proportional to ,

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

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

The term **flicker noise** is sometimes used to refer to noise, although this is more properly applied only to its occurrence in electronic devices. 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.

## Description

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

### Pink noise

**Pink noise** is a term used in acoustics and engineering for noise which has equal power per octave or similar log-bundle^{[1]}. That is, if we consider all the frequencies in the range , the total power should depend only on and not on . We can see that a strict spectrum satisfies this if we calculate the integral,

### Relationship to fractional Brownian motion

The power spectrum of a fractional Brownian motion of Hurst exponent is proportional to:

## References

- ↑
^{1.0}^{1.1}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 spectrum: as
*α*increases, the light becomes darker and darker red.