White noise

For other uses, see White Noise.
Colors of noise
The waveform of a Gaussian white noise signal plotted on a graph

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.[1] The term is used with this or similar meanings in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, not to any specific signal. White noise draws its name from white light,[2] although light that appears white generally does not have a flat power spectral density over the visible band.

An image of salt-and-pepper noise

In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. In some contexts, it is also required that the samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest representation of white noise).[3] In particular, if each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise.[4]

The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus.

The sound of white noise

An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, random signals are considered white noise if they are observed to have a flat spectrum over the range of frequencies that are relevant to the context. For an audio signal, the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz). Such a signal is heard by the human ear as a hissing sound, resembling the /h/ sound in a sustained aspiration. On the other hand, the sh sound /ʃ/ in ash is a colored noise because it has a formant structure. In music and acoustics, the term white noise may be used for any signal that has a similar hissing sound.

In the context of phylogenetically based statistical methods, the term white noise can refer to a lack of phylogenetic pattern in comparative data.[5] In nontechnical contexts, it is sometimes used to mean "random talk without meaningful contents".[6][7]

  1. ^ Carter, Mancini, Bruce, Ron (2009). Op Amps for Everyone. Texas Instruments. pp. 10–11. ISBN 978-0-08-094948-2.{{cite book}}: CS1 maint: multiple names: authors list (link)
  2. ^ Stein, Michael L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer Series in Statistics. Springer. p. 40. doi:10.1007/978-1-4612-1494-6. ISBN 978-1-4612-7166-6. white light is approximately an equal mixture of all visible frequencies of light, which was demonstrated by Isaac Newton
  3. ^ Stein, Michael L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. Springer Series in Statistics. Springer. p. 40. doi:10.1007/978-1-4612-1494-6. ISBN 978-1-4612-7166-6. The best-known generalized process is white noise, which can be thought of as a continuous time analogue to a sequence of independent and identically distributed observations.
  4. ^ Diebold, Frank (2007). Elements of Forecasting (Fourth ed.).
  5. ^ Fusco, G; Garland, T. Jr; Hunt, G; Hughes, NC (2011). "Developmental trait evolution in trilobites". Evolution. 66 (2): 314–329. doi:10.1111/j.1558-5646.2011.01447.x. PMID 22276531. S2CID 14726662.
  6. ^ Claire Shipman (2005), Good Morning America: "The political rhetoric on Social Security is white noise." Said on ABC's Good Morning America TV show, January 11, 2005.
  7. ^ Don DeLillo (1985), White Noise