# White noise

whitenoisestatichissatmospheric hazeband-limited white noisebroadband noisefaint hissGaussian white noiseHiss (white noise)
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.wikipedia
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In particular, if each sample has a normal distribution with zero mean, the signal is said to be additive white Gaussian noise.
AWGN is often used as a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density (expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude.

### Wiener process

Brownian motionWiener measurestandard Brownian motion
White noise is the generalized mean-square derivative of the Wiener process or Brownian motion.
In applied mathematics, the Wiener process is used to represent the integral of a white noise Gaussian process, and so is useful as a model of noise in electronics engineering (see Brownian noise), instrument errors in filtering theory and unknown forces in control theory.

### Pink noise

1/f noisepink1/''f'' noise
Pink noise, which differs from white noise in that it has equal energy in each octave, is used for testing transducers such as loudspeakers and microphones.
This is in contrast with white noise which has equal intensity per frequency interval.

### White noise machine

white noise generatornoise mixingsound machine
White noise machines and other white noise sources are sold as privacy enhancers and sleep aids and to mask tinnitus.
Often such devices do not produce actual white noise, which has a harsh sound, but pink noise, whose power rolls off at higher frequencies, or other colors of noise.

### Gaussian noise

Gaussianwhite Gaussian noiseGaussian random noise
It is often incorrectly assumed that Gaussian noise (i.e., noise with a Gaussian amplitude distribution – see normal distribution) necessarily refers to white noise, yet neither property implies the other.
In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise.

### White

Pure Whitewhite lightwhitish
White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band.

White noise is a common synthetic noise source used for sound masking by a tinnitus masker.
By raising the ambient level of noise (playing white noise into the ear), the apparent loudness of tinnitus is reduced.

### Independent and identically distributed random variables

independent and identically distributedi.i.d.iid
Depending on the context, one may also require 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).

### Autocorrelation

autocorrelation functionserial correlationautocorrelated
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.
The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function) at \tau=0 and will be exactly 0 for all other \tau.

### Brownian motion

BrownianBrownian movementBrownian particle
White noise is the generalized mean-square derivative of the Wiener process or Brownian motion.

### Nuclear space

nuclearnuclear Fréchet spacenuclearity
A generalization to random elements on infinite dimensional spaces, such as random fields, is the white noise measure.
Such measure is called white noise measure.

### Moving-average model

Moving average modelmoving averagemoving average process
In this case the noise process is often modeled as a moving average process, in which the current value of the dependent variable depends on current and past values of a sequential white noise process.
where μ is the mean of the series, the θ 1, ..., θ q are the parameters of the model and the ε t, ε t−1,..., ε t−q are white noise error terms.

### Data compression

compressionvideo compressioncompressed
These concepts are also used in data compression.
Many of these algorithms use convolution with the filter [-1 1] to slightly whiten or flatten the spectrum, thereby allowing traditional lossless compression to work more efficiently.

### Whitening transformation

prewhitened data matrixsignal whiteningSphering transformation
Conversely, a random vector with known covariance matrix can be transformed into a white random vector by a suitable whitening transformation.
The transformation is called "whitening" because it changes the input vector into a white noise vector.

### Digital-to-analog converter

DACDACsD/A
Generating white noise typically entails feeding an appropriate stream of random numbers to a digital-to-analog converter.

### Signal processing

signal analysissignalsignal processor
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.

### Signal

signalselectrical signalsignaling
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.

### Frequency

frequenciesperiodperiodic
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.

### Physics

physicistphysicalphysicists
The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting.

### Acoustical engineering

electroacousticsacoustical designacoustic engineering
The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting.

### Forecasting

forecastforecastsprojection
The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting.

### Sampling (signal processing)

sampling ratesamplingsample rate
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.

### Random variable

random variablesrandom variationrandom
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.

### Mean

mean valueaveragepopulation mean
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.

### Variance

sample variancepopulation variancevariability
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.