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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 ...
First, white noise is a generalized stochastic process with independent values at each time. [12] Hence it plays the role of a generalized system of independent coordinates, in the sense that in various contexts it has been fruitful to express more general processes occurring e.g. in engineering or mathematical finance, in terms of white noise.
The transformation is called "whitening" because it changes the input vector into a white noise vector. Several other transformations are closely related to whitening: the decorrelation transform removes only the correlations but leaves variances intact, the standardization transform sets variances to 1 but leaves correlations intact,
White noise is the simplest example of a stationary process. An example of a discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is a Bernoulli scheme .
The sine-Gordon model is in the same universality class as the effective action for a Coulomb gas of vortices and anti-vortices in the continuous classical XY model, which is a model of magnetism. [28] [29] The Kosterlitz–Thouless transition for vortices can therefore be derived from a renormalization group analysis of the sine-Gordon field ...
In this case all eigenvalues are equal, and the eigenvalue spread is the minimum over all possible matrices. The common interpretation of this result is therefore that the LMS converges quickly for white input signals, and slowly for colored input signals, such as processes with low-pass or high-pass characteristics.
The spectral power density, compared with white noise, decreases by 3.01 dB per octave (10 dB per decade); density proportional to 1/f. For this reason, pink noise is often called "1/ f noise". Since there are an infinite number of logarithmic bands at both the low frequency (DC) and high frequency ends of the spectrum, any finite energy ...
In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). [1] [2] In other words, the values that the noise can take are Gaussian-distributed.