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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 ...
Autocorrelation of white noise [ edit ] The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function ) at τ = 0 {\displaystyle \tau =0} and will be exactly 0 {\displaystyle 0} for all other τ {\displaystyle \tau } .
White noise: The partial autocorrelation is 0 for all lags. Autoregressive model: The partial autocorrelation for an AR(p) model is nonzero for lags less than or equal to p and 0 for lags greater than p. Moving-average model: If , >, the partial autocorrelation oscillates to 0.
Pisarenko's method also assumes that + values of the autocorrelation matrix are either known or estimated. Hence, given the ( p + 1 ) × ( p + 1 ) {\displaystyle (p+1)\times (p+1)} autocorrelation matrix, the dimension of the noise subspace is equal to one and is spanned by the eigenvector corresponding to the minimum eigenvalue.
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.
Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system.
Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. [ citation needed ] A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far ...
If the process generating the residuals is found to be a stationary first-order autoregressive structure, [2] = +, | | <, with the errors {} being white noise, then the Cochrane–Orcutt procedure can be used to transform the model by taking a quasi-difference: