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The autocorrelation matrix is a positive semidefinite matrix, [3]: p.190 i.e. for a real random vector, and respectively in case of a complex random vector. All eigenvalues of the autocorrelation matrix are real and non-negative.
A random vector (that is, a random variable with values in R n) is said to be a white noise vector or white random vector if its components each have a probability distribution with zero mean and finite variance, [clarification needed] and are statistically independent: that is, their joint probability distribution must be the product of the ...
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.
Assumption: signal and (additive) noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation Requirement: the filter must be physically realizable/ causal (this requirement can be dropped, resulting in a non-causal solution)
The intensity of peaks on the autocorrelation spectrum are directly proportional to the relative importance of the intensity change in the original spectra. Hence, if an intense band is present at position x, it is very likely that a true intensity change is occurring and the peak is not due to noise.
A stationary Gauss–Markov process with variance (()) = and time constant has the following properties.. Exponential autocorrelation: () = | |.; A power spectral density (PSD) function that has the same shape as the Cauchy distribution: () = +. (Note that the Cauchy distribution and this spectrum differ by scale factors.)
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.
Schmidt, in particular, accomplished this by first deriving a complete geometric solution in the absence of noise, then cleverly extending the geometric concepts to obtain a reasonable approximate solution in the presence of noise. The resulting algorithm was called MUSIC (MUltiple SIgnal Classification) and has been widely studied.