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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.
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.
This model is called a Gaussian white noise signal (or process). In the mathematical field known as white noise analysis , a Gaussian white noise w {\displaystyle w} is defined as a stochastic tempered distribution, i.e. a random variable with values in the space S ′ ( R ) {\displaystyle {\mathcal {S}}'(\mathbb {R} )} of tempered distributions .
Additive white Gaussian noise; Black noise; Gaussian noise; Pink noise or flicker noise, with 1/f power spectrum; Brownian noise, with 1/f 2 power spectrum; Contaminated Gaussian noise, whose PDF is a linear mixture of Gaussian PDFs; Power-law noise; Cauchy noise; Multiplicative noise, multiplies or modulates the intended signal
All these extensions are also called normal or Gaussian laws, so a certain ambiguity in names exists. The multivariate normal distribution describes the Gaussian law in the k-dimensional Euclidean space. A vector X ∈ R k is multivariate-normally distributed if any linear combination of its components Σ k j=1 a j X j has a (univariate) normal ...
Hoyt distribution, the pdf of the vector length of a bivariate normally distributed vector (correlated and centered) Complex normal distribution, an application of bivariate normal distribution; Copula, for the definition of the Gaussian or normal copula model.
The noise in the measured profile is either i.i.d. Gaussian, or the noise is Poisson-distributed. The spacing between each sampling (i.e. the distance between pixels measuring the data) is uniform. The peak is "well-sampled", so that less than 10% of the area or volume under the peak (area if a 1D Gaussian, volume if a 2D Gaussian) lies outside ...
It concerns linear systems driven by additive white Gaussian noise. The problem is to determine an output feedback law that is optimal in the sense of minimizing the expected value of a quadratic cost criterion. Output measurements are assumed to be corrupted by Gaussian noise and the initial state, likewise, is assumed to be a Gaussian random ...