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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.
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.
Analogous to Laplace mechanism, Gaussian mechanism adds noise drawn from a Gaussian distribution whose variance is calibrated according to the sensitivity and privacy parameters. For any δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} and ϵ ∈ ( 0 , 1 ) {\displaystyle \epsilon \in (0,1)} , the mechanism defined by:
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 ...
This model is called a Gaussian white noise signal (or process). In the mathematical field known as white noise analysis, a Gaussian white noise is defined as a stochastic tempered distribution, i.e. a random variable with values in the space ′ of tempered distributions.
The mutual information of PSK can be evaluated in additive Gaussian noise by numerical integration of its definition. [17] The curves of mutual information saturate to the number of bits carried by each symbol in the limit of infinite signal to noise ratio E s / N 0 {\displaystyle E_{s}/N_{0}} .
The increment process X(t) is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: n-th order fractional Brownian motion, abbreviated as n-fBm. [1] n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order n are stationary. For n = 1, n-fBm is classical fBm.
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,