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An example of a random vector that is Gaussian white noise in the weak but not in the strong sense is = [,] where is a normal random variable with zero mean, and is equal to + or to , with equal probability. These two variables are uncorrelated and individually normally distributed, but they are not jointly normally distributed and are not ...
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.
White noise. 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
Colored noise can be computer-generated by first generating a white noise signal, Fourier-transforming it, then multiplying the amplitudes of the different frequency components with a frequency-dependent function. [26] Matlab programs are available to generate power-law colored noise in one or any number of dimensions.
In probability theory, a branch of mathematics, white noise analysis, otherwise known as Hida calculus, is a framework for infinite-dimensional and stochastic calculus, based on the Gaussian white noise probability space, to be compared with Malliavin calculus based on the Wiener process. [1]
A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1. [1]
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 ...
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.