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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 ...
First, white noise is a generalized stochastic process with independent values at each time. [12] Hence it plays the role of a generalized system of independent coordinates, in the sense that in various contexts it has been fruitful to express more general processes occurring e.g. in engineering or mathematical finance, in terms of white noise.
The AWGN channel is represented by a series of outputs at discrete-time event index . is the sum of the input and noise, , where is independent and identically distributed and drawn from a zero-mean normal distribution with variance (the noise).
The autocorrelation of a continuous-time white noise signal will have a strong ... If a time series ... (for processes with distribution lacking well-behaved ...
is a "deterministic" time series, in the sense that it is completely determined as a linear combination of its past values (see e.g. Anderson (1971) Ch. 7, Section 7.6.3. pp. 420-421). It may include "deterministic terms" like sine/cosine waves of t {\displaystyle t} , but it is a stochastic process and it is also covariance-stationary, it ...
Two simulated time series processes, one stationary and the other non-stationary, are shown above. The augmented Dickey–Fuller (ADF) test statistic is reported for each process; non-stationarity cannot be rejected for the second process at a 5% significance level. White noise is the simplest example of a stationary process.
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Kuo’s book White Noise Distribution Theory provided an introduction to the fundamentals of white noise theory and offered insights into its mathematical foundations and practical applications. The book showed the relevance of white noise analysis in a series of stochastic cable equations. [23]