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In most of the engineering literature I'm familiar with, white noise is introduced as an idealized random process $n(t)$ with a flat power spectrum $$S_N(f)=\frac{N_0}{2}\tag{1}$$ and the corresponding autocorrelation function $$R_N(\tau)=\frac{N_0}{2}\delta(\tau)\tag{2}$$ The reason for defining white noise in this way is because it closely approximates the ...

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White noise is not "WSS by nature" whatever you mean by that phrase but it can be treated as a (zero-mean) WSS process insofar as its effects in linear systems are concerned. For example, standard linear system theory ways when the input to an LTI system is an ordinary WSS process $\{X(t)\}$ with autocorrelation function $R_X(\tau)$, then the ...

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Disclaimer: this might very well be wrong. Still pondering it, but Dilip Sarwate has convincing points. When you say "white" you assume it's WSS to begin with. For non-WSS processes, "white" isn't defined, since no only lag-dependent autocorrelation can be found. (And a process is white, exactly if its autocorrelation takes the form of a ...

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Once you talk about the Spectrum of noise / process you implicitly says it is stationary in the wide sense. What does it mean to have a signal with uncorrelated samples? Do you understand it means you can't using linear predictor, to have any information from all past samples ion the current one? Usually this is not how signals behave. This is exactly why ...

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first order stationary The CDF of any sample is time invariant. $F_X(x;~~ t) = F_X(x;~~ t+\tau)~~~\forall \tau$ Thus, the PDF is time invariant: $f_X(x;~~ t) = f_X(x;~~ t+\tau)~~~\forall \tau$ And Thus, all first order statistics are constant: $\mu_X(t)=\mu=\text{constant}$ $\sigma^2(t)=\sigma^2=\text{constant}$ \$E\Big[X^2(t)\Big] = \text{constant}~~~~\text{(...

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