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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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Here's the best method I've found so far: First, I shifted $B_2(x)$ by $\phi$; this shift aligns the underlying (but unknown) signals $w(x)$ and $w(x + \phi)$. Note that once $B_2(x)$ is shifted, the signals will not begin and end at the same $x$-values. I chopped off the values of each signal that didn't overlap. Parts (a) and (b) of the figure below show ...


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