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Hi I am trying to derive the autocorrelation matrix and I am unsure about how exactly it works. I can see that the $4\times 1$ matrices result in the Hermitiain and Toeplitz matrix? Surely the only non-zero values in each of these is at $n = 0$ which is the variance?

Any help would be greatly appreciated!

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You get a diagonal matrix because the values of $\eta(n)$ at different times (sample indices $n$) are uncorrelated, as shown in your first equation. This means that all off-diagonal elements of the auto-correlation matrix must be zero (they equal $E[\eta(n)\eta(n+m]$ for $m\neq 0$). Only the diagonal elements are non-zero, and they are equal to the variance.

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  • $\begingroup$ @Tricks: Yes, indeed :) $\endgroup$
    – Matt L.
    Commented Aug 15, 2016 at 20:21

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