# hw19 - Y n = X n Z n where the Z n ’s are pairwise...

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ENEE 324 ASSIGNMENT 19 Due Tue 11/17 Let . . . , U 0 , U 1 , U 2 , . . . be pairwise uncorrelated random variables with mean μ = 3 and variance σ 2 = 36. For every n , define X n = U n - U n - 1 2 + U n - 2 3 (i) (4 pts.) Determine Cov( X n , X n + k ) for every k Z . (ii) (3 pts.) Determine the linear minimum mean-squared error (MMSE) estimate of X 2 based on X 1 , and the resulting MSE. (iii) (5 pts.) Determine the linear MMSE estimate of X 2 based on X 0 and X 1 , and the resulting MSE. Suppose now that the sequence { X n } is corrupted by noise, so that its measurements are given by
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Unformatted text preview: Y n = X n + Z n , where the Z n ’s are pairwise uncorrelated with mean 0 and variance σ 2 = 1, and also Cov( X i ,Z n ) = 0 for every i and n . (iv) (3 pts.) Determine the linear MMSE estimate of X 2 based on Y 2 , and the resulting MSE. (v) (5 pts.) Determine the linear MMSE estimate of X 2 based on Y and Y 1 , and the resulting MSE....
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