hw3_solution2

# hw3_solution2 - ECE514 Random Process Fall 2010 HW3...

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ECE514 Random Process Fall 2010 HW3 Solution For any questions, please contact [email protected] 3.1 a) where Det(A)=2*1-1*1=1 b) Using the eig() function in Matlab, we compute eigen-values/vectors, Because we now have where , and We can now write Y=U(X-EX), where EX=; let us verify this solution: i)

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ECE514 Random Process Fall 2010 HW3 Solution For any questions, please contact [email protected] ii) 3.3 a) and = where we employed independence of X and N. = Having computed the optimal linear estimator, let us compute its mean square error,
ECE514 Random Process Fall 2010 HW3 Solution For any questions, please contact [email protected] = = where the second equality (second line) relies on the orthogonality principle, and the last equality relies on the following, Substituting values we computed before, b) To show that it suffices to construct such that Consider Clearly, because To show strict inequality, i.e.,

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ECE514 Random Process Fall 2010 HW3 Solution For any questions, please contact [email protected] it suffices to show For we have ==0 For any , and in particular , we have . Therefore, and so is strictly better than , that is, the new estimator
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hw3_solution2 - ECE514 Random Process Fall 2010 HW3...

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