7.6 Consider estimating the function by a linear filter estimator of the form where t is defined by (7.43). Show a sufficient condition for t

7.6 Consider estimating the function

by a linear filter estimator of the form

where βt is defined by (7.43). Show a sufficient condition for ψt to be an unbiased estimator; i.e., E ψt = ψt, is H(ω)Z(ω) = I for all ω. Similarly, show any other unbiased estimator satisfying the above condition has minimum variance (see Shumway and Dean, 1968), so the estimator given is a best linear unbiased (BLUE) estimator.

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