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D) For a desired response d(n) = α(n) exp(− j ωτ ) 30 PROBLEM 2.6. The cross-correlation vector p is p =E[u(n)(d∗ n)] =E[(α(n)s(n) + v(n)) α∗ (n) exp(− j ωτ )] =s(n) exp(j ωτ )E[|α(n)|2 ] =σ 2α s(n) exp(j ωτ ) =σ α2 =σ α2 1 exp(− j ω). V(n − M + 1) rv (n) rv (n − 1). Accordingly, the tap-weight vector of the (optimum) wiener filter is w0 =R−1 p =R−1 v p where p is defined in Equation (3). Adaptive filter theory by simon haykin pdf file download. Rv (k − M + 1), 0≤k ≤M −1 (3) where rv (k) is the autocorrelation of v(n) for lag k.