How about minimizing the square error? J=∑(xn-sn)2 Mean square error(MSE) Example:Estimating DC in white noise xln A+wln] J(A)=(xm)-A)2 Minimize J(A)w.r.t A o∑m-N个-0→1=∑w Q:Is this estimator MVU? A:yes,iff w[n]is AWGN E[A]=A+Elw(n)] whxiong@uestc.edu.cn 8whxiong@uestc.edu.cn 8 J = Mean square error (MSE) X n (x[n] ¡ s[n]) 2 How about minimizing the square error? Minimize J(A) w.r.t A Example: Estimating DC in white noise x[n] = A + w[n] J(A) = X n (x[n]) ¡ A) 2 @J(A) @A = 2 hXx[n] ¡ NA i = 0 A b = 1 N X n x(n) Q: Is this estimator MVU? A: yes, iff w[n] is AWGN E[A b ] = A + E[w(n)]