Let 𝜆 1 denote the maximum eigenvalue of the matrix 𝐑 v − 1 𝐑 𝐱 , and let 𝐭 1 denote the corresponding eigenvector.  a) Show that the filter that maximizes the output SNR is given by where 𝜍 ≠ 0...

Let 𝜆₁
denote the maximum eigenvalue of the matrix 𝐑_v
^−
1
𝐑_𝐱, and let 𝐭₁
denote the corresponding eigenvector.

 a) Show that the filter that maximizes the output SNR is given by

where 𝜍 ≠ 0 is an arbitrary real number

b) Show that the MSE obtained with the maximum SNR filter is

c) Show that the maximum SNR filter, 𝐡_max, that minimizes the MSE is given by