Show that in the case of a rank deficient noise correlation matrix, a) the distortion-based MSE can be written as b) and the minimization of J d ( 𝐀 ) yields the optimal infinite noise reduction...

Show that in the case of a rank deficient noise correlation matrix,

a) the distortion-based MSE can be written as

b) and the minimization of J_d
( 𝐀 ) yields the optimal infinite noise reduction filtering matrix:

Show that in the case of a rank deficient noise correlation matrix,

 a) the MSE of the residual noise can be written as

b) and the minimization of J_n
( 𝐇 ) yields the optimal distortion less filtering matrix: