Show that with the filter 𝐡 𝛼 ( f , cos 𝜃 d ) , the narrowband output SNR is related to the MSC between Z( f ) and X( f ) by Show that the filter 𝐡 𝛼 ( f , cos 𝜃 d ) that minimizes the...

Show that with the filter 𝐡_𝛼
( f , cos 𝜃_d
) , the narrowband output SNR is related to the MSC between Z( f ) and X( f ) by

Show that the filter 𝐡_𝛼
( f , cos 𝜃_d
) that minimizes the distortion-based MSE,J_d
[ 𝐡_𝛼
( f , cos 𝜃d )], is identical to the MVDR beamformer: