Show that with the MVDR filter, the broadband output SNR is always greater than or equal to the broadband input SNR, i.e., oSNR( 𝐡 MVDR ) ≥ iSNR. Show that by minimizing the narrowband desired signal...

Show that with the MVDR filter, the broadband output SNR is always greater than or equal to the broadband input SNR, i.e., oSNR( 𝐡_MVDR) ≥ iSNR.

Show that by minimizing the narrowband desired signal distortion index with the constraint that the narrowband noise reduction factor is equal to a positive value 1/ℵ we obtain the tradeoff filter:

where 𝜇 is a Lagrange multiplier.