Show that the single-channel Wiener gain H W ( f ) is related to the pseudo coherence matrix, 𝚪 𝐲 ( f ), of the observations by Show that the MSC between Z( f ) and X( f ) plus the MSC between Z( f...

Show that the single-channel Wiener gain H_W( f ) is related to the pseudo coherence matrix, 𝚪_𝐲( f ), of the observations by

Show that the MSC between Z( f ) and X( f ) plus the MSC between Z( f ) and V₂( f ) is equal to 1:

Show that maximization of the MSC between Z( f ) and X( f ) yields the filter:

where 𝛼( f ) ≠  is an arbitrary complex number.