Show that the maximum eigenvalue corresponding to the eigenvector of the matrix 𝜙X1 ( f )𝚽 𝐯 − 1 ( f )𝜸∗ X 1 𝐱 ( f )𝜸 T X 1 𝐱 ( f ) is given by Show that the maximum SNR filter is given by...

Show that the maximum eigenvalue corresponding to the eigenvector of the matrix 𝜙X1 ( f )𝚽
_𝐯

^−
1
( f )𝜸∗ X_1
𝐱( f )𝜸^T
X_1
𝐱( f ) is given by

Show that the maximum SNR filter is given by

where 𝜍( f ) is an arbitrary frequency-dependent complex number different from zero.

Denote by oSNR^(m)
_max( f ) the maximum narrowband output SNR of an array with m sensors. Show that