Consider multichannel noise reduction filters that have the form 𝐡 1 ∶ N ( f ) = 𝐓 1 ∶ N ( f )𝐚( f ). Show that a) the narrowband WNG can be expressed as b) the vector 𝐚( f ) that maximizes W [...

Consider multichannel noise reduction filters that have the form 𝐡_1
∶
N
( f ) = 𝐓_1
∶
N
( f )𝐚( f ). Show that

a) the narrowband WNG can be expressed as

b) the vector 𝐚( f ) that maximizes W [ 𝐚( f ) ] is

where 𝜍( f ) ≠ 0 is an arbitrary complex number,

c) the MSE is given by

d) and the minimization of J [ 𝐡_1
∶
N
( f ) ] leads to