Show that by minimizing the LSE with a constraint on the coefficients, we obtain the regularized LS filter: Show that by minimizing the LSE subject to the distortion less constraint and a constraint...

Show that by minimizing the LSE with a constraint on the coefficients, we obtain the regularized LS filter:

Show that by minimizing the LSE subject to the distortion less constraint and a constraint on the coefficients, we obtain the regularized CLS filter:

Show that with the constraint 𝐁_N
( f )𝐡( f ) = 𝐛_N
, the error signal between the array beam pattern and the desired directivity pattern can be expressed as