TEST BANK FOR Adaptive Filter Theory 4th Edition By Simon Haykin

1.1 Let (1) (2) We are given that (3) Hence, substituting Eq. (3) into (2), and then using Eq. (1), we get 1.2 We know that the correlation matrix R is Hermitian; that is Given that the inverse matrix R-1 exists, we may write where I is the identity matrix. Taking the Hermitian transpose of both sides: Hence, That is, the inverse matrix R-1 is Hermitian. 1.3 For the case of a two-by-two matrix, we may ru(k) = E[u(n)u*(n – k)] ry(k) = E[y(n)y*(n – k)] y(n) = u(n + a) – u(n –...