On the factorization of discrete-time rational spectral density matrices
M. Denham · IEEE Transactions on Automatic Control · 1975
For a discrete-time rational spectral density matrix\Phi(z), the relationship between the factorizations\Phi(z) = Z(z) + Z^{T} (z^{-1})and\Phi(z) = W(z)QW^{T}(z), in terms of minimal state space realizations ofZ(z)andW(z), are derived in a straightforward way, without resorting to the use of the bilinear transformation. The obvious application of this result to performing a spectral factorizafion of\Phi(z)is discussed.