A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm

An implementation of the Newton-Raphson approach to compute the minimum phase moving-average spectral factor of a finite positive definite correlation sequence is presented. Each step in the successive approximation method involves a system of linear equations that is solved using either the Levinson algorithm backwards (the Jury stability test), or a symmetrized version of the Euclid algorithm. Various properties of the Newton-Raphson map are studied. The algorithm is generalized to other symmetries (other than with respect to the unit circle). The special case of the symmetry with respect to the imaginary axis is presented and related to the Routh-Hurwitz stability test for continuous time transfer function