Spectral Factorization and Nevanlinna–Pick Interpolation

We develop a spectral factorization algorithm based on linear fractional transformations and on the Nevanlinna–Pick interpolation theory. The algorithm is recursive and depends on a choice of points (zₖ ,k = 1,2, ⋯ ) inside the unit disk. Under a mild condition on the distribution of the zₖ ’s, the convergence of the algorithm is established. The algorithm is flexible and convergence can be influenced by the selection of zₖ’s.