Spectral factorization revisited

Paul Sava and Sergey Fomel

paul@sep.stanford.edu, sergey@sep.stanford.edu

ABSTRACT

In this paper, we review some of the iterative methods for the square root, showing that all these methods belong to the same family, for which we find a general formula. We then explain how those iterative methods for real numbers can be extended to spectral factorization of auto-correlations. The iteration based on the Newton-Raphson method is optimal from the convergence stand point, though it is not optimal as far as stability is concerned. Finally, we show that other members of the iteration family are more stable, though slightly more expensive and slower to converge.