Characterization of the behavior of outer functions with applications to spectral factorization and system design

The outer factorization is the key operation in spectral factorization and in the determination of filters with minimal phase and given amplitude response. This paper investigates the continuity behavior of the outer factorization mapping and it gives a characterization of all outer functions which belong to the same smoothness class as the corresponding data. In general, the outer factorization yields a certain loss in smoothness, which has an impact on the approximation behavior of the spectral factors and desired filters, respectively.