Boundedness Behavior of the Spectral Factorization for Polynomial Data in the Wiener Algebra

Spectral factorization is of fundamental importance in many areas of signal processing. This paper investigates the boundedness behavior of the spectral factorization mapping in the Wiener algebra. Thereby, the focus lies on the factorization of polynomial spectral densities with a finite degree N since such spectra are especially important for practical applications. The paper presents a lower and an upper bound on the boundedness behavior which will show that the boundedness constant of the spectral factorization mapping gets worse as the degree N of the spectra increases. Therewith, one obtains independently the known result that the spectral factorization mapping is unbounded on the Wiener algebra.