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.