On the boundedness behavior of the spectral factorization in the Wiener algebra for FIR data

It is known that the spectral factorization mapping is unbounded in the Wiener algebra, in general. However in applications, the given data are often polynomials. For such finite dimensional spectra, the spectral factorization mapping is bounded, of course, but the boundedness constant depends on the degree of the given polynomial spectra. This paper presents lower and upper bounds for this boundedness constant depending on the degree N of the given data.