Robustness of the Spectral Factorization for Polynomials

Spectral factorization is a key method in many different applications, and it is known that it is bounded but discontinuous with respect to the supremum norm. This paper considers the spectral factorization for polynomial spectra, since they are related to finite impulse response systems, and therefore especially important in practical applications. For such spectra, the spectral factorization is continuous, but the continuity behavior will depend strongly on the degree of the spectra. The paper will show that the continuity behavior deteriorates proportional with the logarithm of the degree of the spectra.