On the Algorithmic Solvability of the Spectral Factorization and the Calculation of the Wiener Filter on Turing Machines
Holger Boche, Volker Pohl · 2019
The spectral factorization is an important operation in many different applications. This paper studies whether the spectral factor of a given computable spectral density can always be computed on an abstract machine (a Turing machine). It is shown that there are computable spectral densities with very comfortable analytic properties (smoothness and finite energy) such that the corresponding spectral factor can not be determined on a Turing machine. As an application, the paper discusses the possibility of calculating the optimal Wiener filter from computable spectral densities.