Additive and multiplicative minimum-phase decompositions of 2-D rational power density spectra

This paper considers the multiplicative and additive minimum-phase decompositions of a two-dimensional (2-D) rational power density spectrum (commonly known as the spectral factorization and partial fraction expansion problems). It is shown that both of these decompositions generally involve filters which are ratios of 2-D minimum-phase filters, with finite support in one variable, and infinite support in the other variable. It is shown that a sufficient condition for a 2-D autoregressive (AR) spectrum to have a rational additive decomposition is for the minimum-phase whitening filter to have finite reflection coefficient support.