Phase unwrapping for multidimensional rational and finite-length sequences

A direct relationship between a multidimensional time series with finite support and its unwrapped phase is shown. This relationship shows that the unwrapped phase of a multidimensional sequence is unique in the sense that once the phase at the origin is specified the phase everywhere in the frequency domain follows. Additionally, the uniqueness of the unwrapped phase for multidimensional sequences which have a rational Z transform is shown. In either case, the unwrapped phase at a given point is shown to be compatible using a real 1-d finite-length phase unwrapping procedure based on Sturm sequence polynomials