Algebraic phase unwrapping with self-reciprocal polynomial algebra

Algebraic phase unwrapping gives the exact expression of the unwrapped phase of a complex polynomial. However, in computation of a Sturm sequence, there exist numerical instabilities due to coefficient growth. In this paper, we refine algebraic phase unwrapping by modifying the Sturm sequence with the newly defined self-reciprocal polynomial division. The proposed refinement enables us to compute the unwrapped phase, without suffering from the coefficient growth, by using the self-reciprocal subresultant which is newly defined as the determinant of a certain matrix. Numerical experiments show that algebraic phase unwrapping is greatly stabilized by the proposed method.