Mixed Trigonometric Interpolation Techniques for Fast and Stable Algebraic Phase Unwrapping

摘要

The algebraic phase unwrapping was established in 1998 as a rigorous symbolic algebraic solution to the phase unwrapping problem, i.e., the problem of computing the continuous phase function of a given complex polynomial. In this paper, we propose a simple but a powerful numerical stabilization technique named the mixed trigonometric interpolation for the algebraic phase unwrapping. This technique is based on replacing a certain set of arithmetic operations in polynomial ring by an interpolation of a certain mixed trigonometric function. By this technique we can obtain numerical stable approximation of general Sturm sequence without suffering the coefficient growth. Moreover, by combining the mixed trigonometric interpolation with FFT, we succeeded in making the mixed trigonometric interpolation faster and more stable. The proposed techniques allow us to solve phase unwrapping problem along the unit circle stably even if the degree of a given polynomial is very large.