Computation of the One-Dimensional Unwrapped Phase

In this paper, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 2 pi discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This paper compares existing algorithms for computing the unwrapped phase. Then, two composite algorithms are proposed that build upon the existing ones. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.