Phase unwrapping by factorization

An algorithm for the numerical factorization of very high degree but well-conditioned polynomials is developed. This is used to factor the z-transform of finite-length signals, and the zeros are used to calculate the unwrapped phase. The method has been tested on signals up to 512 points in length. A complete Fortran 77 program is given for the case of a real-valued signal. Two related analytical issues are treated. First, the interpretation of phase unwrapping as an interpolation problem is discussed. Second, an explanation is given for the observed numerical difficulties in the method of phase unwrapping using adaptive integration of the phase derivative. The trouble is due to the clustering of the zeros of high degree polynomials near the unit circle.