Positive trigonometric polynomials and one-dimensional discrete phase retrieval problem

In this paper some results on Schur transform are reviewed to address the problem of one-dimensional discrete phase retrieval. The goal is to provide a test whether a sequence of input magnitude data gives a solution to one-dimensional discrete phase retrieval problem. It has been previously shown that this issue is related to the nonnegativity of trigonometric polynomials. The proposed method is similar to the table procedure for counting the multiplicities of zeros on unit circle. Examples and numerical results are also provided to indicate that the problem of one-dimensional discrete phase retrieval often does not have a solution.