About magnitude input data in 1-D discrete phase retrieval problem

In this paper we consider 1-D (one dimensional) phase retrieval problem from the point of view of magnitude input data. We claim that magnitude input data should satisfy certain requirements in order to provide the acceptable minimum-phase solution. The Fejér-Riesz Theorem guarantees us that 1-D discrete phase retrieval problem has always a solution if the trigonometric polynomial is positive definite, but an arbitrary set of magnitudes does not provide always a positive definite trigonometric polynomial. Sometimes this may be the reason for iterative methods to stagnate or for direct methods to give undesired results. Finally we discuss a criterium to decide whether a set of magnitude input data can solve the 1-D phase retrieval problem.