About positive trigonometric polynomials and 1-D discrete phase retrieval problem

We reconsider the discrete form of the one dimensional phase retrieval problem from the point of view of magnitude input data. It has been previously mentioned that input magnitude of DFT should satisfy certain conditions in order to provide the correct solution. These requirements ask for the corresponding trigonometric polynomial to be positive definite. Alternatively, an arbitrary set of DFT magnitude may not provide a correct solution. In this paper we study whether this may be a reason for iterative methods to stagnate. We present a sequence of steps in order to obtain a correct solution to the one dimensional phase retrieval problem. Experimental results are also provided.