On some properties of positive trigonometric polynomials related to one-dimensional discrete phase retrieval problem

In this paper some results on positive trigonometric polynomials related to one-dimensional discrete phase retrieval problem are presented. The closed forms of the z-transform and Fourier transform of the folded of circular autocorrelation are provided to show that whether scaling or biasing of the input magnitude data should have an effect on non-negativity. Some results to enlighten the relationship between the nearest autocorrelation method and the one-dimensional phase retrieval problem are also discussed.