Procedures for signal reconstruction from noisy phase

In this paper a class of iterative procedures is presented for reconstructing a finite duration sequence from noisy samples of its Fourier transform phase. These measurements are combined with a knowledge of the true transform magnitude and/or hard constraints on the phase noise variations to define sets whose intersection must contain the true sequence. The algorithms iterate between the sequence domain and the transform domain applying the known constraints (i.e. finite duration and known limits on phase variation) in each domain. Results of an experimental investigation are presented. A method is described for the case where limits on both the magnitude and phase variation of a finite length sequence are known.