1-D non-minimum phase retrieval by gain differences

The phase retrieval problem arises when the phase of a signal is apparently lost or impractical to measure and must be reconstructed from only the magnitude of its Fourier transform. The previous solutions for the continuous non-minimum phase retrieval problem usually employed an iterative algorithm applied on a discrete approximation of a signal. The utilization of these algorithms is seriously limited by the unpredictability of their convergence. Our novel solution uses relationships between the phase and the gain differences. Its advantages are its simplicity and stability. The effects of Gibbs phenomenon are studied and a method to alleviate them is presented. The effectiveness of our solution is illustrated with some numerical examples