1-D direct phase retrieval

The problem of reconstructing a one-dimensional signal from only the magnitude of its Fourier transform is known as the phase retrieval problem. This problem emerges when the phase of a signal is apparently lost or impractical to measure. In this paper, we introduce new solutions that compute the phase by directly using the magnitudes of the samples in nepers. These solutions use relationships between the phase and the gain differences, or gain samples. From the obtained minimum phase solution, the non-minimum phase solutions are derived. The advantages consist in simplicity and stability. We compare our solutions by using some numerical examples. The performances under noisy conditions for the two approaches are also considered.

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