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In this paper, we show that a one-dimensional or multidimensional sequence is uniquely specified under mild restrictions by its signed Fourier transform magnitude (magnitude and 1 bit of phase information). In addition, we develop a numerical algorithm to reconstruct a one-dimensional or multidimensional sequence from its Fourier transform magnitude. Reconstruction examples obtained using this algorithm are also provided.
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Hove et al. (1983) studied this question.
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