Reconstruction from Zero Crossings
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High Quality Content by WIKIPEDIA articles! The problem of reconstruction from zero crossings can be stated as: given the zero crossings of a continuous signal, is it possible to reconstruct the signal (to within a constant factor)? Worded differently, what are the conditions under which a signal can be reconstructed from its zero crossings? This problem has 2 parts. Firstly proving that there is a unique reconstruction of the signal from the zero crossings and secondly how to actually go about reconstructing the signal. Though there have been quite a few attempts before, no conclusive…mehr

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High Quality Content by WIKIPEDIA articles! The problem of reconstruction from zero crossings can be stated as: given the zero crossings of a continuous signal, is it possible to reconstruct the signal (to within a constant factor)? Worded differently, what are the conditions under which a signal can be reconstructed from its zero crossings? This problem has 2 parts. Firstly proving that there is a unique reconstruction of the signal from the zero crossings and secondly how to actually go about reconstructing the signal. Though there have been quite a few attempts before, no conclusive solution has been found. Ben Logan from the Bell laboratories wrote a paper in 1977 in the Bell Systems Technical Journal giving some criteria under which unique reconstruction is possible. Though this has been a major step towards the solution, many people are dissatisfied with the type of condition which results from his paper.