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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 two 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, no conclusive solution has yet been found. Ben Logan from Bell Labs wrote a paper in 1977 in the ''Bell System 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. According to Logan a signal is uniquely reconstructible from its zero crossings if: #The signal x(t) and its Hilbert transform xt have no zeros in common with each other. #The frequency domain representation of the signal is at most 1 octave long, in other words, it is bandpass-limited between some B and 2B. == Further reading == * BF Logan, Jr. "Information in the Zero Crossings of Bandpass Signals", ''Bell System Technical Journal'', vol. 56, pp. 487-510, April 1977 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reconstruction from zero crossings」の詳細全文を読む スポンサード リンク
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