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?
Ben Logan from Bell Labs wrote an article in 1977 in the Bell System Technical Journal giving some criteria under which unique reconstruction is possible.
are dissatisfied with the type of condition that results from his article.
According to Logan, a signal is uniquely reconstructible from its zero crossings if: