Behavior of the hard-limiter for bandpass signals and possibilities of signal reconstruction

In many fields of applications it is of considerable interest to reconstruct a bandlimited response bandpass signal from its zero crossings, which are obtained from the signal by means of the so-called hard-limiter. There are several algorithms known which are expected to render this reconstruction, but there are no formal proofs of either convergence nor uniqueness. This paper gives the proof that for uniqueness at least one additional property of the signals is to be demanded, and gives an example