Zero-Crossing Waveform Interferometry: an Alternative to Correlation in Signal Processing

It is shown that multiple representations (such as replicas or Hilbert transforms) of a random waveform can interfere constructively to form a compact pattern, akin to a wave packet, when the representations are created in synchrony with zero crossings of the waveform. A function of such 'engineered' zero-crossing interferograms can exhibit time-delay resolution superior to that associated with a conventional correlation function, especially for waveforms with slowly-decaying power spectra. A phenomenon of local slew rate at zero crossings is exploited to substantially reduce the Cram\'er-Rao bound on time-delay estimators. A system, based on a concept of elapsed time, is proposed to determine zero-crossing interferograms in real time.