Coherence in signal processing: a fundamental redefinition

The term "coherence" in the signal processing community has been defined for nearly 50 years in terms of a narrowband statistical power spectral density ratio. This definition is very limiting with modern digital electronics and sensor array technology that is very broadband and which uses sophisticated wideband modulations. In this paper, we provide a fundamental overhaul of the definition of coherence, with many specialized variations that revert to the old coherence definition in one case and that also handle the wideband cases as well.