Signal Analysis with Time-Delay Onset-Arrival Thresholds

A technique for analyzing signals with time-delay onset thresholds is presented. The idea, suggested from experience in describing certain data in elementary particle physics, is found to be useful in the description of signals arriving at a given point from different origins in a spatially extended system, typical of some EMC/EMP situations. We expand the signal in a nonorthogonal overcomplete set of functions which contains translations in both time and frequency as well as dilations in time. We thus respect both the Gabor coherent-state and the Aslaksen-Klauder-Grossmann-Morlet formalisms. Prony analysis is a special case. Moreover, arbitrary power behavior above thresholds is incorporated, including complex powers. In practice, signals are least-squares fit to a few functions characterized in the frequency variable by simple or multiple poles (or cuts in the general case) with exponentially varying residues (or discontinuities). Some numerical examples are exhibited.