Time reference for measurements of arbitrarily shaped pulses

Abstract

This paper addresses measurements of relative timing of irregularly and differently shaped pulses (by which we mean signals that are zero beyond a finite interval). For such pulses the usual time reference points become useless: rising edges may change their slopes and shapes, and maxima might split. We propose a definition of the time reference applicable to smooth but otherwise arbitrary pulses. It is applicable to signal scaling, simplifies the covariance matrix (of parameters' error estimates) and yields an effective analytic estimate of timing error.