An algorithm for the removal of noise and jitter in signals and its application to picosecond electrical measurement (Q1315235)

In many physical measurements, uncertainty is introduced both by noise, random variations in the quantity measured, and jitter, random fluctuation in response time to a trigger event. If the measured quantities are \(v(t)\), representing a function \(g(t)\), the continuous model of such a measurement will be \(v(t) = g(t + \xi) + \psi\), where \(\xi\), \(\psi\) are random variables with probability distribution \(P_ J\), \(P_ N\) respectively, or zero means and variances \(\tau^ 2\), \(\omega^ 2\), respectively. It is shown that the maximum deviation of \(E(v(t))\) from \(g(t)\) resulting from noise occurs at the extrema of \(g\) (at the peaks and throughs of the underlying signal) and that resulting from jitter occurs at maxima of \(| g'(t)|\); e.g. at inflection points. Based on this analysis, a 5-step algorithm is presented to estimate and remove the influences of noise and jitter. On the way, it is made plausible that the uncertainties in the variances have to be estimated using the jackknife technique. A final remark notes that for real-life applications, amplitude dependent jitter should be introduced.