Impact of non-white noises in pulse amplitude measurements: a time-domain approach

The contribution of the 1f-noise to the spectral line broadening in pulse amplitude measurements is derived with a time-domain analysis. The known time-domain relationships which provide the contributions of the series and parallel white noises are generalised for the case of 1f and other typical non-white noises, by using the fractional derivative of either the system impulse response (time-invariant linear filters) or its weight function folded (time-variant linear filters). It is shown that a time-domain approach is also effective to determine the contribution of Lorentzian noises. A simple rule suitable to derive numerically the fractional derivative is given, which permits to calculate the effect of non-white noises even when the filter impulse response is not known analytically but only in sampled form.