Abstract
Analytical solutions for amplitude and time measurements from digitized signals of the pseudo-Gaussian shape are considered. The least squares method (l.s.m.) is chosen as the algorithm to determine amplitude A and timestamp t0. For a profile with an uncorrelated sampling the l.s.m. is reduced to analytical formulas consistent with the experiment. This permits to estimate the desired number of points Ns on a profile. The obtained results for Ns are illustrated with qualitative estimates in accordance with the Nyquist–Shannon–Kotelnikov sampling theorem. The optimality of the electronic filters forming the waveform is analyzed in terms of the excess noise factor. An analytical solution is found for the autocorrelation function from stochastic noise sources. It permits to define non-diagonal weight matrix elements in the l.s.m. with formulation of requirements for neglecting sampling correlations.
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