Time and amplitude reconstruction from sampling measurements of the PHOS signal profile in the ALICE project

This paper presents the analysis of procedures dedicated for time and amplitude reconstruction from sampling measurements of the ALICE electromagnetic spectrometer PHOS signal profile. The proposed approach is based on the least squares method to fit the profile measured in discrete number of points to the known impulse response function of electronic filter. Assuming semi-Gaussian shape of this function one can reduce the problem of simultaneous determination of signal time mark t0 and amplitude A to the solution of algebraic equation of the nth power, where n is the order of used electronic filter. The proper analytical formulae to define parameters A and t0 as well as their uncertainties σA and σt are proposed. This approach allows one to reduced substantially the processing time for effective estimation of A and t0 with simplification of the used software. The application of obtained formulae to the analysis of beam test data from the prototype of electromagnetic spectrometer PHOS equipped with the ALTRO electronics are considered together with corresponding Monte-Carlo simulation.