Sampling and optimum data processing of detector signals

The optimum processing of data, obtained by sampling detector signals, is developed for signals known a priori in shape, their time of occurrence and amplitude being unknown. The processing is based on the maximum-likelihood method. The resolutions in the time and amplitude estimations of the pulse are compared with those obtained from an optimum analog filter. Results are presented for a fixed number of samples points at different sampling rates. It is shown that undersampling does not introduce systematic errors because of the pulse shape known a priori but only decreases the resolution and makes it somewhat sensitive to the position of the pulse in relation to the sampling comb. The paper gives the criteria needed for reconstructing the weighting function for digital processors, stressing the links between conventional analog processing and sampled data processing. This makes it possible to choose the best compromise between achievable resolution and computational requirements. (orig.)