Quality factor analysis and optimization of digital filtering signal reconstruction for liquid ionization calorimeters

The Optimal Filtering (OF) reconstruction of the sampled signals from a particle detector such as a liquid ionization calorimeter relies on the knowledge of the normalized pulse shapes. This knowledge is always imprecise, since there are residual differences between the true ionization pulse shapes and the predicted ones, whatever the method used to model or fit the particle--induced signals. The systematic error introduced by the residuals on the signal amplitude estimate is analyzed, as well as the effect on the quality factor provided by the OF reconstruction. An analysis method to evaluate the residuals from a sample of signals is developed and tested with a simulation tool. The correction obtained is showed to preserve the original amplitude normalization, while restoring the expected $\chi^2 $--like behavior of the quality factor.