Optimum Filters with Time Width Constraints for Liquid Argon Total-Absorption Detectors

Optimum filter responses are found for triangular current input pulses occurring in liquid argon ionization chambers used as total absorption detectors. The filters considered are subject to the following constraints: finite width of the output pulse having a prescribed ratio to the width of the triangular input current pulse and zero area of a bipolar antisymmetrical pulse or of a three lobe pulse, as required for high event rates. The feasibility of pulse shaping giving an output equal to, or shorter than, the input one is demonstrated. It is shown that the signal-to-noise ratio remains constant for the chamber interelectrode gap which gives an input pulse width (i.e., electron drift time) greater than one third of the required output pulse width (i.e., resolving time).