A Method for Correction of Piled-Up Events for Trapezoidal Filter Digitizers*

Modern digitizers for pre-amplifier outputs often use trapezoidal filters to measure input signal energy. Though superior to analog energy computation methods, such digitizers are not immune to the effects of pile-up. The Alpha-Gamma collaboration at the NIST Center for Neutron Research developed a precise method to characterize pile-up and recover data that would have otherwise been discarded. The trapezoidal filter method compares the height of the trapezoid with a baseline value to extract a signal's energy; in cases of piled-up events, these trapezoids overlap, causing data acquisition algorithms to report incorrect values of energy. By observing the extent of energy distortion as a relation of known input energy and trapezoid rise and flat-top times, we are able to experimentally generate functions to map piled-up events to their undistorted energies. These functions need only the recorded energies and time-tags of event triggers as inputs. With this method of pile-up correction, we avoid the need to collect additional data to quantify pile-up. Instead, functions made with trapezoid settings from previously collected data sets can be used to retroactively correct the energies of piled-up events.