Performance of Optimal Linear Filtering Methods for Signal Estimation in High-Energy Calorimetry

Discrete linear estimation methods, which are based on a weighted sum of the received time samples and the filter coefficients, are extensively employed in many applications. In conditions where the expected pulse shape is known and the received signal is mainly corrupted from additive Gaussian noise, such approaches perform close to the optimal operation. However, the readout signal may also suffer from pile-up, which potentially deteriorates the estimation process. In this paper, signal estimation is carried out for high-event rate experiments in high-energy physics, which aim at reconstructing particle collisions. In particular, the energies of the subproducts resulting from the collisions are measured by the calorimeter systems using shaped signals and estimating their amplitudes. The paper presents four linear estimation approaches and compares their performance in high signal pile-up conditions: two versions of an Optimal Filter that minimizes the noise variance impacts, a Wiener Filter to cope with the uncertainties arising from both the noise and the signal fluctuations, and a signal deconvolution technique that recovers the original signals within a calorimeter readout window. The efficiency is measured from simulated data where various signal pile-up scenarios and noise conditions are considered.