On the performance of linear optimal filter and Wiener filter for signal detection in liquid ionization calorimeters

The performance of the linear optimal filter (LOF) is compared to the newly reported Wiener filter for signal detection in ATLAS liquid ionization calorimeters. The equivalence between the two methods is established, and further related to the conventional notion of (whitening + matched) filter configuration for optimal signal detection in presence of colored noise. Without arrival time spread, the LOF and Wiener results converge to each other, regardless of the SNR of the calorimeter readout path. In addition, the LOF performance displays a dependence on the pulse arrival time delay-manifested as a non-zero mean and an elevated standard deviation of the amplitude estimation error-due to the truncation of high-order terms in deriving the linear filter. In contrast, once trained with the exact signal statistics of the calorimeter, i.e., the arrival time spread and noise structure, the Wiener filter can always adapt to an optimal, unbiased solution using the same linear FIR filter structure. However, when such prior knowledge is removed, the Wiener outcomes nearly coincide with those of the LOF. All the results are obtained via Monte Carlo simulations of a readout signal-processing chain assuming identical electrical parameters of the ATLAS liquid argon calorimeter system with a sample rate of 80 MSPS. The equivalence between the two approaches is also examined and confirmed using a Gaussian pulse shape and an invertible pulse-shaping function without any finite zeroes on the jω-axis.