Optimum filter synthesis with DPLMS method for energy reconstruction

Optimum filters are granted increasing recognition as valuable tools for parametric estimation in many scientific and technical fields. The DPLMS method, introduced some twenty years ago, is especially effective among the synthesis algorithms since it derives the optimum filters directly from the experimentally acquired signal and noise waveforms. Two new extensions of the DPLMS method are here presented. The first one speeds up the synthesis phase and improves the energy estimation results by synthesizing optimum filters with automatically designed flat-top length. The second one improves the quality of parameter estimation in multi-channel systems by taking advantage of the inter-channel noise correlation properties. In this paper, the theoretical and functional aspects behind the DPLMS method for optimum filter synthesis are first recalled and illustrated in more detail. The two new DPLMS extensions are subsequently briefly introduced from the theoretical viewpoint and more thoroughly considered from the applicative perspective. The DPLMS optimum filters have been applied first to simulated signals with various amounts and characteristics of superimposed noise and then to the experimental waveforms acquired from a solid-state Ge detector. The results obtained are considered from both the absolute viewpoint and in comparison with those of more traditional, suboptimal filters. The obtained results demonstrate the effectiveness of the two new DPLMS extensions. For single-channel energy estimations, the synthesized optimum filters provide comparatively better results than the other tested filters. The DPLMS multi-channel optimum filters further enhance the quality of the estimations, compared to single-channel optimum filters, with non-negligible inter-channel noise correlation. The effectiveness and robustness of the DPLMS method in synthesizing high-quality filters for energy estimation will be tested soon within leading-edge multi-channel physics experiments.