Implementing Double Trapezoidal Filters on FPGAs for Data Analysis

The Nab experiment at Oak Ridge National Laboratory studies correlations in neutron beta decay to help resolve longstanding conflicts in the ratio $lambda$ of the weak axial to vector coupling coefficients in the Standard Model and search for scalar and tensor interactions or other new physics.

This is the first experiment using an electro-magnetostatic spectrometer to reconstruct the entire kinematic phase space from the detected energy of the decay protons and electrons, to find the electron-neutrino correlation parameter ‘a’ and the Fierz interference term ‘b’.

The signals produced in the silicon detectors are exponential tail pulses, with the decay determined by the RC circuit of a bleed resistor. A novel “double trapezoid filter” was developed in our group to extract the amplitude and timing from the ambient noise, as it has the benefit of 1) integrates the total charge subtract exponential background (pile-up) while avoiding ballistic deficit, 2) a flat top to extract a time-insensitive energy amplitude, 3) has zero area to reject the pedestal, and 4) has a sharp zero-crossing for amplitude-independent timing.

By implementing this filter on an FPGA(Field Programmable Gate Array), you can execute a recursive convolution at the speeds required for the Nab experiment. Using the Hardware Description Language (HDL) Verilog, I designed the filter module, and completed non intensive testbenches with these filters. This module will eventually be implemented on the Red Pitaya, a type of FPGA which serves as an inexpensive RND platform for the Nab experiment.