DCT trigger rate as a function of anti-aliasing Bessel filter environmental variation

The standard triggers T1 and ToT for the surface detectors of the Pierre Auger Observatory based on 3-fold (T1) or 2-fold (ToT) coincidences in the time domain. The Discrete Cosine Transform (DCT) algorithm implemented as 3 engines for 3 PMT channels implemented into the surface detector Front-End Board (FEB) FPGA analyzes online shapes of the signal waveforms (ADC traces) and generates a trigger if selected number (7-9) of sub-triggers (as scaled DCT[k]/DCT[1]) are “fired” in at least two channels simultaneously. For assumed sampling frequency f_S = 120 MHz, the filter is built from RLC components on relatively small values. Resistors and inductors are available in 0.1 % and 5 % tolerance, however, capacitors in pF range are available even in 0.1 pF, but the parasitic capacitance on the FEB can dramatically change the frequency characteristics. Daily temperature variations reach even 40 ° C, which additionally change the characteristic of the analog FEB section. The paper analyzes the influence of the Bessel filter frequency characteristics on the efficiency of the DCT trigger.