Strenghs and weaknesses of digital filtering

The use of digital ltering to achieve the best signal to noise ratio, over a wide range of luminosities, is required for the ATLAS electromagnetic calorimeter. A theoretical frequency analysis of this method, validated by experimental measurements, explains its potential limitations : spectral aliasing exacerbates any 40 MHz or high frequency noise oor. The application of the method to the ATLAS environment with the pile-up noise shows that the use of the chosen shaper time constant ( = 13 ns) is not the best to cover the full luminosity range : the use of a longer shaper time constant or a system with two shaper time constants are suggested.