Multiple delay line shaping: a new class of weighting functions suitable for digital signal processing

We introduce a whole class of weighting functions, that can be implemented with an analog prefilter, an analog-to-digital converter and a FIR or IIR digital filter. These weighting functions feature a finite duration and can have a flat top within less than 1%. General rules are given about the design of such general class of filters. The shape of the obtained weighting function is strictly related to the chosen prefilter, and its duration may be effectively shrinked by the digital processing. However the number of samples required in order to keep a finite duration of the weighting function is shown to increase with the complexity of the prefilter. The developed class of weighting functions can be alternatively implemented with analog delay lines or switched-capacitor filters.