The impact of ADC specifications on the performance of digital (DL) N shaping

Multiple Delay Line Shaping (DL)^N of nuclear pulses is performed in practice by introducing an Analog to Digital converter ADC and a digital filter within the noise-shaping circuit. The critical component of the processor is the ADC; since its non-idealities can modify the entire filter Weighting Function WF, rather than affect only the final pulse classification in a histogram. In this paper we discuss the specifications that a candidate ADC should fulfill in order to be suitable for (DL)^N shaping and, conversely, the specifications of the digital portion of (DL)^N shaper suitable to reduce the impact of ADC nonidealities: say, linearity, conversion time and number of bits, on the obtained spectra. For what concerns the quantization error, new WF allow the use of ADC with up to three bits less than those necessary in previous implementations. This is obtained with little penalty (a factor four) on the required ADC speed. The effects of the lack of synchronization between the incoming pulse and the sampling comb are shown to be useful, since they result in a sort of “sliding scale” effect, which allows to reduce the effects of ADC differential non linearity by an estimated factor of at least five