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A sigma-delta analog-to-digital converter (ADC) featuring a time-continuous low-pass filter in the modulator was designed and built. Its second-order modulator runs at a sampling frequency of up to 128 MHz and includes a simple comparator, that is, a one-bit ADC. Its output is decimated by a programmable factor up to 64 by the following digital filter, which can be also initialized in order to optimize the signal-to-noise ratio in the actual experimental conditions. Differently from a standard sigma delta ADC, this decimation can be synchronized with an external random event, such as a trigger pulse. The suitability of the converter in high resolution digital nuclear spectroscopy was theoretically investigated and experimentally tested by including it in a setup based on the multiple delay line principle. Among the many advantages of employing sigma delta converters in high resolution spectroscopy setups, the most important is its easy integrability in a digital chip. Therefore, the way is open for the realization of single-chip digital spectroscopy setups.