Tracking the best level set in a level-crossing analog-to-digital converter

In this paper, we investigate level-crossing (LC) analog-to-digital converters (ADC)s in a competitive algorithm framework. In particular, we study how the level sets of an LC ADC should be selected in order to track the dynamical changes in the analog signal for effective sampling. We introduce a sequential LC sampling algorithm asymptotically achieving the performance of the best LC sampling method which can choose both its LC sampling levels (from a large class of possible level sets) and the intervals (from the continuum of all possible intervals) that these levels are used based on observing the whole analog signal in hindsight. The results we introduce are guaranteed to hold in an individual signal manner without any stochastic assumptions on the underlying signal.