Probability of Interpolation for a Mute Sample Interpolative A/D Converter with Horizon-Length Two

There are two major issues which underly the design of an analog to digital converter; namely "when to sample?" and "how to represent the amplitude of each sample?". In the majority of past work, these two aspects have typically been treated separately. Recently (Derpich et al., 2005) we have introduced a novel algorithm called MSIC which uses moving horizon optimization ideas to determine both when and how to sample. Our earlier work (Derpich et al., 2005) gave a heuristic description of the algorithm and showed, via simulations, that a performance gain was achieved in both the required bit rate and the achieved distortion level. This seemingly paradoxical result is due to the interpolative capabilities inherent in MSIC. The goal of the current paper is to give theoretical support to the MSIC algorithm. In particular, we provide bounds on the probability that beneficial interpolation occurs for the particular case of horizon length 2 with flat, unity gain error weighting filter.