Optimal High-Resolution Adaptive Sampling of Deterministic Signals

In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a clear connection to classic analyses of high-rate quantization. More specifically, we formulate solutions to the task of optimal high-resolution sampling of one-dimensional signals, which are shown as the counterparts of well-known results for high-rate scalar quantization. Our results reveal that the optimal high-resolution sampling structure is determined by the density of the signal-derivative energy, just as the probability-density-function defines the optimal high-rate quantization form. This paper has three main contributions: the first is establishing a fundamental paradigm bridging the topics of sampling and quantization. The second is a theoretical analysis of sampling that is relevant to the emerging field of high-resolution signal processing. The third is a new approach for nonuniform sampling of one-dimensional signals that is experimentally shown to outperform an optimized tree-structured sampling technique.