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arXiv · 1611.01850

On High-Resolution Adaptive Sampling of Deterministic Signals

Yehuda Dar·Alfred M. Bruckstein
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Abstract

In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal high-resolution sampling, counterparts of well-known results for high-rate quantization. Our results reveal that the optimal high-resolution sampling structure is determined by the density of the signal-gradient 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 nonuniform sampling relevant to the emerging field of high-resolution signal processing. The third is a new practical approach to nonuniform sampling of one-dimensional signals that enables reconstruction based only on the sampling time-points and the signal extrema locations and values. Experiments for signal sampling and coding showed that our method outperforms an optimized tree-structured sampling technique.

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Yehuda Dar, Alfred M. Bruckstein. 2018-04-19. On High-Resolution Adaptive Sampling of Deterministic Signals. https://arxiv.org/abs/1611.01850

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