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arXiv · 1811.01436

On Quasi-Isometry of Threshold-Based Sampling

Bernhard Moser
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Abstract

The problem of isometry for threshold-based sampling such as integrate-and-fire (IF) or send-on-delta (SOD) is addressed. While for uniform sampling the Parseval theorem provides isometry and makes the Euclidean metric canonical, there is no analogy for threshold-based sampling. The relaxation of the isometric postulate to quasi-isometry, however, allows the discovery of the underlying metric structure of threshold-based sampling. This paper characterizes this metric structure making Hermann Weyl's discrepancy measure canonical for threshold-based sampling.

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Bernhard Moser. 2018-11-04. On Quasi-Isometry of Threshold-Based Sampling. https://doi.org/10.1109/tsp.2019.2919415

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