On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling
Metric Geometry
2018-06-19 v1 Signal Processing
Abstract
Recalling recent results on the characterization of threshold-based sampling as quasi-isometric mapping, mathematical implications on the metric and topological structure of the space of event sequences are derived. In this context, the space of event sequences is extended to a normed space equipped with Hermann Weyl's discrepancy measure. Sequences of finite discrepancy norm are characterized by a Jordan decomposition property. Its dual norm turns out to be the norm of total variation. As a by-product a measure for the lack of monotonicity of sequences is obtained. A further result refers to an inequality between the discrepancy norm and total variation which resembles Heisenberg's uncertainty relation.
Cite
@article{arxiv.1806.06273,
title = {On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling},
author = {Bernhard A. Moser},
journal= {arXiv preprint arXiv:1806.06273},
year = {2018}
}