On unlimited sampling

Ayush Bhandari, Felix Krahmer, Ramesh Raskar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

85 Scopus citations

Abstract

Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called analog-to-digital converters (ADCs). Unlike Shannon's sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some preset threshold, the ADC saturates, resulting in aliasing due to clipping. The goal of this paper is to analyze an alternative approach that does not suffer from these problems. Our work is based on recent developments in ADC design, which allow for ADCs that reset rather than to saturate, thus producing modulo samples. An open problem that remains is: Given such modulo samples of a bandlimited function as well as the dynamic range of the ADC, how can the original signal be recovered and what are the sufficient conditions that guarantee perfect recovery? In this paper, we prove such sufficiency conditions and complement them with a stable recovery algorithm. Our results are not limited to certain amplitude ranges, in fact even the same circuit architecture allows for the recovery of arbitrary large amplitudes as long as some estimate of the signal norm is available when recovering. Numerical experiments that corroborate our theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold.

Original languageEnglish
Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
EditorsGholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages31-35
Number of pages5
ISBN (Electronic)9781538615652
DOIs
StatePublished - 1 Sep 2017
Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
Duration: 3 Jul 20177 Jul 2017

Publication series

Name2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Conference

Conference12th International Conference on Sampling Theory and Applications, SampTA 2017
Country/TerritoryEstonia
CityTallinn
Period3/07/177/07/17

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