On unlimited sampling
File(s)
Accepted version
Author(s)
Bhandari, Ayush
Krahmer, Felix
Raskar, Ramesh
Type
Conference Paper
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.
Date Issued
2017-07-03
Date Acceptance
2017-07-03
Citation
2017 International Conference on Sampling Theory and Applications (SampTA), 2017, pp.31-35
ISBN
9781538615652
Publisher
IEEE
Start Page
31
End Page
35
Journal / Book Title
2017 International Conference on Sampling Theory and Applications (SampTA)
Copyright Statement
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Source
2017 International Conference on Sampling Theory and Applications (SampTA)
Publication Status
Published
Start Date
2017-07-03
Finish Date
2017-07-07
Coverage Spatial
Tallin, Estonia
Date Publish Online
2017-09-04