Generalized Modulo Hysteresis Encoding
Abstract
Unlimited sensing and its extension via modulo hysteresis provide an efficient encoding scheme for high dynamic range signals by folding the signal's amplitude into the range of the analog-to-digital converter prior to sampling. Motivated by shortcomings of the modulo hysteresis model, in this work we introduce generalized modulo encoders that flexibly design the folding by incorporating a general transition function and allowing the folding times to depend on the nonideality of the folding transition. We rigorously study mathematical properties of the respective operators and derive conditions under which a bandlimited signal is uniquely determined by its generalized modulo samples. Finally, we propose a recovery algorithm backed by mathematical guarantees and illustrate our theoretical results through numerical experiments.
Related
- Generalized Frobenius Partitions Modulo Powers of $2$
- Numerical analysis of parabolic equations with Prandtl--Ishlinskii hysteresis of play type
- One-way pressure-independent valves with hysteresis and chattering
- The three Kanade-Russell identities modulo nine
- Galois groups of Apéry-like series modulo primes
BibTeX
@misc{beckmann2026generalized,
title = {{Generalized Modulo Hysteresis Encoding}},
author = {Matthias Beckmann and Jürgen Jeschke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.01270},
eprint = {2608.01270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01270},
}
RIS
TY - UNPB
TI - Generalized Modulo Hysteresis Encoding
AU - Matthias Beckmann
AU - Jürgen Jeschke
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.01270
UR - https://arxiv.org/abs/2608.01270
AB - Unlimited sensing and its extension via modulo hysteresis provide an efficient encoding scheme for high dynamic range signals by folding the signal's amplitude into the range of the analog-to-digital converter prior to sampling. Motivated by shortcomings of the modulo hysteresis model, in this work we introduce generalized modulo encoders that flexibly design the folding by incorporating a general transition function and allowing the folding times to depend on the nonideality of the folding transition. We rigorously study mathematical properties of the respective operators and derive conditions under which a bandlimited signal is uniquely determined by its generalized modulo samples. Finally, we propose a recovery algorithm backed by mathematical guarantees and illustrate our theoretical results through numerical experiments.
ER -