# Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC

arXiv: https://arxiv.org/abs/2105.05818 · HTML: https://mlsanity.com/paper/2105.05818/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2021.

## Built on by (most cited first, 17 of 17)

- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [High Dynamic Range Modulo Imaging for Robust Object Detection in Autonomous Driving](https://mlsanity.com/paper/2504.11472/) (2025)
- [Compressed Sensing Based Residual Recovery Algorithms and Hardware for Modulo Sampling](https://mlsanity.com/paper/2412.12724/) (2024)
- [Autoregressive High-Order Finite Difference Modulo Imaging: High-Dynamic Range for Computer Vision Applications](https://mlsanity.com/paper/2504.04228/) (2025)
- [Spiked Covariance Estimation from Modulo-Reduced Measurements](https://mlsanity.com/paper/2110.01150/) (2021)
- [Blind-Adaptive Quantizers](https://mlsanity.com/paper/2409.04077/) (2024)
- [Blind Time-of-Flight Imaging: Sparse Deconvolution on the Continuum with Unknown Kernels](https://mlsanity.com/paper/2411.00893/) (2024)
- [Modulo Sampling: Performance Guarantees in The Presence of Quantization](https://mlsanity.com/paper/2501.01506/) (2025)
- [mSQUID: Model-Based Leanred Modulo Recovery at Low Sampling Rates](https://mlsanity.com/paper/2510.18729/) (2025)
- [One-Bit-Aided Modulo Sampling for DOA Estimation](https://mlsanity.com/paper/2309.04901/) (2023)
- [Line Spectral Estimation with Unlimited Sensing](https://mlsanity.com/paper/2408.06597/) (2024)
- [1-Bit Unlimited Sampling Beyond Fourier Domain: Low-Resolution Sampling of Quantization Noise](https://mlsanity.com/paper/2508.19408/) (2025)
- [Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude](https://mlsanity.com/paper/2510.16948/) (2025)
- [Modulo Video Recovery via Selective Spatiotemporal Vision Transformer](https://mlsanity.com/paper/2511.07479/) (2025)
- [Deep Lightweight Unrolled Network for High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.12526/) (2026)
- [Lattice Modulo Sampling](https://mlsanity.com/paper/2605.24974/) (2026)
- [Fold First, Detect Directly: Communication Symbol Detection Without Unfolding for Low-Bitrate Modulo-ADCs](https://mlsanity.com/paper/2609.11298/) (2026)

## Abstract (arXiv)

Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware implementation considerations. Our starting point is a class of non-idealities that we observe in prototyping an unlimited sampling based analog-to-digital converter. To address these non-idealities, we provide a new Fourier domain recovery algorithm. Our approach is validated both in theory and via extensive experiments on our prototype analog-to-digital converter, providing the first demonstration of unlimited sampling for data arising from real hardware, both for the current and previous approaches. Advantages of our algorithm include that it is agnostic to the modulo threshold and it can handle arbitrary folding times. We expect that the end-to-end realization studied in this paper will pave the path for exploring the unlimited sampling methodology in a number of real world applications.