# 1-Bit Unlimited Sampling Beyond Fourier Domain: Low-Resolution Sampling of Quantization Noise

arXiv: https://arxiv.org/abs/2508.19408 · HTML: https://mlsanity.com/paper/2508.19408/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 61 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 11 of 11)

- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)
- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [Above the Nyquist Rate, Modulo Folding Does Not Hurt](https://mlsanity.com/paper/1903.12289/) (2019)
- [Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with its Hardware Validation](https://mlsanity.com/paper/2207.13230/) (2022)
- [The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments](https://mlsanity.com/paper/2111.12675/) (2021)
- [Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation](https://mlsanity.com/paper/2208.10234/) (2022)
- [Unlimited Sampling of Bandpass Signals: Computational Demodulation via Undersampling](https://mlsanity.com/paper/2307.04917/) (2023)
- [Affine Frequency Division Multiplexing for Next Generation Wireless Communications](https://mlsanity.com/paper/2204.12798/) (2022)
- [AFDM-SCMA: A Promising Waveform for Massive Connectivity over High Mobility Channels](https://mlsanity.com/paper/2312.11302/) (2023)
- [From OTFS to AFDM: A Comparative Study of Next-Generation Waveforms for ISAC in Doubly-Dispersive Channels](https://mlsanity.com/paper/2401.07700/) (2024)

## Abstract (arXiv)

Analog-to-digital converters (ADCs) play a critical role in digital signal acquisition across various applications, but their performance is inherently constrained by sampling rates and bit budgets. This bit budget imposes a trade-off between dynamic range (DR) and digital resolution, with ADC energy consumption scaling linearly with sampling rate and exponentially with bit depth. To bypass this, numerous approaches, including oversampling with low-resolution ADCs, have been explored. A prominent example is 1-Bit ADCs with Sigma-Delta Quantization (SDQ), a widely used consumer-grade solution. However, SDQs suffer from overloading or saturation issues, limiting their ability to handle inputs with arbitrary DR. The Unlimited Sensing Framework (USF) addresses this challenge by injecting modulo non-linearity in hardware, resulting in a new digital sensing technology. In this paper, we introduce a novel 1-Bit sampling architecture that extends both conventional 1-Bit SDQ and USF. Our contributions are twofold: (1) We generalize the concept of noise shaping beyond the Fourier domain, allowing the inclusion of non-bandlimited signals in the Fourier domain but bandlimited in alternative transform domains. (2) Building on this generalization, we develop a new transform-domain recovery method for 1-Bit USF. When applied to the Fourier domain, our method demonstrates superior performance compared to existing time-domain techniques, offering reduced oversampling requirements and improved robustness. Extensive numerical experiments validate our findings, laying the groundwork for a broader generalization of 1-Bit sampling systems.