# USF Spectral Estimation: Prevalence of Gaussian Cram'er-Rao Bounds Despite Modulo Folding

arXiv: https://arxiv.org/abs/2505.03098 · HTML: https://mlsanity.com/paper/2505.03098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2025.

## Built on by (most cited first, 1 of 1)

- [Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude](https://mlsanity.com/paper/2510.16948/) (2025)

## Abstract (arXiv)

Spectral Estimation (SpecEst) is a core area of signal processing with a history spanning two centuries and applications across various fields. With the advent of digital acquisition, SpecEst algorithms have been widely applied to tasks like frequency super-resolution. However, conventional digital acquisition imposes a trade-off: for a fixed bit budget, one can optimize either signal dynamic range or digital resolution (noise floor), but not both simultaneously. The Unlimited Sensing Framework (USF) overcomes this limitation using modulo non-linearity in analog hardware, enabling a novel approach to SpecEst (USF-SpecEst). However, USF-SpecEst requires new theoretical and algorithmic developments to handle folded samples effectively. In this paper, we derive the Cram'er-Rao Bounds (CRBs) for SpecEst with noisy modulo-folded samples and reveal a surprising result: the CRBs for USF-SpecEst are scaled versions of the Gaussian CRBs for conventional samples. Numerical experiments validate these bounds, providing a benchmark for USF-SpecEst and facilitating its practical deployment.