# Unlimited Sampling Theorem Based on Fractional Fourier Transform

arXiv: https://arxiv.org/abs/2110.13003 · HTML: https://mlsanity.com/paper/2110.13003/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2021.

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

- [mSQUID: Model-Based Leanred Modulo Recovery at Low Sampling Rates](https://mlsanity.com/paper/2510.18729/) (2025)

## Abstract (arXiv)

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. We study the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain (FD) based on the fractional Fourier transform (FRFT). First, a mathematical signal model for unlimited sampling is proposed. Then, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel unlimited sampling theorem in the FRFD is obtained. The results show that the non-bandlimited signal can be reconstructed in the FD based on the FRFT, and it is not affected by the ADC threshold.