Unlimited Sampling Theorem Based on Fractional Fourier Transform

TL;DR

This paper introduces a new unlimited sampling theorem using the fractional Fourier transform, enabling high dynamic range signal recovery without ADC saturation effects.

Contribution

It develops a mathematical model and an annihilation filtering method for unlimited sampling in the fractional Fourier domain, extending the theory to non-bandlimited signals.

Findings

Signal can be reconstructed in the fractional Fourier domain.

Reconstruction is unaffected by ADC threshold.

The method extends unlimited sampling to non-bandlimited signals.

Abstract

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.