Unlimited Sampling Theorem Based on Fractional Fourier Transform

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. Since the non-bandlimited signal in the Fourier domain cannot be directly applied to its existing theory, the non-bandlimited signal in the Fourier domain may be bandlimited in the fractional Fourier domain. Therefore, this brief report studies the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. Firstly, a mathematical signal model for unlimited sampling is proposed. Secondly, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel fractional Fourier domain unlimited sampling theorem is obtained. The theory proves that, based on the folding characteristics of the self-reset ADC, the number of samples is not affected by the modulo threshold, and any folding time can be handled.

Automated summary

This brief report examines the problem of unlimited sampling of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. It proposes a mathematical signal model for unlimited sampling and uses the annihilation filtering method to estimate arbitrary folding time. A novel fractional Fourier domain unlimited sampling theorem is obtained.