A Novel Reconstruction Algorithm based on Fractional Fourier Transform for Unlimited Sampling

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 nonbandlimited signals in the Fourier domain (FD) based on the fractional Fourier transform (FRFT). First, the modular nonlinear folding is performed in the fractional Fourier domain (FRFD) for modular arithmetic. Then, the fractional spectrum is estimated for any folding time by means of annihilation filtering. Finally, a novel unlimited sampling algorithm 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.