Analog to Information Conversion for Sparse Signals Band-limited in Fractional Fourier Domain

The Shannon-Nyquist sampling theorem plays an important role in digital signal processing and digital communications. In practice, it is difficult for the analog-to-digital converter to sample an analog signal with very high bandwidth using Nyquist sampling rate. In recent years, the analog-to-information conversion (AIC) technology provides an effective method to solve this problem. However, the signal model of the AIC is only suitable for analog sparse signals band-limited in the frequency domain. Our objective in this paper is to investigate the AIC for the signals that are not sparse in the frequency domain but sparse in the fractional Fourier transform (FRFT) domain. We first revisit the ordinary random demodulator (RD) for sampling analog sparse signals. Then, we propose a new architecture for the RD associated with the FRFT, which has the ordinary RD embedded as a special case. Finally, the validity of the theoretical derivations is demonstrated via simulations.