A Sub-Nyquist Sampling Algorithm for Fractional Bandlimited Signals Based on AIC

Abstract

Sampling theorems for fractional Fourier bandlimited signals have been developed due to the advantages of the fractional Fourier transformation. It may be difficult to put those theories into practice, because the sampling rate must be no less than twice the maximum fractional “frequency” of signal. This brief investigates sampling theorems of the fractional bandlimited signal, then introduces a sub-Nyquist sampling method which extends the modulated wideband converter to the fractional Fourier domain by a fractional shift invariant operator. The proposed method can effectively reduce the sampling rate for the fractional multiband signal. The sampled signals can be recovered by a matching pursuit algorithm. Simulation results verify the effectiveness of the proposed algorithm by discussing the robustness, recovery accuracy, and influence of the fractional order.