Compressed sensing based sub-Nyquist sampling of multiple sinusoids with dual rate channels

Abstract

In this paper, we propose a reconstruction approach for a multiple-sinusoidal signal. The signal reconstruction requires a small number of samples and is based on a sub-Nyquist sampling scheme with dual rate channels. In the proposed sampling scheme, the samples are grouped into multiple cosets. To obtain enough different cosets to reconstruct a signal, the sampling rates of channels are required to be relative coprime. For each coset, the Whittaker–Shannon interpolation formula is employed to construct the relation between the sub-Nyquist samples and the original signal, which is used to construct the measurement matrix. Since the multiple-sinusoidal signal is sparse in the frequency domain, compressed sensing theory can be adopted to reconstruct the signal. Simulation results are reported to demonstrate the feasibility and effectiveness of the proposed approach.