Sub-Nyquist Sampling of Multiple Sinusoids

Abstract

In this letter, we propose new sub-Nyquist sampling schemes for multiple sinusoids, which require fewer number of samples than previous works. Since it is impossible to resolve the frequency ambiguity using a single sub-Nyquist sample sequence, an additional sampling channel is used to determine the correct frequencies. First, a time-staggered sampling system, with the staggered time less than or equal to the Nyquist sampling interval, is proposed. This approach requires only $\text{3}K$ samples to estimate the $K$ frequency components in the signal. However, aliasing can occur when the differences between some frequencies are integer multiples of the sampling rate. Then, another sampling strategy that makes use of feedback is proposed to prevent aliasing. We demonstrate that using two sampling channels and with feedback, $\text{4}K$ samples suffice to resolve both frequency ambiguity and image frequency aliasing. Simulation results are provided to demonstrate the effectiveness of the proposed systems.