Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences

In many applications of frequency estimation, the frequencies of the signals are so high that the data sampled at Nyquist rate are hard to acquire due to hardware limitation. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using two sub-Nyquist sample sequences, provided that the two under-sampled ratios are relatively prime integers. We analyze the impact of under-sampling and expand the estimated frequencies which suffer from aliasing. Through jointing the results estimated from these two sequences, the frequencies approximate to the frequency components really contained in the signals are screened. The method requires a small quantity of hardware and calculation. Numerical results show that this method is valid and accurate at quite low sampling rates.