Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences

In many applications of frequency estimation, the frequencies contained in 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 via ESPRIT. A series of possible frequencies are obtained by expansion. They include both the frequencies approximate to the frequencies contained in the signals and the false frequencies caused by under-sampling. Then the other sample sequence is used to screen correct frequencies from these possible frequencies. The pseudo-spectrum of these possible frequencies are drawn and the correct frequencies are identified. Numerical results show that this method is valid and accurate at quite low sampling rates.