Frequency Estimation of Multiple Sinusoids with Sub-Nyquist Sampling Sequences

TL;DR

This paper introduces a novel subspace-based method for estimating multiple sinusoid frequencies from sub-Nyquist sampled data, demonstrating accuracy and feasibility at low sampling rates.

Contribution

A new approach using three sub-Nyquist sequences for accurate frequency estimation of multiple sinusoids from under-sampled data.

Findings

Method is feasible and accurate at low sampling rates.

Three sequences are sufficient for frequency estimation under certain conditions.

Simulations validate the theoretical analysis.

Abstract

In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the frequencies by using under-sampled samples. We analyze the impact of under-sampling and demonstrate that three sub-Nyquist sequences are general enough to estimate the frequencies under some condition. The frequencies estimated from one sequence are unfolded in frequency domain, and then the other two sequences are used to pick the correct frequencies from all possible frequencies. Simulations illustrate the validity of the theory. Numerical results show that this method is feasible and accurate at quite low sampling rates.